Real numbers Any number that we can think of in the real world is a real number . set of real number is denoted by R. real numbers include natural numbers (N) , whole numbers (W), Integers (Z/I), rational numbers (Q) and irrational numbers (R-Q) . For example:- 1,3.5,√7,3.¯2,22/7,π,1.234 etc are real numbers . In this chapter we also learn about LCM and HCF

Real numbers Any number that we can think of in the real world is a real number . set of real number is denoted by R. real numbers include natural numbers (N) , whole numbers (W), Integers (Z/I), rational numbers (Q) and irrational numbers (R-Q) . For example:- 1,3.5,√7,3.¯2,22/7,π,1.234 etc are real numbers . In this chapter we also learn about LCM and HCF

Real numbers Any number that we can think of in the real world is a real number . set of real number is denoted by R. real numbers include natural numbers (N) , whole numbers (W), Integers (Z/I), rational numbers (Q) and irrational numbers (R-Q) . For example:- 1,3.5,√7,3.¯2,22/7,π,1.234 etc are real numbers . In this chapter we also learn about LCM and HCF

LCM and HCF LEAST COMMON MULTIPLE (LCM)  COMMON MULTIPLE :- A common multiple of two numbers is a number which is exactly divisible by each of given numbers . e.g. 45 is a common multiple of 3,5,9,15  LEAST COMMON MULTIPLE :- The least common multiple of two or given numbers is the least number which is exactly divisible by each one of them . e.g.12 is common multiple of 2,3,4 & 24 is also common multiple of 2,3,4 but 12 is LCM of 2,3,4 HIGHEST COMMON FACTOR (HCF) Highest common factor is also known as greatest common divisor (GCD)  COMMON FACTOR :- A common factor of two or more numbers is a number which divides each of them exactly . e.g. 3 is a common factor of 3,12,18

SIMPLIFICATION Simplification is a process of reducing a complex expression into a simpler form. ‘VBODMAS’ Rule This rule gives the correct order in which various operations regarding simplification are to be performed, so as to find out the values of given expressions in simple ways. Let us see what these letters mean. Order of operations is as same as the order of letters in the ‘VBODMAS’ from the left to right as V B O D M A S Left to right Clearly, the order will be as follows First Vinculum bracket is solved, (Remember – 6 – 8 = - 14 but – 6- 8 = - (-2) = 2) Second Brackets are to be solved in order given below • First, small brackets (circular brackets ) ‘( )’ • Second , middle brackets (curly brackets) ‘{ }’ • Third , square brackets (big brackets) ‘[ ]’ Third Operation of ‘Of’ is performed. Fourth Operation of division is performed. Fifth Operation of multiplication is performed. Sixth Operation of addition is performed. Seventh Operation of subtraction is performed

SIMPLIFICATION Simplification is a process of reducing a complex expression into a simpler form. ‘VBODMAS’ Rule This rule gives the correct order in which various operations regarding simplification are to be performed, so as to find out the values of given expressions in simple ways. Let us see what these letters mean. Order of operations is as same as the order of letters in the ‘VBODMAS’ from the left to right as V B O D M A S Left to right Clearly, the order will be as follows First Vinculum bracket is solved, (Remember – 6 – 8 = - 14 but – 6- 8 = - (-2) = 2) Second Brackets are to be solved in order given below • First, small brackets (circular brackets ) ‘( )’ • Second , middle brackets (curly brackets) ‘{ }’ • Third , square brackets (big brackets) ‘[ ]’ Third Operation of ‘Of’ is performed. Fourth Operation of division is performed. Fifth Operation of multiplication is performed. Sixth Operation of addition is performed. Seventh Operation of subtraction is performed

SIMPLIFICATION Simplification is a process of reducing a complex expression into a simpler form. ‘VBODMAS’ Rule This rule gives the correct order in which various operations regarding simplification are to be performed, so as to find out the values of given expressions in simple ways. Let us see what these letters mean. Order of operations is as same as the order of letters in the ‘VBODMAS’ from the left to right as V B O D M A S Left to right Clearly, the order will be as follows First Vinculum bracket is solved, (Remember – 6 – 8 = - 14 but – 6- 8 = - (-2) = 2) Second Brackets are to be solved in order given below • First, small brackets (circular brackets ) ‘( )’ • Second , middle brackets (curly brackets) ‘{ }’ • Third , square brackets (big brackets) ‘[ ]’ Third Operation of ‘Of’ is performed. Fourth Operation of division is performed. Fifth Operation of multiplication is performed. Sixth Operation of addition is performed. Seventh Operation of subtraction is performed

Percentage Percent means per hundred. It is denoted by the symbol % .Here x% means x/100.Thus ,any percentage can be converted into an equivalent fraction by dividing it by 100. Short Tricks 1. When a value/number/quantity 'A' is increased or decreased by b%, then new value/number/quantity will be = (100 ±b)/100* A 2. If A is a% more than B, then b is less than a by [a/(100+a)* 100 ]% 3. If A is a % less than B, then b is more than a by [a/(100-a)* 100 ]% 4. When the value of an object is first changed (increased or decreased) by x% and then changed by y % then net effect is given as = [± x ±y + ((± x) (± y)))/100] % (+ ve sign indicates increase, - ve sign indicates decrease.) 5. If the price of a commodity increases or decreases by a%, then the decrease or increase in consumption so as not to increase or decrease the expenditure is equal to ( a/(100 ±a )) * 100%

Ratio If a and b are two quantities of same kind, then a/b is known as the ratio of a and b . It is written as a:b. The first of the ratio is called antecedent while the second term is called consequent. e.g., Ratio between 30kg and 50kg is 3: 5. Proportion The equality of two ratios is called proportion a, b, c, d are said to be in proportion if a : b = c : d or a : b : : c : d. Here, ‘a’ is the first second term ‘c’ is the third term and ‘d’ is the fourth term. Here, first and fourth terms are called extremes i.e., a and d while the second and third terms are called as means i.e., b and c. e.g., if 3 : 2 : : 135 : 90, then 3, 90 are the extremes while 2, 135 are called the means. In a proportion, we always have: Product of extremes = product of means a x d = b x c

Mixture To determine the mean value of the mixture when the prices of the individual items being mixed together and the proportion in which they are being mixed are given. Here, the value of the mixture is always higher than the lowest value and lower than highest value of the items being mixed. According to the Rule of Alligation, if two quantities are in a ratio, then (Quantity of cheaper)/(Quantity of dearer) = (Cost price of dearer-Mean price)/(Mean price-Cost price of cheaper) It can also be expressed as, Cost price of 1 unit Cost price of 1 unit quantity of cheaper (x) quantity of dearer (y) Mean price (m) (y-m) (m-x)

AVERAGE Average is the mean value of a set of numbers or values. Therefore average of a set of numbers is, Average= (X_1+ X_2+ X_3+ ……..〖+ X〗_n)/n or in other words, Average of some observations = (Sum of all observations)/(Number of all observations) Remarks:- If each observation of the given data is increased by same quantity, say x, then their average also increases by x. If each observation of the given data is decreased by same quantity, say x their then average also decreases by x. If each observation of the given data is multiplied same quantity, say x then their average also multiplied by x. If each observation of the given data is divided by same quantity, say, x then their average also divided by x.

In our daily life, we have to complete different kinds of work in different stipulated time and if we are not able to complete the work in definite time,we arrange some more persons for it.Different persons have different abilities to do work. Basic Rules 1. If time taken by a person to complete a work in x days,then work done in 1day is 1/x 2. If a person can do 1/x part in 1day , then he completes that work in x days

Clock A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand. The face of a clock is a circular dial which subtends an angle of 360° at the centre. The circumference of the dial is divided into 12 equal parts to be called hour spaces. Every hour space is further divided into 5 equal parts to be called minute space. Hence, the total circumference is divided into 12 x 5= 60 equal minute space. Fundas In one hour, both the hands coincide once. In one hour, the hands are straight (point in opposite directions) once. In one hour, the hands are twice perpendicular to each other. In 60 min, the minute hand covers 360°. Thus, in 1 min the minute hand covers (360/60)° = 6° In 12 h, the hour hand covers 360°. Thus, in 1 min, the hour hand covers (360/(12*60))° = (1°)/2 Thus, in one minute, the minute hand gains ( 6 - 1/2) = 5 - 1/2, then the hour hand. When the two hands are at right angles, they are 15 min spaces apart When the two hands are in opposite directions, they are 30 min spaces apart In 60 min, the minute hand gains 55 min on the hour hand. The minute hand moves 12 times as fast as the hour hand.

CALENDAR ORDINARY YEAR -An ordinary year has 365 days LEAP YEAR-Leap year has 366 days (a)Any year (except a century) which is divisible by 4 is a leap year. (b)Century is a leap year if it is divisible by 400 Example: 1924, 1964, 1660, 1880, 1808 are all leap years. 400, 800, 1200, 1600, 2000 are all leap years. Total leap year /29 Feb in 100 years=24 Total leap year/29 Feb in 400 years=97 Total 29th Date in 100 years =1124 Total 29th Date in 400 years=4497 ODD DAYS - The number of days more than the complete weeks for a given period called odd days HOW TO CALCULATE ODD DAYS FOR "n" NUMBER OF DAYS: (a) Divide the number of days by 7. (b) The remainder so obtained is the number of odd days NUMBER OF ODD DAYS DAY OF THE WEEK 0 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday NOTE 1ordinary year =365 days =(52 weeks +1day) 1ordinary year =1odd day 1leap year =366days =(52 weeks+2days) 1leap year=2 odd days 100years =76 ordinary years +24 leap years =(76*1+24*2)odd days = 124 odd days =(17weeks+5days) = 5 odd days 200 years =( 5*2 =10 odd days) = 1week +3 days = 3 odd days 300 years =(5*3 = 15 odd days) = 2weeks +1 day = 1 odd day 400 years = (5*4 +1 = 21 odd days) = 3weeks +0 day = 0 odd day • Similarly, 800 year, 1200 year, 1600year, 2000year have 0 odd days • Last day of the century may be Sunday, Monday, Wednesday, Friday • Last day of the century cannot be Tuesday, Thursday, Saturday • The day on which ordinary year begins it ends on its same day Example: If 1st Jan 2001 was Monday then 31st Dec 2001 was also Monday REPETITION OF SAME CALENDAR IN YEARS IN CASE OF COMPLETE REPEAT (a) Divide the Given Year by 4 (b) You will get one of the following remainders 1, 2, 3, 0 (c) Add the following years in the remainders: Remainders Number of years to be added 1 6 2 11 3 11 0 28 IN CASE OF PARTIAL REPEAT (a) Year will match only from January 1st to February 28. (b) Ordinary year will match the Leap year and vice-versa. *Number of odd days must be multiple of 7.

• Binary system: In the binary system, only two symbols 0 and 1 are used. Since, in this system only two numbers are used, so its base or radix is 2. • Decimal system: in the decimal, we use 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Since, 10 basic symbols are used in this system, so its base or radix 10. In this chapter we will do; 1. Decimal to binary conversion 2. Binary to decimal conversion

Profit and loss and discount Cost price (CP) the price at which an article is bought is called its cost price. All the overhead expenses in the transaction are added to the cost price . Selling price (SP) The price at which an article is sold is Called the selling price. Profit →if SP > CP then there is a profit Profit = SP-CP & P% = (SP-CP)/CP × 100 LOSS → If CP > SP then there is a loss. Loss = CP – SP & L% = (CP-SP)/CP × 100 MARKED PRICE OR LIST PRICE :- it is marked on the article Discount :- The Reduction allowed on the marked price of an article is called as discount . discount is always calculated on marked price . Discount = marked price – selling price D% = (MP-SP)/MP × 100

1. Principal: The money borrows or lend out for a certain period is called the principal or the sum. 2. Interest: Extra money paid for using other's money is called interest. 3. Simple Interest: If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest. Let principal = P, Rate = R% per annum (p.a.) and Time = T year. 4. Compound interest : Someti¬mes borrower & the lender agree to fix up a certain units of time, say yearly or halfly or quarterly to settle the previous account. After a specified period, the difference between the amount and money is borrowed called the compound interest (C.I.) for that period.

1. Principal: The money borrows or lend out for a certain period is called the principal or the sum. 2. Interest: Extra money paid for using other's money is called interest. 3. Simple Interest: If the interest on a sum borrowed for a certain period is reckoned uniformly, then it is called simple interest. Let principal = P, Rate = R% per annum (p.a.) and Time = T year. 4. Compound interest : Someti¬mes borrower & the lender agree to fix up a certain units of time, say yearly or halfly or quarterly to settle the previous account. After a specified period, the difference between the amount and money is borrowed called the compound interest (C.I.) for that period.

Mensuration :- Mensuration is a branch of mathematical science that is concerned with the measurement of areas and volumes of various geometric figures . It is of two types 2D and 3D mensuration 2D Mensuration applies to two dimensional figures like squares, rectangles, triangles, trapezium etc. 3D Mensuration applies to three dimensional figures like cube, cuboids, sphere, cone, cylinder etc. Area: Total space inside the boundary of a plane figure is called the area of that particular figure. Area is measured in square Unit. Perimeter:- It is the length of border around enclosed plane. Therefore, Sum of the sides of the a plane figure is the perimeter of that particular figure. Volume: volume is the space occupied by an object considering 3dimensional view.The formulas for calculating Volume vary with the shape of the object. The units of volume is cubic meters, cubic centimetre etc

Mensuration :- Mensuration is a branch of mathematical science that is concerned with the measurement of areas and volumes of various geometric figures . It is of two types 2D and 3D mensuration 2D Mensuration applies to two dimensional figures like squares, rectangles, triangles, trapezium etc. 3D Mensuration applies to three dimensional figures like cube, cuboids, sphere, cone, cylinder etc. Area: Total space inside the boundary of a plane figure is called the area of that particular figure. Area is measured in square Unit. Perimeter:- It is the length of border around enclosed plane. Therefore, Sum of the sides of the a plane figure is the perimeter of that particular figure. Volume: volume is the space occupied by an object considering 3dimensional view.The formulas for calculating Volume vary with the shape of the object. The units of volume is cubic meters, cubic centimetre etc

Mensuration :- Mensuration is a branch of mathematical science that is concerned with the measurement of areas and volumes of various geometric figures . It is of two types 2D and 3D mensuration 2D Mensuration applies to two dimensional figures like squares, rectangles, triangles, trapezium etc. 3D Mensuration applies to three dimensional figures like cube, cuboids, sphere, cone, cylinder etc. Area: Total space inside the boundary of a plane figure is called the area of that particular figure. Area is measured in square Unit. Perimeter:- It is the length of border around enclosed plane. Therefore, Sum of the sides of the a plane figure is the perimeter of that particular figure. Volume: volume is the space occupied by an object considering 3dimensional view.The formulas for calculating Volume vary with the shape of the object. The units of volume is cubic meters, cubic centimetre etc

Mensuration :- Mensuration is a branch of mathematical science that is concerned with the measurement of areas and volumes of various geometric figures . It is of two types 2D and 3D mensuration 2D Mensuration applies to two dimensional figures like squares, rectangles, triangles, trapezium etc. 3D Mensuration applies to three dimensional figures like cube, cuboids, sphere, cone, cylinder etc. Area: Total space inside the boundary of a plane figure is called the area of that particular figure. Area is measured in square Unit. Perimeter:- It is the length of border around enclosed plane. Therefore, Sum of the sides of the a plane figure is the perimeter of that particular figure. Volume: volume is the space occupied by an object considering 3dimensional view.The formulas for calculating Volume vary with the shape of the object. The units of volume is cubic meters, cubic centimetre etc

Mensuration :- Mensuration is a branch of mathematical science that is concerned with the measurement of areas and volumes of various geometric figures . It is of two types 2D and 3D mensuration 2D Mensuration applies to two dimensional figures like squares, rectangles, triangles, trapezium etc. 3D Mensuration applies to three dimensional figures like cube, cuboids, sphere, cone, cylinder etc. Area: Total space inside the boundary of a plane figure is called the area of that particular figure. Area is measured in square Unit. Perimeter:- It is the length of border around enclosed plane. Therefore, Sum of the sides of the a plane figure is the perimeter of that particular figure. Volume: volume is the space occupied by an object considering 3dimensional view.The formulas for calculating Volume vary with the shape of the object. The units of volume is cubic meters, cubic centimetre etc

Statistics is concerned with collection of data, presentation of data and analysis of data in the numerical form. Collection of data involves collection of primary as well as secondary data. Primary data is the data which is collected for the first time for statistical investigation. Secondary data refers to the data which is already collected and used for current statistical investigation. Measures of central tendency includes the measures of Mean, Median and Mode. Mean also known as average is the sum of all the items divided by number of items. Median refers to the middle number sorted ascending or descending. Mode refers to the mostly appearing figure in the given series.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Time and distance Speed The distance travelled in a unit time is known as speed. Speed = (distance travelled)/(Time Taken) Units of speed are km/h, m/s etc. To convert speed of an object from km/h to m/s, multiply the speed by 5/18 . To convert speed of an object from m/s to km/h, multiply the speed by 18/5 . Average speed Average speed is the ratio of total distance covered to total time of journey. Average speed = (Total distance covered)/(Total time of journey) Rules for Solving Time and Distance Problems Rule 1 If a certain distance is covered with a speed of ‘x’ km/h and another equal distance with a speed of ‘y’ km/h then the average speed for the whole journey is the harmonic mean of the two speeds Average speed = (2xy/(x+y))km/h (This formula is applicable only when the distance is constant) Rule 2 If a certain distance is covered with a speeds of ‘x’ km/h and another distance with a speed of ‘y’ km/h but time interval for both journeys being same, then average speed for the whole journey is given by Average speed = ((x+y)/2)km/h Rule 3 If the ratio of speed A and B is x : y, then the ratio of time taken by them to cover the same distance is y : x.

Time and distance Speed The distance travelled in a unit time is known as speed. Speed = (distance travelled)/(Time Taken) Units of speed are km/h, m/s etc. To convert speed of an object from km/h to m/s, multiply the speed by 5/18 . To convert speed of an object from m/s to km/h, multiply the speed by 18/5 . Average speed Average speed is the ratio of total distance covered to total time of journey. Average speed = (Total distance covered)/(Total time of journey) Rules for Solving Time and Distance Problems Rule 1 If a certain distance is covered with a speed of ‘x’ km/h and another equal distance with a speed of ‘y’ km/h then the average speed for the whole journey is the harmonic mean of the two speeds Average speed = (2xy/(x+y))km/h (This formula is applicable only when the distance is constant) Rule 2 If a certain distance is covered with a speeds of ‘x’ km/h and another distance with a speed of ‘y’ km/h but time interval for both journeys being same, then average speed for the whole journey is given by Average speed = ((x+y)/2)km/h Rule 3 If the ratio of speed A and B is x : y, then the ratio of time taken by them to cover the same distance is y : x.

Time and distance Speed The distance travelled in a unit time is known as speed. Speed = (distance travelled)/(Time Taken) Units of speed are km/h, m/s etc. To convert speed of an object from km/h to m/s, multiply the speed by 5/18 . To convert speed of an object from m/s to km/h, multiply the speed by 18/5 . Average speed Average speed is the ratio of total distance covered to total time of journey. Average speed = (Total distance covered)/(Total time of journey) Rules for Solving Time and Distance Problems Rule 1 If a certain distance is covered with a speed of ‘x’ km/h and another equal distance with a speed of ‘y’ km/h then the average speed for the whole journey is the harmonic mean of the two speeds Average speed = (2xy/(x+y))km/h (This formula is applicable only when the distance is constant) Rule 2 If a certain distance is covered with a speeds of ‘x’ km/h and another distance with a speed of ‘y’ km/h but time interval for both journeys being same, then average speed for the whole journey is given by Average speed = ((x+y)/2)km/h Rule 3 If the ratio of speed A and B is x : y, then the ratio of time taken by them to cover the same distance is y : x.

Polynomial An expression in term of some variable(s) is called a polynomial. f(x)=2x-5 is a polynomial in variable x The expressions like 3x^2 –√(x,) 1/( x^2 7× +6) , 5x^3 - 4/x,etc., are not polynomials. Thus, a rational integral function of ‘x’ is said to be a polynomial, if the powers of ‘x’ in the terms of the polynomial are neither fractions nor negative. Thus, an expression of the form f (x) = a_n x^n + a_(n-1 ) x^(n-1) +……+ a_1x + a_o is called a polynomial in variable x where n be a positive integer anda_o, a_1, …….., a_n be constants ( real numbers). Degree of a polynomial The exponent of the highest degree term in a polynomial is known as its degree. e.g. , f(x) = 4x -3/2 is a polynomial in the variable x of degree 1. Linear polynomial A polynomial of degree one is called a linear polynomial. In general, f(x) = ax + b, where a ≠0 is a linear polynomial. Quadratic polynomial A polynomial of degree two is called a quadratic polynomial. In general, f (x) = 〖ax〗^(2 ) + bx + c, where a≠ 0 is a quadratic polynomial e.g. , f(x) = x^2 – 7x + 8 is a trinomial as it contains 3 terms. Cubic polynomial A polynomial of degree 3 is called a cubic polynomial in general f (x) = 〖ax〗^3 + 〖bx〗^2 + cx + d, a ≠ 0 is a cubic polynomial. f (x) = 〖2x〗^3 - x^(2 ) + 8x + 4 Biquadratic polynomial A fourth degree polynomial is called a biquadratic polynomial in general. f (x) =〖ax〗^4 + 〖bx〗^3 + 〖cx〗^2 + dx + e, a ≠ 0 is a biquadratic polynomial. Zero of a polynomial A real number ∝ is a zero (or root) of a polynomial f (x), if f (∝) = 0 e.g., if x = 1 is a root of the polynomial 〖3x〗^3 - 〖2x〗^(2 )+ x – 2, then f (1) = 0

Linear Equations when we equate two algebraic expressions using the signs of equality it forms an equation. Linear equations are first degree equations and may contain one or more variables. If the equation has only one variable, then the equation itself is sufficient to obtain the value of the variable. If the equation has two variables then two consistent equations are required to get the value of the variables. In general, an equation has n variables then n consistent equations are required to obtain all the value of the n variables. Linear Equation in One Variable These are first degree equations in one unknown. An equation of the form ax + b = 0 where a, b ∈ R and a ≠ 0 and x is the variable, is called a linear equation in one variable. We have, only one variable x whose value we have to find out. Linear Equation in two Variables These are first in two unknowns. An equation of the ax + by + c = 0, where a, b, c ∈ R and a ≠ 0, b ≠ 0 and x, y are variables is called linear equation in two variables have, two variables x and y whose values we have to find out. Any pair of values of x and y which satisfy the equations ax + by + c = 0, is called its solution. When two or more equations are satisfied by the same set values of the variables involved in them, then the termed as simultaneous equations.

Quadratic Equation These are second degree equations of the form 〖ax〗^(2 ) + bx + c = 0, where a, b, c ∈ R and a ≠ 0 are quadratic equations. Like a first degree equation in x has one value of x satisfying the equation, a quadratic equation in x will have two values of x that satisfy the equation. The value of x that satisfy the equation are called the roots of the equation. These roots may be real or imaginary. x^(2 ) + 5x + 6 = 0 has roots x = -2,- 3 Using Formula If the quadratic is 〖ax〗^(2 )+ bx + c = 0, then we can use the standard formula given below to find out the roots of the equation. If α and β are the roots of the quadratic equation, then ∝=(-b+√(b^2-4ac))/2a and β=(-b-√(b^2-4ac))/2a Sum and product of Roots of a Quadratic Equation If ∝ and β are the roots of the quadratic equation 〖ax〗^(2 ) + bx + c = 0 Sum of the roots = ∝ + β = - b/a Product of the roots = ∝β = c/a

Trigonometric Ratios The ratios between different sides of a right angled triangle w.r.t. its acute angles are called trigonometric ratios. Trigonometric ratios for right angled ∆ABC w.r.t angle A are given below. sin A = BC/AC = P/H cos A = AB/AC = B/H tan A = BC/AB = P/B cosec A = AC/BC = H/P sec A = AC/AB = H/B cot A =AB/BC =B/P Relation between Trigonometric Ratios sin A = 1/(cosec A) or cosec A = 1/sin⁡A cos A = 1/sec⁡A or sec A = 1/(cos A) tan A = sin⁡A/cos⁡〖A 〗 or cot A = cos⁡A/sin⁡A

Quadrants The axes X'OX and Y'OY divide the whole plane into four parts which are called quadrants. Here, OX and OX' are called the positive and negative directions respectively of x-axis and similarly OY and OY’ prime are the positive and negative directions, respectively of y-axis. In 1st quadrant, x > 0, y > 0 In 2nd quadrant, x < 0 y > 0 In 3rd quadrant, x < 0 , y < 0 In 4th quadrant, x > 0, y < 0 The coordinates of any point on the x-axis are of the form (x, 0) and on the y-axis are of the form (0, y).If the x-coordinate or abscissa of a point is zero, then it would be somewhere on the y-axis and if its y-coordinate or ordinate is zero, then it would be on x-axis. Distance Formulae The distance between any two points is the length of the line segment joining them. i.e. D = √(〖(x_2- x_1)〗^2+〖(y_2- y_1)〗^2 ) Or D = √(〖(Difference of bscissa)〗^2+ 〖(Difference of ordinates)〗^2 ) The distance between any two points is the length of the line segment joining them. Section formula Case I For external division x=(〖mx〗_2- 〖nx〗_1)/(m-n),y= (〖my〗_2- 〖ny〗_1)/(m-n) Case II For Internal division x=(〖mx〗_2+ 〖nx〗_1)/(m+ n),y= (〖my〗_2+ 〖ny〗_1)/(m+n) Area of Triangle Let A (x_1 y_1), B (x_2 y_2) and C (x_3 y_3) be the coordinates of the vertices of ∆ABC. Area of ∆ABC = 1/2 [x_1 (y_2- y_3 )+ x_2 (y_3- y_1 )+x_3 (y_1- y_2)]

Trigonometric Ratios The ratios between different sides of a right angled triangle w.r.t. its acute angles are called trigonometric ratios. Trigonometric ratios for right angled ∆ABC w.r.t angle A are given below. sin A = BC/AC = P/H cos A = AB/AC = B/H tan A = BC/AB = P/B cosec A = AC/BC = H/P sec A = AC/AB = H/B cot A =AB/BC =B/P Relation between Trigonometric Ratios sin A = 1/(cosec A) or cosec A = 1/sin⁡A cos A = 1/sec⁡A or sec A = 1/(cos A) tan A = sin⁡A/cos⁡〖A 〗 or cot A = cos⁡A/sin⁡A Trigonometric Ratios The ratios between different sides of a right angled triangle w.r.t. its acute angles are called trigonometric ratios. Trigonometric ratios for right angled ∆ABC w.r.t angle A are given below. sin A = BC/AC = P/H cos A = AB/AC = B/H tan A = BC/AB = P/B cosec A = AC/BC = H/P sec A = AC/AB = H/B cot A =AB/BC =B/P Relation between Trigonometric Ratios sin A = 1/(cosec A) or cosec A = 1/sin⁡A cos A = 1/sec⁡A or sec A = 1/(cos A) tan A = sin⁡A/cos⁡〖A 〗 or cot A = cos⁡A/sin⁡A

GEOMETRY Geometry is the most important topic of maths section in PSTET. Geometry can be defined as the study of shapes. Plane Geometry is related to the properties and relation of plane figures, such as angles, triangles, other polygons and circles. Line is defined by its length but has no breadth. A line contains infinite points. Through a given point , there passes infinite lines. Line Segment is the part of the line that contains two points and all points between them. The two points are called end points. Ray is a line segment when extended infinitely in one direction Parallel lines Two lines in the same plane are said to be parallel, if they never meet. Transversal is a line which cuts a pair of parallel is called a transversal.

GEOMETRY Geometry is the most important topic of maths section in PSTET. Geometry can be defined as the study of shapes. Plane Geometry is related to the properties and relation of plane figures, such as angles, triangles, other polygons and circles. Line is defined by its length but has no breadth. A line contains infinite points. Through a given point , there passes infinite lines. Line Segment is the part of the line that contains two points and all points between them. The two points are called end points. Ray is a line segment when extended infinitely in one direction Parallel lines Two lines in the same plane are said to be parallel, if they never meet. Transversal is a line which cuts a pair of parallel is called a transversal.

GEOMETRY Geometry is the most important topic of maths section in PSTET. Geometry can be defined as the study of shapes. Plane Geometry is related to the properties and relation of plane figures, such as angles, triangles, other polygons and circles. Line is defined by its length but has no breadth. A line contains infinite points. Through a given point , there passes infinite lines. Line Segment is the part of the line that contains two points and all points between them. The two points are called end points. Ray is a line segment when extended infinitely in one direction Parallel lines Two lines in the same plane are said to be parallel, if they never meet. Transversal is a line which cuts a pair of parallel is called a transversal.

GEOMETRY Geometry is the most important topic of maths section in PSTET. Geometry can be defined as the study of shapes. Plane Geometry is related to the properties and relation of plane figures, such as angles, triangles, other polygons and circles. Line is defined by its length but has no breadth. A line contains infinite points. Through a given point , there passes infinite lines. Line Segment is the part of the line that contains two points and all points between them. The two points are called end points. Ray is a line segment when extended infinitely in one direction Parallel lines Two lines in the same plane are said to be parallel, if they never meet. Transversal is a line which cuts a pair of parallel is called a transversal.

GEOMETRY Geometry is the most important topic of maths section in PSTET. Geometry can be defined as the study of shapes. Plane Geometry is related to the properties and relation of plane figures, such as angles, triangles, other polygons and circles. Line is defined by its length but has no breadth. A line contains infinite points. Through a given point , there passes infinite lines. Line Segment is the part of the line that contains two points and all points between them. The two points are called end points. Ray is a line segment when extended infinitely in one direction Parallel lines Two lines in the same plane are said to be parallel, if they never meet. Transversal is a line which cuts a pair of parallel is called a transversal.

TRAINGLES Summary In this chapter you have studied the following points : 1. Two figures having the same shape but not necessarily the same size are called similar figures. 2. All the congruent figures are similar but the converse is not true. 3. Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (i.e., proportion). 4. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. 5. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. 6. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion). 7. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion). 8. If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar (SSS similarity criterion). 9. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar (SAS similarity criterion). 10. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 11. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other. 12. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). 13. If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

TRAINGLES Summary In this chapter you have studied the following points : 1. Two figures having the same shape but not necessarily the same size are called similar figures. 2. All the congruent figures are similar but the converse is not true. 3. Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (i.e., proportion). 4. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. 5. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. 6. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion). 7. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion). 8. If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar (SSS similarity criterion). 9. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar (SAS similarity criterion). 10. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 11. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other. 12. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). 13. If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

TRAINGLES Summary In this chapter you have studied the following points : 1. Two figures having the same shape but not necessarily the same size are called similar figures. 2. All the congruent figures are similar but the converse is not true. 3. Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (i.e., proportion). 4. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. 5. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. 6. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar (AAA similarity criterion). 7. If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion). 8. If in two triangles, corresponding sides are in the same ratio, then their corresponding angles are equal and hence the triangles are similar (SSS similarity criterion). 9. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar (SAS similarity criterion). 10. The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 11. If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other. 12. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagoras Theorem). 13. If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Arithmetic Progression An arithmetic progression is a sequence in which terms increase or decrease by a constant number called the common difference. E.g., The sequence 2, 6, 10, 14, 18, 22, .… Is an arithmetic progression, whose first term is 2 and common difference is 4. An arithmetic progression is represented by a, (a + d), (a + 2d), (a + 3d), ….., a + (n – 1) d. Here a = first term d = common difference n = number of terms in the progression The general term of an arithmetic progression is given by Tn = a + (n – 1) d The sum of n terms of an arithmetic progression is given by S_n = n/2 [2a + (n – 1) d] 0r S_n = n/2[a+l] where l is the last term of arithmetic progression. If a, b, c are in arithmetic progression, then b = (a+c)/2 where b is the arithmetic mean. Fundas If the same quantity is added or multiplied to each term of an AP, then the resulting series is also an AP. If three terms are in AP, then they can be taken as (a – d), a, (a + d). If four terms are in AP, then they can be taken as (a – 3d), (a – d), (a + d), (a +3d). If five terms are in AP, then they can be taken as (a – 2d), (a – d), a, (a + d), (a + 2d).

Mensuration

The universe is everything. It includes all of space, and all the matter and energy that space contains. It even includes time itself and, of course, it includes you. Earth and the Moon are part of the universe, as are the other planets and their many dozens of moons.

The solar system comprises the sun, 8 planets their moon and other non stellar objects . The sun is at the centre of the solar system and all the planets rolled around it in elliptical orbit . The sun is the nearest star to the earth .The plants are classified in 2 types inner planets and outer plants .Mercury, venus ,earth ,mars are the inner planets .

The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water.[1] Another definition is "any of the large bodies of water into which the great ocean is divided".[2] Separate names are used to identify five different areas of the ocean.

Cyclones In meteorology, a cyclone is a large scale air mass that rotates around a strong center of low atmospheric pressure, counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere .

In geography we learn about origin of universe ,mountains ,lakes ,rivers ,glaciers In this chapter we learnt about so many geographical terms like apogee perigee aphilian perihelion So here are some mcq related this chapter

Dams of india Description - In this lecture we will learn The concept of the dams of india with tricks . The location of dam is very important topic So with the tricks we will learn the river and the state of a dam

Winds Wind is the movement of air, caused by the uneven heating of the Earth by the sun and the Earth's own rotation. There are 3 types of winds- trade winds,Westerly winds, easterlies winds.

Geography of India Longitude and latitude of india /Tropic of cancer states/Physical features of india/ Himalaya/Plaines of india /Peninsular plateau of india /Coastal plains of india /location of India geographical facts of India/ map of india with sources/islands of India/Thar desert/Geographical regions of india /Size of india /Neighbouring countries of india

Volcanism is the eruption of molten rock (magma) onto the surface of a planet. A volcano is the vent through which magma and gases are discharged. Magma that reaches the surface is called “lava.” Volcanos are named for Vulcan — the Roman god of fire!

The layers of atmosphere The composition and characteristics of the atmosphere Of the earth vary with height from the surface . Temperature pressure and intensity of the most important characteristics of the atmosphere that vary with altitude .On the basis of the thermal and other characteristics the atmosphere can be divided into a number of almost concentric layers .

International boundaries Description - In this lecture we will learn international boundaries with very interesting tricks .It national boundaries are very important topic .With the help of tricks we can learn easily these international boundaries .

An eclipse occurs when one heavenly body such as a moon or planet moves into the shadow of another heavenly body. Let's learn about the two types of eclipses on Earth. What Is a Lunar Eclipse? The Moon moves in an orbit around Earth. At the same time, Earth orbits the Sun.

An earthquake Description -An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves.

The structure of the earth is divided into four major components: the crust, the mantle, the outer core, and the inner core. Each layer has a unique chemical composition, physical state, and can impact life on Earth's surface.

Lakes of india- In this lecture we are going to learn the lakes of india in very entertaining manner .With these tricks you can easily learn all the lakes of india .In this lecture we learn the lakes with their states .

There are three kinds of rock: igneous, sedimentary, and metamorphic. Igneous rocks form when molten rock (magma or lava) cools and solidifies. Sedimentary rocks originate when particles settle out of water or air, or by precipitation of minerals from water. They accumulate in layers.

Ocean currents are the continuous, predictable, directional movement of seawater driven by gravity, wind (Coriolis Effect), and water density. Ocean water moves in two directions: horizontally and vertically. Horizontal movements are referred to as currents, while vertical changes are called upwellings or downwellings.

French Revolution, also called Revolution of 1789, revolutionary movement that shook France between 1787 and 1799 and reached its first climax there in 1789.The feudal regime had been weakened step-by-step and had already disappeared in parts of Europe.

The French Revolution opened up the possibility of creating a dramatic change in the way in which society was structured. Not everyone in Europe, however, wanted a complete transformation. Some were ‘conservatives’, while others were ‘liberals’ or ‘radicals’.

The French Revolution opened up the possibility of creating a dramatic change in the way in which society was structured. Not everyone in Europe, however, wanted a complete transformation. Some were ‘conservatives’, while others were ‘liberals’ or ‘radicals’.

The Nazi Party then began to eliminate all political opposition and consolidate its power. Hindenburg died on 2 August 1934 and Hitler became dictator of Germany by merging the offices and powers of the chancellery and presidency.

The problem of deforestation has become more complicated for some reasons. For a huge increase in population, the food demand increased and the cultivation area was extended by clearing forests.

Pastoralism is a way of keeping animals such as cattle, sheep, that involves moving from one place to another to find water and food. Nomads are people who do not live in one place but move from one area to another to earn their living.Mainly pastoral communities are found in mountainous regions..

Peasants cultivated open fields which were strips of land near their villages. These strips were of varying quality. This was a measure to ensure that everyone had a mix of good and bad land.

National awakening also grew out of an intellectual reaction to the Enlightenment that emphasized national identity and developed an authentic view of cultural self-expression through nationhood.

The Indo-China region of modern-day Vietnam, Cambodia and Laos struggled with colonisation from the Europeans just like India. They too fought back to gain their independence and this where their nationalist movement started. Vietnam actually gained formal independence even before India

The making of the global world has a long history of trade, migration of people in search of work, the movement of capital, etc.Globalisation’ is often referred to as an economic system that has emerged Since last 50 years and so on .

The Age of Industrialisation begins by explaining the scenario before the Industrial Revolution and how it changed over time in terms of labour, setting up of factories, etc.In Britain, the most dynamic industries were cotton and metals.

In India and as in many other colonies, the growth of modern nationalism is intimately connected to the anti-colonial movement. People began discovering their unity in the process of their struggle with colonialism. The sense of being oppressed under colonialism provided a shared bond that tied many different groups together. The Congress under Mahatma Gandhi tried to forge these groups together within one movement. But the unity did not emerge without conflict.

The modern city worldwide has developed over the last 200 years. Three historical processes have shaped modern cities in decisive ways. The rise of capitalism. The establishment of colonial rule over large parts of the world.

In this lecture you will learn about Development in Indian Economy. By watching this video, you will learn about: Concept of Development. Income and other criteria’s for measuring the development of the economy. Different development goals for the different category of persons. Concept of Infant Mortality ratio, Literacy ratio, Body mass Index, Per Capita Income and National Income etc. Human Development Index prepared by UNDP. World Bank Report and HDI. Concept of Sustainable Development, SDGs of India. Objective Questions on the development topic.

In this lecture you will learn about the different sectors of Indian Economy. By watching this video, you will learn about: Sector of Indian Economy: Primary sector, secondary sector and tertiary sector. Sectors on the basis of operation and ownership. MGNREGA scheme of generating employment, GDP (Gross Domestic Product) and Disguised unemployment.

In this lecture you will learn about the concept of Money and Credit. By watching this video, you will learn about: Concept of Money. Barter System and concept of Double Coincidence of Wants. Evolution of Money. Modern forms of money: Currency, Deposits in Banks and Cheques. Loan activities of banks, Two different credit situations and the terms of credit. Formal Sector Credit in India: Formal and Informal Sector. Self Help Groups for people. Objective Questions on the topic of Money and Credit.

In this lecture you will learn about the concept of Globalization and its Impact on Indian Economy. By watching this video, you will learn about: Production across countries and interlinking the production across countries. Foreign trade and integration of foreign markets. Concept of Globalization; Factors enabling Globalization: Technology, Trade liberalization, Foreign Investment policy. World Trade Organization, Structure of WTO, World Trade Group. Impact of Globalization on Indian Economy.

Consumer Rights are referred to a set of laws that represent the right to be informed about the quantity, quality, purity, potency, price of goods and their standards so that the consumer is protected against all sorts of unfair trade practices. The Consumer Bill of Rights upholds the right to safety of every citizen.

Geography MCQ's - Lecture 19

Geography MCQ's - Lecture 20

Geography MCQ's - Lecture 21

Geography MCQ's - Lecture 22

Geography MCQ's - Lecture 23

Geography MCQ's - Lecture 24

Introductory (Reasoning) - Lecture 1

Number Series Number series is a sequential arrangement of numbers following a certain defined pattern. In this section, we deal with questions in which a series of numbers, (which are generally called the terms of the series) is given. These numbers/terms follow a certain pattern throughout the series. Candidates are asked either to find a missing term or to find the wrong term of the series.

Blood relation is an important topic for all sorts of competitive exams like Banking , SSC, RBI grade B , PSPCL, PPSC , Punjab Sub Inspector etc. It almost carries a weightage of 3 to 5 marks and may vary exam to exam. So, basically questions Blood relations involve analysis of certain blood relations and then inferring on the basis of the given information. In the questions , a chain of relationships is given in the form of information and on the basis of which, relation between any two members of the chain is asked. Following are some of the basic tricks which helps to solve blood relations questions easily and efficiently . After understanding the basic concept relation , Solve blood relations question in an MCQ format which helps you in exams.

Coding –decoding is one of the most important topic reasoning. It is repeatedly asked in competitive exams and also in AFPI. It carries a weightage of 2-3 marks. Generally, there are three different types of coding – decoding. • Pattern based • Direct based • Elimination based While solving questions of coding –decoding one should memorise alphabetical positions of alphabets from A to Z (1-26) and opposite pairs like B is opposite to Y.

Direction is one of the most important topic of reasoning. Direction has its relevance in all types of competitive exam like banking exams, SSC, UPSC, PPSC, AFPI etc. The position towards which someone or something moves or faces is known as direction. Basically there are four main directions are: 1. North 2. South 3. East 4. West CARDINAL DIRECTION : A direction between two consecutive main directions is called sub or cardinal direction. 1. North-east 2. North-west 3. South-east 4. South-west Here, angle formed between two consecutive main directions is 90 degree and angle formed between cardinal and main direction is 45 degree.

Order and ranking There are two types of ranking test in analytical reasoning: 1. Sequential Order of arrangement: In this type of questions, persons or objects are arranged based on the comparison of parameers such as age, marks, salary, weight etc. 2. Ranking: If a certain person sitting in a row, let L be the rank from left end and R be the rank from right end. Total = L+R-1

Missing number series is one such topic which has its importance in MRSAFPI Exam. It carries weight age of 3 marks. So, Below are basic tricks which can help you to solve questions based on number series. • Before solving questions always observe the flow of series whether it is increasing order or in decreasing order. • If there is gradual increase in series , then it has highly chances of addition. • If there is gradual decrease in series, then it has highly chances of subtraction • If there is huge increase in series then probably there would be multiplication or along with it addition and subtraction or square and cube. • If there is huge decrease in series then probably there would be division or along with it addition and subtraction or square and cube • Memorise square from 1 to 50 and cubes from 1 to 13. • One should good with tables as they can help a lot while solving questions.

Letter series is series of alphabets which arranged in certain pattern . It is one of the easiest topic in reasoning which helps to score more in exam. To solve letter series one can take help of numeric postions of alphabets from A(1) TO Z(26). There are 10 MCQS given below on letter series for your practice.

Analogy means similarity shared by two things that are compared. Questions on verbal analogy judge your ability to understand the diverse relationship between various elements, things etc. Analogy topic is an important topic of reasoning and it has its relevance in MRAFPI. Questions asked on analogy carries a weightage of 2-3 marks. There are three types of analogy : • Number based analogy questions • Alphabet based analogy questions • Vocab based analogy questions

Odd one out / classification in these type of questions , a group of words , letters or numbers is given. On behalf of alphabetical values and their positions letters form a group same as numbers follow mathematical operations/ rules, hence form a group. Candidates are required to select the option which does not belong to that same group.

Symbol and Notation is one of the most scoring part of reasoning. In these type of questions, a mathematical equation is given with arthimetical notification. Candidates are required to solve these questions by using basic concept of BODMAS rule.

Logical venn-diagram is one of the important topic in non-verbal reasoning. It has important role in competitive exam like MRSAFPI and other sort of competitive exams. A venn diagram shows all possible relations among the given groups of elements in a single figure. The most common type of questions that we encounter in venn – diagram are based on circular venn diagrams.

Counting figure is an interesting topic of non-verbal reasoning. In this topic, one has to count number of triangles or square or rectangles in the given figure. If one knows certain basic tricks to count the figures then this topic can be scoring. For instance, counting the numbers of squares in figure one can easily take sum of squares of number of columns if number of rows and column are equal .

Cube and Dice is one of the most important topic of non-verbal reasoning. Generally, questions asked on this topic are based on opposite and related side of a dice or cube. Candidates are required to relate the given dice and cube and transform the relation between more than once dice or cube. • Ordinary dice : A dice in which the total of two adjacent side equals to 7 , although the total opposite sides does not equal to 7. • Standard Dice : A dice in which total of two opposite sides equals to 7 although the total of two adjacent does not equal to 7.

Mirror and Water image is an important topic of non- verbal reasoning. This is the most scoring topic also. It is based on basic concept of visualisation .

A cell is capable of independent existence and can carry out all the functions which are necessary for a living being. A cell carries out nutrition, respiration, excretion, transportation and reproduction, the way an individual organism does. Unicellular organisms are capable of independent existence which shows a cell's capability to exist independently. Due to this, a cell is called the functional unit of life. All living beings are composed of the basic unit of life, i.e. cell. So, cell is called the structural unit of life. If you combine both the aspects, i.e. functional unit and structural unit, you can say that a cell is the fundamental unit of life.

All the living organisms need energy to perform various life processes. They get this energy from food. Food is a kind of fuel which provides energy to all the living organisms. Food is an organic substance. Nutrient: A nutrient can be defined as a substance which an organism obtains from its surroundings and uses it as a source of energy or for the biosynthesis of its body constituents. Nutrition is the process of intake of nutrients (like carbohydrates, fats, proteins, minerals, vitamins and water) by an organism as well as the utilization of these nutrients by the organism. Mode of nutrition means method of obtaining food by an organism. There are mainly two modes of nutrition 1. Autotrophic mode of nutrition 2. Heterotrophic mode of nutrition

Transportation is a vital process in plants and Animals. Trees transport all the water and nutrients from roots to the other parts of plants for survival from its roots to the tips of the leaves. For the verious metabolic process of plants like photosynthesis, transpiration, guttation raw materials should be transported from root to the leaves. For transport in plants, they need a transport system to move food, water, and minerals around because for them no heart, no blood, and since these plants do not have a circulatory system, transportation makes up for it. Plants have two transport systems - xylem and phloem. Xylem tissue transports water and mineral salts from the roots to the other parts of the plant, while phloem transports Carbohydrates, sucrose and amino acids from roots to the leaves and other parts of the plant.

Plants are mostly multicellular organisms however, few unicellular organism like algae are also considered as plants. So, we can say term plant is very broad and it includes single celled algae to flower and fruit bearing trees. Plants may be terrestrial or aquatic, plants which are present on the land surface is called terrestrial plant while the plant which floats, submerged or remain suspended in water is called aquatic plants. The first level of classification among plants depends on whether the plant body has well differentiated, distinct components. The next level of classification is based on whether the differentiated plant body has special tissues for the transport of water and other substances within it. Further classification looks at the ability to bear seeds and whether the seeds are enclosed within fruits. Animals are multicellular, eukaryotic life forms, characterized by heterotrophic mode of nutrition and inhabit all types of ecosystems including terrestrial, freshwater and marine. They can be further segregated into two groups based on the presence of notochord- chordates and invertebrates. Chordates constitute only 5% of the animal kingdom while the invertebrates claim the remaining majority. Vertebrates form a subphylum under chordates and are characterized by the presence of a vertebral column or backbone. With an exception of sponges, all animal cells are organized into tissues and in majority, the tissues organize to form well-defined organs and organ systems for carrying out essential bodily functions. Most animals are also diploid in nature and reproduce sexually by the formation of gametes.

Biological classification is the scientific procedure of arranging organisms into groups and subgroups on the basis of their similarities and dissimilarities and placing the group in a hierarchy of categories. Importance of classification- • It is not possible to study every organism. Study of one or two organism of a group gives sufficient information about the essential features of the group. • It helps in identification of new organism. • Classification helps in knowing the relationship amongst different groups of organisms. • The organism of past cannot be studied without a proper system of classification Five kingdom systems- R.H.Whittaker divided all the organism into five kingdom namely 1. Monera : It includes all the prokaryotes (Eubacteria, Actinomycetes, blue green algae, Mycoplasma) and Akaryote (virus). 2. Protista : It includes all the unicellular eukaryotes (Protozoans, Dinoflagellates, Diatoms, Euglenoids, Slime molds). 3. Mycota : It includes true fungi. 4. Plantae : It includes multicellular eukaryotic plants (Algae, Bryophyte, Pteridophyte, Gymnosperm and Angiosperm). 5. Animalia : It includes multicellular animals.

Biological classification is the scientific procedure of arranging organisms into groups and subgroups on the basis of their similarities and dissimilarities and placing the group in a hierarchy of categories. Importance of classification- • It is not possible to study every organism. Study of one or two organism of a group gives sufficient information about the essential features of the group. • It helps in identification of new organism. • Classification helps in knowing the relationship amongst different groups of organisms. • The organism of past cannot be studied without a proper system of classification Five kingdom systems- R.H.Whittaker divided all the organism into five kingdom namely 1. Monera : It includes all the prokaryotes (Eubacteria, Actinomycetes, blue green algae, Mycoplasma) and Akaryote (virus). 2. Protista : It includes all the unicellular eukaryotes (Protozoans, Dinoflagellates, Diatoms, Euglenoids, Slime molds). 3. Mycota : It includes true fungi. 4. Plantae : It includes multicellular eukaryotic plants (Algae, Bryophyte, Pteridophyte, Gymnosperm and Angiosperm). 5. Animalia : It includes multicellular animals.

Microorganisms are very small organisms that they cannot be seen with naked eyes. They can be seen under a microscope. These include a number of varieties such as bacteria, viruses, fungi, algae, protozoa, etc. These microbes can be friends or foe to human beings. Microorganisms are omnipotent i.e; they are present everywhere, in air, in water, in soil and in the body of living organisms. Some microorganisms can tolerate extreme conditions like a place as hot as boiling water, or a place as cold as ice. Some microorganisms are found alone, while the others are found in colonies.

Microorganisms are very small organisms that they cannot be seen with naked eyes. They can be seen under a microscope. These include a number of varieties such as bacteria, viruses, fungi, algae, protozoa, etc. These microbes can be friends or foe to human beings. Microorganisms are omnipotent i.e; they are present everywhere, in air, in water, in soil and in the body of living organisms. Some microorganisms can tolerate extreme conditions like a place as hot as boiling water, or a place as cold as ice. Some microorganisms are found alone, while the others are found in colonies.

Microorganisms are very small organisms that they cannot be seen with naked eyes. They can be seen under a microscope. These include a number of varieties such as bacteria, viruses, fungi, algae, protozoa, etc. These microbes can be friends or foe to human beings. Microorganisms are omnipotent i.e; they are present everywhere, in air, in water, in soil and in the body of living organisms. Some microorganisms can tolerate extreme conditions like a place as hot as boiling water, or a place as cold as ice. Some microorganisms are found alone, while the others are found in colonies.

The food that we eat is to be digested by our body for deriving nutrients from it. Digestion means breaking down of food into simpler substances in the presence of oxygen to release energy. It is a complex process involving following steps , Ingestion, Digestion, Absorption, Assimilation, Egestion. The parts of digestive tract are: • Mouth and buccal cavity • Food pipe/Oesophagus • Stomach • Small intestine • Large intestine • Rectum • Anus There are some associated glands that secrete enzymes which help in digestion of food. These include: • Salivary glands • Liver • Pancreas The digestive tract and the associated glands together constitute digestive system.

The food that we eat is to be digested by our body for deriving nutrients from it. Digestion means breaking down of food into simpler substances in the presence of oxygen to release energy. It is a complex process involving following steps , Ingestion, Digestion, Absorption, Assimilation, Egestion. The parts of digestive tract are: • Mouth and buccal cavity • Food pipe/Oesophagus • Stomach • Small intestine • Large intestine • Rectum • Anus There are some associated glands that secrete enzymes which help in digestion of food. These include: • Salivary glands • Liver • Pancreas The digestive tract and the associated glands together constitute digestive system.

The respiratory system includes some tissues and organs that help you breathe. It includes parts like nasal air passage, lungs , alveoli, bronchioles and blood vessels. The muscles that power your lungs are also part of the respiratory system. These all parts work together to transport oxygen throughout the body and clean waste gases like carbon dioxide. The oxygen inhaled is used for the breakdown of food to release energy. FUNCTION • helps you to smell and taste • Warms air to match your body temperature and moisturizes it to the humidity level your body needs. • Transports oxygen to all cells of your body to release energy • Removes waste gases like carbon dioxide from the body • Protects your air passage from harmful particles of dust and microorganisms

In humans, the excretory system removes nitrogenous waste along with other metabolic wastes from the body. It consists of few parts, viz. a pair of kidneys, renal arteries and veins, ureters, urinary bladder and urethra. The overall structure of the system is briefly discussed below. 1. The kidneys are bean-shaped organs. These are located on each side of the vertebral column. It performs the filtration blood to produce excretory fluid or urine. The structural and functional unit of the kidney is nephron. A nephron consists of: Bowman’s capsule, glomerulus, proximal tubule, Henle’s loop, distal tubule and collecting duct. 2. Renal arteries carry blood (to be filtered) to the kidneys from heart and renal veins carry filtered blood from kidneys to the inferior vena cava. 3. The kidneys open into the ureters at renal hilum. Ureters are tubes, each of which attach to a kidney and carries urine from kidneys to the urinary bladder. 4. Ureters open into the urinary bladder which is a muscular sac. These urine is stored temporarily. When filled, it contracts and passes the urine to the urethra. 5. A thin, fibro-muscular tube called urethra carries the urine from urethra to the exterior.

Control is defined as the power of restraining and regulating by which a process can be started, regulated in pace to speed up or slow down or stop completely. Coordination can be defined as the working together of the different systems of an organism in order to produce an appropriate reaction to stimuli. Control and coordination are brought about by the nervous system and the chemical control and coordination occurs with the help of endocrine systems. It regulates all the systems of the body to ensure proper coordination and efficient functioning of an organism. They are important for an organism to adapt to the changes and perform important functions like metabolism, homeostasis, etc. It also helps in responding to stimuli that help in the fight, or flight responses.

The circulatory system is made up of blood vessels that carry blood away from and towards the heart. Arteries carry blood away from the heart and veins carry blood back to the heart. The circulatory system carries oxygen, nutrients, and hormones to cells, and removes waste products, like carbon dioxide. Circulatory system, system that transports nutrients, respiratory gases, and metabolic products throughout a living organism, permitting integration among the various tissues. The process of circulation includes the intake of metabolic materials, the conveyance of these materials throughout the organism, and the return of harmful by-products to the environment.

Reproduction is essential for species survival. Asexual reproduction involves only one parent, occurs only in lower organisms like Amoeba, yeast, Hydra, etc. Sexual reproduction involves fertilisation or fusion of gametes from males and females. Fertilisation may be external or internal. The sexual reproduction in human beings is a complex process. Both male and female individuals attain maturity by going through a adolescent phase. Male Reproductive System: Male reproductive system comprises of- a pair of testis, glands, accessory ducts, and male genitalia. 1. Testis is the site where male gametes or germ cells are produced. They are located outside the abdominal cavity in a sac-like structure known as scrotum. This is to maintain lower temperature required for the formation of sperm. Testes produce male hormone called testosterone. 2. Vas deferens is a duct that transport sperm to urethra, which is a common passage for both urine and sperm ejaculation. 3. Prostate glands and seminal vesicles are also found in males to nourish and for easy transport of sperm in the female genital tract. Female reproductive system consists of 1. Ovaries produce female cell, ovum. Also secrete hormones oestrogen and progesterone. 2. Fallopian tube facilitates smooth passage of fertilised egg to uterus 3. Uterus a muscular bag, where foetus is established and develops fully into a baby, 4. Cervix and vagina.

u Motion : An object which changes its position with respect to a fixed point is said to be in motion. u Motion is a relative term : An object at rest with respect to one object may also be in motion with respect to another object. u Reference point : A fixed point with respect to which an object changes its position is known as a reference point. u Distance : The length of actual path between the initial position and the final position of a moving object or body is known as distance travelled by the particle. u Displacement : The shortest distance between the initial and final positions of a moving object or body in a direction from initial to the final position of the particle is known as displacement of the particle. u Units of distance and displacement : SI unit of distance and displacement is metre (m). u Distance travelled by a body is always positive. u Displacement of body may be positive, negative or zero. u Ratio of the magnitude of displacement and the distance is equal to less than 1. u Uniform Motion : The motion of a body is said to be uniform if (i) it moves along a straight line and (ii) it covers equal distance in equal intervals of time, how-so-ever, small these intervals may be. u Non-uniform motion : The motion of a body is said to be non-uniform if it covers unequal distance in equal intervals of time. u Speed : The distance travelled by a body in unit time is known as the speed of the body. That is u Unit of speed : SI unit of speed is ms–1. u Uniform speed : If a moving body covers equal distances in equal intervals of time, the speed of the body is uniform. u Non-Uniform speed : If a moving body covers unequal distances in equal intervals of time, the speed of the body is non-uniform. u Average speed : The total distance travelled by a body during non-uniform motion divided by the time taken to travel this distance is called average speed. i.e. Average speed = u Velocity : The displacement of the body per unit time is known as the velocity of the body. That is, u Unit of velocity : SI unit of velocity is ms–1. u Uniform velocity : Velocity of a body is said to be uniform velocity if it covers equal displacements in equal intervals of time. u Non-uniform velocity : Velocity of a body is said to be non-uniform if it covers unequal displacement in equal intervals of time. u u Speed is a scalar quantity, whereas velocity is a vector quantity. u Speed of a body is always positive. u Velocity of body can be positive as well as negative. u Acceleration : Acceleration of a body is defined as the change in velocity per unit time. i.e. u Positive acceleration : When the velocity of a body increases with time, acceleration of body is said to be positive acceleration. Or When the change in velocity (Dv) of a body takes place in the direction of the motion of the body, then the acceleration of the body positive. u Negative acceleration or retardation or deceleration : If the velocity of the body decreases with time, then acceleration of body is negative acceleration of retardation. Or When the change in velocity (Dv) of a body takes place in a direction opposite to the direction of motion of the body, then the acceleration of the body is negative. u S.I. unitof acceleration is m/s2 u

u Motion : An object which changes its position with respect to a fixed point is said to be in motion. u Motion is a relative term : An object at rest with respect to one object may also be in motion with respect to another object. u Reference point : A fixed point with respect to which an object changes its position is known as a reference point. u Distance : The length of actual path between the initial position and the final position of a moving object or body is known as distance travelled by the particle. u Displacement : The shortest distance between the initial and final positions of a moving object or body in a direction from initial to the final position of the particle is known as displacement of the particle. u Units of distance and displacement : SI unit of distance and displacement is metre (m). u Distance travelled by a body is always positive. u Displacement of body may be positive, negative or zero. u Ratio of the magnitude of displacement and the distance is equal to less than 1. u Uniform Motion : The motion of a body is said to be uniform if (i) it moves along a straight line and (ii) it covers equal distance in equal intervals of time, how-so-ever, small these intervals may be. u Non-uniform motion : The motion of a body is said to be non-uniform if it covers unequal distance in equal intervals of time. u Speed : The distance travelled by a body in unit time is known as the speed of the body. That is u Unit of speed : SI unit of speed is ms–1. u Uniform speed : If a moving body covers equal distances in equal intervals of time, the speed of the body is uniform. u Non-Uniform speed : If a moving body covers unequal distances in equal intervals of time, the speed of the body is non-uniform. u Average speed : The total distance travelled by a body during non-uniform motion divided by the time taken to travel this distance is called average speed. i.e. Average speed = u Velocity : The displacement of the body per unit time is known as the velocity of the body. That is, u Unit of velocity : SI unit of velocity is ms–1. u Uniform velocity : Velocity of a body is said to be uniform velocity if it covers equal displacements in equal intervals of time. u Non-uniform velocity : Velocity of a body is said to be non-uniform if it covers unequal displacement in equal intervals of time. u u Speed is a scalar quantity, whereas velocity is a vector quantity. u Speed of a body is always positive. u Velocity of body can be positive as well as negative. u Acceleration : Acceleration of a body is defined as the change in velocity per unit time. i.e. u Positive acceleration : When the velocity of a body increases with time, acceleration of body is said to be positive acceleration. Or When the change in velocity (Dv) of a body takes place in the direction of the motion of the body, then the acceleration of the body positive. u Negative acceleration or retardation or deceleration : If the velocity of the body decreases with time, then acceleration of body is negative acceleration of retardation. Or When the change in velocity (Dv) of a body takes place in a direction opposite to the direction of motion of the body, then the acceleration of the body is negative. u S.I. unitof acceleration is m/s2 u

u Motion : An object which changes its position with respect to a fixed point is said to be in motion. u Motion is a relative term : An object at rest with respect to one object may also be in motion with respect to another object. u Reference point : A fixed point with respect to which an object changes its position is known as a reference point. u Distance : The length of actual path between the initial position and the final position of a moving object or body is known as distance travelled by the particle. u Displacement : The shortest distance between the initial and final positions of a moving object or body in a direction from initial to the final position of the particle is known as displacement of the particle. u Units of distance and displacement : SI unit of distance and displacement is metre (m). u Distance travelled by a body is always positive. u Displacement of body may be positive, negative or zero. u Ratio of the magnitude of displacement and the distance is equal to less than 1. u Uniform Motion : The motion of a body is said to be uniform if (i) it moves along a straight line and (ii) it covers equal distance in equal intervals of time, how-so-ever, small these intervals may be. u Non-uniform motion : The motion of a body is said to be non-uniform if it covers unequal distance in equal intervals of time. u Speed : The distance travelled by a body in unit time is known as the speed of the body. That is u Unit of speed : SI unit of speed is ms–1. u Uniform speed : If a moving body covers equal distances in equal intervals of time, the speed of the body is uniform. u Non-Uniform speed : If a moving body covers unequal distances in equal intervals of time, the speed of the body is non-uniform. u Average speed : The total distance travelled by a body during non-uniform motion divided by the time taken to travel this distance is called average speed. i.e. Average speed = u Velocity : The displacement of the body per unit time is known as the velocity of the body. That is, u Unit of velocity : SI unit of velocity is ms–1. u Uniform velocity : Velocity of a body is said to be uniform velocity if it covers equal displacements in equal intervals of time. u Non-uniform velocity : Velocity of a body is said to be non-uniform if it covers unequal displacement in equal intervals of time. u u Speed is a scalar quantity, whereas velocity is a vector quantity. u Speed of a body is always positive. u Velocity of body can be positive as well as negative. u Acceleration : Acceleration of a body is defined as the change in velocity per unit time. i.e. u Positive acceleration : When the velocity of a body increases with time, acceleration of body is said to be positive acceleration. Or When the change in velocity (Dv) of a body takes place in the direction of the motion of the body, then the acceleration of the body positive. u Negative acceleration or retardation or deceleration : If the velocity of the body decreases with time, then acceleration of body is negative acceleration of retardation. Or When the change in velocity (Dv) of a body takes place in a direction opposite to the direction of motion of the body, then the acceleration of the body is negative. u S.I. unitof acceleration is m/s2 u

u Motion : An object which changes its position with respect to a fixed point is said to be in motion. u Motion is a relative term : An object at rest with respect to one object may also be in motion with respect to another object. u Reference point : A fixed point with respect to which an object changes its position is known as a reference point. u Distance : The length of actual path between the initial position and the final position of a moving object or body is known as distance travelled by the particle. u Displacement : The shortest distance between the initial and final positions of a moving object or body in a direction from initial to the final position of the particle is known as displacement of the particle. u Units of distance and displacement : SI unit of distance and displacement is metre (m). u Distance travelled by a body is always positive. u Displacement of body may be positive, negative or zero. u Ratio of the magnitude of displacement and the distance is equal to less than 1. u Uniform Motion : The motion of a body is said to be uniform if (i) it moves along a straight line and (ii) it covers equal distance in equal intervals of time, how-so-ever, small these intervals may be. u Non-uniform motion : The motion of a body is said to be non-uniform if it covers unequal distance in equal intervals of time. u Speed : The distance travelled by a body in unit time is known as the speed of the body. That is u Unit of speed : SI unit of speed is ms–1. u Uniform speed : If a moving body covers equal distances in equal intervals of time, the speed of the body is uniform. u Non-Uniform speed : If a moving body covers unequal distances in equal intervals of time, the speed of the body is non-uniform. u Average speed : The total distance travelled by a body during non-uniform motion divided by the time taken to travel this distance is called average speed. i.e. Average speed = u Velocity : The displacement of the body per unit time is known as the velocity of the body. That is, u Unit of velocity : SI unit of velocity is ms–1. u Uniform velocity : Velocity of a body is said to be uniform velocity if it covers equal displacements in equal intervals of time. u Non-uniform velocity : Velocity of a body is said to be non-uniform if it covers unequal displacement in equal intervals of time. u u Speed is a scalar quantity, whereas velocity is a vector quantity. u Speed of a body is always positive. u Velocity of body can be positive as well as negative. u Acceleration : Acceleration of a body is defined as the change in velocity per unit time. i.e. u Positive acceleration : When the velocity of a body increases with time, acceleration of body is said to be positive acceleration. Or When the change in velocity (Dv) of a body takes place in the direction of the motion of the body, then the acceleration of the body positive. u Negative acceleration or retardation or deceleration : If the velocity of the body decreases with time, then acceleration of body is negative acceleration of retardation. Or When the change in velocity (Dv) of a body takes place in a direction opposite to the direction of motion of the body, then the acceleration of the body is negative. u S.I. unitof acceleration is m/s2 u

 Force : Force is that cause which produces acceleration in the body on which it acts. A force or a set of forces can (a) change the speed of the body, (b) change the direction of motion of the body, and (c) change the shape of the body. If a single force acting on a body produces the same acceleration as produced by a number of forces, this single force is called the resultant or net of the individual forces. The SI unit of force is the newton, denoted by the symbol (N).  Balanced and unbalanced forces : If a set of forces acting on a body produces no acceleration in it, the forces are called balanced. If it produces a non zero acceleration, the forces are said to be unbalanced.  Some common forces : Friction is a force exerted parallel to two surfaces in contact. The effect of friction is to oppose slipping of the two surfaces against each other. A stretched spring pulls the bodies connected to its ends. A compressed spring pushes the bodies connected to its ends. A string always pulls an object tied at its end. The magnitude of the force of the pull is called the tension in the string. The force by which the earth attracts a body is called the weight of the body. It is equal to the mass of the body multiplied by the acceleration due to gravity (W = mg).  Newton’s laws of motion : First law :A body at rest will remain at rest and a body in motion will remain in uniform motion unless in motion will remain in uniform motion unless acted upon by an unbalanced force. Second law :The net force acting on a body is proportional to the product of the mass of the body and its acceleration. Third law :In any interaction between two bodies, the force applied by the first body on the second is equal and opposite to the force applied by the second body on the first.  Definition of newton : If a force acting on a 1 kg mass produces an acceleration of 1 m/s2 in it, the force is called one newton.  Linear momentum : The product of the mass of a body and its velocity is called the linear momentum of the body. The net force on a body is equal to change in its momentum per unit time.  Conservation of linear momentum : If the net external force acting on a system of particles is zero, the total linear momentum of the system remains constant.0

 Force : Force is that cause which produces acceleration in the body on which it acts. A force or a set of forces can (a) change the speed of the body, (b) change the direction of motion of the body, and (c) change the shape of the body. If a single force acting on a body produces the same acceleration as produced by a number of forces, this single force is called the resultant or net of the individual forces. The SI unit of force is the newton, denoted by the symbol (N).  Balanced and unbalanced forces : If a set of forces acting on a body produces no acceleration in it, the forces are called balanced. If it produces a non zero acceleration, the forces are said to be unbalanced.  Some common forces : Friction is a force exerted parallel to two surfaces in contact. The effect of friction is to oppose slipping of the two surfaces against each other. A stretched spring pulls the bodies connected to its ends. A compressed spring pushes the bodies connected to its ends. A string always pulls an object tied at its end. The magnitude of the force of the pull is called the tension in the string. The force by which the earth attracts a body is called the weight of the body. It is equal to the mass of the body multiplied by the acceleration due to gravity (W = mg).  Newton’s laws of motion : First law :A body at rest will remain at rest and a body in motion will remain in uniform motion unless in motion will remain in uniform motion unless acted upon by an unbalanced force. Second law :The net force acting on a body is proportional to the product of the mass of the body and its acceleration. Third law :In any interaction between two bodies, the force applied by the first body on the second is equal and opposite to the force applied by the second body on the first.  Definition of newton : If a force acting on a 1 kg mass produces an acceleration of 1 m/s2 in it, the force is called one newton.  Linear momentum : The product of the mass of a body and its velocity is called the linear momentum of the body. The net force on a body is equal to change in its momentum per unit time.  Conservation of linear momentum : If the net external force acting on a system of particles is zero, the total linear momentum of the system remains constant.0

 Force : Force is that cause which produces acceleration in the body on which it acts. A force or a set of forces can (a) change the speed of the body, (b) change the direction of motion of the body, and (c) change the shape of the body. If a single force acting on a body produces the same acceleration as produced by a number of forces, this single force is called the resultant or net of the individual forces. The SI unit of force is the newton, denoted by the symbol (N).  Balanced and unbalanced forces : If a set of forces acting on a body produces no acceleration in it, the forces are called balanced. If it produces a non zero acceleration, the forces are said to be unbalanced.  Some common forces : Friction is a force exerted parallel to two surfaces in contact. The effect of friction is to oppose slipping of the two surfaces against each other. A stretched spring pulls the bodies connected to its ends. A compressed spring pushes the bodies connected to its ends. A string always pulls an object tied at its end. The magnitude of the force of the pull is called the tension in the string. The force by which the earth attracts a body is called the weight of the body. It is equal to the mass of the body multiplied by the acceleration due to gravity (W = mg).  Newton’s laws of motion : First law :A body at rest will remain at rest and a body in motion will remain in uniform motion unless in motion will remain in uniform motion unless acted upon by an unbalanced force. Second law :The net force acting on a body is proportional to the product of the mass of the body and its acceleration. Third law :In any interaction between two bodies, the force applied by the first body on the second is equal and opposite to the force applied by the second body on the first.  Definition of newton : If a force acting on a 1 kg mass produces an acceleration of 1 m/s2 in it, the force is called one newton.  Linear momentum : The product of the mass of a body and its velocity is called the linear momentum of the body. The net force on a body is equal to change in its momentum per unit time.  Conservation of linear momentum : If the net external force acting on a system of particles is zero, the total linear momentum of the system remains constant.0

 Force : Force is that cause which produces acceleration in the body on which it acts. A force or a set of forces can (a) change the speed of the body, (b) change the direction of motion of the body, and (c) change the shape of the body. If a single force acting on a body produces the same acceleration as produced by a number of forces, this single force is called the resultant or net of the individual forces. The SI unit of force is the newton, denoted by the symbol (N).  Balanced and unbalanced forces : If a set of forces acting on a body produces no acceleration in it, the forces are called balanced. If it produces a non zero acceleration, the forces are said to be unbalanced.  Some common forces : Friction is a force exerted parallel to two surfaces in contact. The effect of friction is to oppose slipping of the two surfaces against each other. A stretched spring pulls the bodies connected to its ends. A compressed spring pushes the bodies connected to its ends. A string always pulls an object tied at its end. The magnitude of the force of the pull is called the tension in the string. The force by which the earth attracts a body is called the weight of the body. It is equal to the mass of the body multiplied by the acceleration due to gravity (W = mg).  Newton’s laws of motion : First law :A body at rest will remain at rest and a body in motion will remain in uniform motion unless in motion will remain in uniform motion unless acted upon by an unbalanced force. Second law :The net force acting on a body is proportional to the product of the mass of the body and its acceleration. Third law :In any interaction between two bodies, the force applied by the first body on the second is equal and opposite to the force applied by the second body on the first.  Definition of newton : If a force acting on a 1 kg mass produces an acceleration of 1 m/s2 in it, the force is called one newton.  Linear momentum : The product of the mass of a body and its velocity is called the linear momentum of the body. The net force on a body is equal to change in its momentum per unit time.  Conservation of linear momentum : If the net external force acting on a system of particles is zero, the total linear momentum of the system remains constant.0

1. The force of attraction between two bodies in the universe is known as gravitational force. 2. Gravitational force between two bodies of masses m1 and m2 separated by a distance r is given by F = 3. G = 6.673 × 10–11 Nm2 kg–2 is gravitational constant. 4. Gravitational force is large if masses of two bodies are very large. 5. Gravitational force of the earth on a body is known as gravity. 6. The fall of a body is known as free fall if it falls only under the action of gravitational force of earth in the absence of air resistance. 7. Acceleration with which a body falls towards the earth, the gravitational force of the earth is called acceleration due to gravity. It is denoted by 'g'. 8. In S.I., unit of 'g' is m s–2. 9. g=, where M is the mass of the earth and R is the radius of the earth. 10. The value of 'g' on the surface of the earth is 9.8 m s–2. 11. The value of 'g' on the surface of the moon = 1/6 times value of 'g' on the surface of the earth. 12. The value of 'g' decreases with height and depth from surface of the earth. 13. The value of 'g' at poles is more than at equator. 14. The value of 'g' is zero at the centre of the earth. 15. Mass is the quantity of matter contained in a body. 16. In S.I. unit of mass is kg. 17. Weight of a body is the force with which the earth attracts the body. Weight of body always acts at its centre of gravity and in the downward direction, W = mg. 18. In S.I., unit of weight is newton (N). 19. Mass of a body does not change but weight of a body is different at different places.

1. The force of attraction between two bodies in the universe is known as gravitational force. 2. Gravitational force between two bodies of masses m1 and m2 separated by a distance r is given by F = 3. G = 6.673 × 10–11 Nm2 kg–2 is gravitational constant. 4. Gravitational force is large if masses of two bodies are very large. 5. Gravitational force of the earth on a body is known as gravity. 6. The fall of a body is known as free fall if it falls only under the action of gravitational force of earth in the absence of air resistance. 7. Acceleration with which a body falls towards the earth, the gravitational force of the earth is called acceleration due to gravity. It is denoted by 'g'. 8. In S.I., unit of 'g' is m s–2. 9. g=, where M is the mass of the earth and R is the radius of the earth. 10. The value of 'g' on the surface of the earth is 9.8 m s–2. 11. The value of 'g' on the surface of the moon = 1/6 times value of 'g' on the surface of the earth. 12. The value of 'g' decreases with height and depth from surface of the earth. 13. The value of 'g' at poles is more than at equator. 14. The value of 'g' is zero at the centre of the earth. 15. Mass is the quantity of matter contained in a body. 16. In S.I. unit of mass is kg. 17. Weight of a body is the force with which the earth attracts the body. Weight of body always acts at its centre of gravity and in the downward direction, W = mg. 18. In S.I., unit of weight is newton (N). 19. Mass of a body does not change but weight of a body is different at different places.

1. The force of attraction between two bodies in the universe is known as gravitational force. 2. Gravitational force between two bodies of masses m1 and m2 separated by a distance r is given by F = 3. G = 6.673 × 10–11 Nm2 kg–2 is gravitational constant. 4. Gravitational force is large if masses of two bodies are very large. 5. Gravitational force of the earth on a body is known as gravity. 6. The fall of a body is known as free fall if it falls only under the action of gravitational force of earth in the absence of air resistance. 7. Acceleration with which a body falls towards the earth, the gravitational force of the earth is called acceleration due to gravity. It is denoted by 'g'. 8. In S.I., unit of 'g' is m s–2. 9. g=, where M is the mass of the earth and R is the radius of the earth. 10. The value of 'g' on the surface of the earth is 9.8 m s–2. 11. The value of 'g' on the surface of the moon = 1/6 times value of 'g' on the surface of the earth. 12. The value of 'g' decreases with height and depth from surface of the earth. 13. The value of 'g' at poles is more than at equator. 14. The value of 'g' is zero at the centre of the earth. 15. Mass is the quantity of matter contained in a body. 16. In S.I. unit of mass is kg. 17. Weight of a body is the force with which the earth attracts the body. Weight of body always acts at its centre of gravity and in the downward direction, W = mg. 18. In S.I., unit of weight is newton (N). 19. Mass of a body does not change but weight of a body is different at different places.

1. Sound : Sound is a form of energy which produces a sensation of hearing in our ears. 2. Source of sound and its propagation : A source of vibration motion of an object is normally a source of sound. 3. Characteristics of the medium required for the propagation of sound: (i) Medium must be elastic so that the medium particles have the tendency to return back to their original positions after the displacement. (ii) Medium must have the inertia so that its particles have the capacity to store the energy. The frictional resistance of the medium should be negligible to minimise the loss of energy in propagation. 4. Types of waves (i) Mechanical waves : A mechanical wave is a periodic disturbance which requires a material medium for its propagation. On the basis of motion of particles the mechanical waves are classified into two parts. (a) Transverse wave (b) Longitudinal wave (a) Transverse wave : When the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave, the wave is known as the transverse wave. For example, waves produced in a stretched string. (b) Longitudinal wave : When the particles of the medium vibrate along the direction of propagation of the wave then the wave is known as the longitudinal wave. For example sound wave in air. (ii) Electromagnetic waves : The waves which do not require medium for propagation are called electromagnetic waves these waves can travel through vacuum also. For example, light waves, X-rays. 5. Characteristics of a sound wave Frequency : The number of vibrations per second is called frequency. The unit of frequency is hertz (ii) Amplitude: The maximum displacement of each particle from its mean position is called amplitude. The S.I. unit of amplitude is metre (m). (iii) Time period: The time taken to complete one vibration is called time period. Frequency= 1/(Time period) or v = 1/T (iv) Wavelength: The distance between two nearest (adjacent) crests or troughs of a wave is called its wavelength. (v) Velocity of wave: The distance travelled by a wave in one second is called velocity of the wave (or speed of the wave). The S.I. unit for the velocity of a wave is metres per second (m/s or ms-1). (vi) Pitch : Pitch is the sensation (brain interpretation) of the frequency of an emitted sound and is the characteristic which distinguishes a shrill (or sharp) sound from a grave (or flat) sound. (vii) Loudness : It is a measure of the sound energy reaching the ear per second. 6. Reflection of sound : When sound waves strike a surface, they return back into the same medium. This phenomenon is called reflection. 7. Laws of reflection : Angle of incidence is equal the angle of reflection. The incident wave, the reflected wave and the normal all lie in the same plane. 8. Echo : Phenomenon of hearing back our own sound is called an echo. It is due to successive reflection from the surfaces obstacles of large size. 9. Relation between speed of sound, time of hearing echo and distance of reflection body :Ift is the time at which an echo is heard, d is the distance between the source of sound and the reflecting body and v is the speed of sound. The total distance travelled by the sound is 2d. speed of sound, v = 2d/t or d = vt/2 10. Conditions for the formation of Echoes (i) The minimum distance between the source of sound and the reflecting body should be 17.2 metres. (ii) The wavelength of sound should be less than the height of the reflecting body. (iii) The intensity of sound should be sufficient so that it can be heard after reflection. 11. Reverberation : Persistence of sound after its production is stopped, is called reverberation. A short reverberation is desirable in a concert hall (where music is being played) because it gives ‘life’ to sound. Too much reverberation confuses the programmers and must be reduced to reduce reverberation. 12. Range of Hearing : The audible range of sound for human beings extends from about 20 Hz to 20,000 Hz (one Hz = one cycle/s). Sounds of frequencies below 20 Hz are called infrasonic sound or infrasound. Frequencies higher than 20 kHz are called ultrasonic sound or ultra sound. Ultrasound is produced by dolphins. 13. Applications of ultrasound : The ultrasound is commonly used for medical diagnosis and therapy, and also as a surgical tool. It is also used in a wide variety of industrial applications and processes. Some creatures use ultrasound for information exchange and for the detection and location of objects. Also some bats and porpoises are found to use ultrasound for navi gation and to locate food in darkness or at a place where there is inadequate light for vision (method of search is called echolocation). 14. Sonar : SONAR means Sound Navigation Rang-ing. In this sound waves (ultrasonic) are used [microwaves are absorbed by water)]. Sound waves are emitted by a source. These waves travel in water with velocity v. The waves re-flected by targets (like submarine bottom sea) are detected. Uses (i) The SONAR system is used for detecting the presence of unseen underwater objects, such as a submerged submarine, a sunken ship, sea rock or a hidden iceberg, and locating them accurately. (ii) The principle of SONAR is also used in industry of detection of flaws in metal blocks or sheets without damaging them. 15. Human ear : It is a highly sensitive part of the human body which enables us to hear a sound. It converts the pressure variations in air with audiable frequencies into electric signals which travel to the brain via the auditory nerve. The human ear has three main parts. Their auditory functions are as follows: (i) Outer ear : The outer ear is called `pinna’. It collects the sound from the suri-ounding. The collected sound passes through the auditory canal. At the end of the auditory canal there is a thin membrane called the ear drum or tympanic membrane. When compression of the medium produced due to vibration of the object reaches the ear drum, the pressure on the outside of the membrane increases and forces the eardrum inward. Similarly, the eardrum moves outward when a rarefaction reaches. In this way the ear drum vibrates. (ii) Middle ear: The vibrations are amplified several times by three bones (the hammer, anvil and stirrup) in the middle ear which act as levers. The middle ear transmits the amplified pressure variations received from the sound wave to the inner ear. (iii) Inner ear: In the inner ear, the pressure variations are turned into electrical signals by the cochlea. These electrical signals are sent to the brain via the auditory nerve, and the brain interprets them as sound.

1. Sound : Sound is a form of energy which produces a sensation of hearing in our ears. 2. Source of sound and its propagation : A source of vibration motion of an object is normally a source of sound. 3. Characteristics of the medium required for the propagation of sound: (i) Medium must be elastic so that the medium particles have the tendency to return back to their original positions after the displacement. (ii) Medium must have the inertia so that its particles have the capacity to store the energy. The frictional resistance of the medium should be negligible to minimise the loss of energy in propagation. 4. Types of waves (i) Mechanical waves : A mechanical wave is a periodic disturbance which requires a material medium for its propagation. On the basis of motion of particles the mechanical waves are classified into two parts. (a) Transverse wave (b) Longitudinal wave (a) Transverse wave : When the particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave, the wave is known as the transverse wave. For example, waves produced in a stretched string. (b) Longitudinal wave : When the particles of the medium vibrate along the direction of propagation of the wave then the wave is known as the longitudinal wave. For example sound wave in air. (ii) Electromagnetic waves : The waves which do not require medium for propagation are called electromagnetic waves these waves can travel through vacuum also. For example, light waves, X-rays. 5. Characteristics of a sound wave Frequency : The number of vibrations per second is called frequency. The unit of frequency is hertz (ii) Amplitude: The maximum displacement of each particle from its mean position is called amplitude. The S.I. unit of amplitude is metre (m). (iii) Time period: The time taken to complete one vibration is called time period. Frequency= 1/(Time period) or v = 1/T (iv) Wavelength: The distance between two nearest (adjacent) crests or troughs of a wave is called its wavelength. (v) Velocity of wave: The distance travelled by a wave in one second is called velocity of the wave (or speed of the wave). The S.I. unit for the velocity of a wave is metres per second (m/s or ms-1). (vi) Pitch : Pitch is the sensation (brain interpretation) of the frequency of an emitted sound and is the characteristic which distinguishes a shrill (or sharp) sound from a grave (or flat) sound. (vii) Loudness : It is a measure of the sound energy reaching the ear per second. 6. Reflection of sound : When sound waves strike a surface, they return back into the same medium. This phenomenon is called reflection. 7. Laws of reflection : Angle of incidence is equal the angle of reflection. The incident wave, the reflected wave and the normal all lie in the same plane. 8. Echo : Phenomenon of hearing back our own sound is called an echo. It is due to successive reflection from the surfaces obstacles of large size. 9. Relation between speed of sound, time of hearing echo and distance of reflection body :Ift is the time at which an echo is heard, d is the distance between the source of sound and the reflecting body and v is the speed of sound. The total distance travelled by the sound is 2d. speed of sound, v = 2d/t or d = vt/2 10. Conditions for the formation of Echoes (i) The minimum distance between the source of sound and the reflecting body should be 17.2 metres. (ii) The wavelength of sound should be less than the height of the reflecting body. (iii) The intensity of sound should be sufficient so that it can be heard after reflection. 11. Reverberation : Persistence of sound after its production is stopped, is called reverberation. A short reverberation is desirable in a concert hall (where music is being played) because it gives ‘life’ to sound. Too much reverberation confuses the programmers and must be reduced to reduce reverberation. 12. Range of Hearing : The audible range of sound for human beings extends from about 20 Hz to 20,000 Hz (one Hz = one cycle/s). Sounds of frequencies below 20 Hz are called infrasonic sound or infrasound. Frequencies higher than 20 kHz are called ultrasonic sound or ultra sound. Ultrasound is produced by dolphins. 13. Applications of ultrasound : The ultrasound is commonly used for medical diagnosis and therapy, and also as a surgical tool. It is also used in a wide variety of industrial applications and processes. Some creatures use ultrasound for information exchange and for the detection and location of objects. Also some bats and porpoises are found to use ultrasound for navi gation and to locate food in darkness or at a place where there is inadequate light for vision (method of search is called echolocation). 14. Sonar : SONAR means Sound Navigation Rang-ing. In this sound waves (ultrasonic) are used [microwaves are absorbed by water)]. Sound waves are emitted by a source. These waves travel in water with velocity v. The waves re-flected by targets (like submarine bottom sea) are detected. Uses (i) The SONAR system is used for detecting the presence of unseen underwater objects, such as a submerged submarine, a sunken ship, sea rock or a hidden iceberg, and locating them accurately. (ii) The principle of SONAR is also used in industry of detection of flaws in metal blocks or sheets without damaging them. 15. Human ear : It is a highly sensitive part of the human body which enables us to hear a sound. It converts the pressure variations in air with audiable frequencies into electric signals which travel to the brain via the auditory nerve. The human ear has three main parts. Their auditory functions are as follows: (i) Outer ear : The outer ear is called `pinna’. It collects the sound from the suri-ounding. The collected sound passes through the auditory canal. At the end of the auditory canal there is a thin membrane called the ear drum or tympanic membrane. When compression of the medium produced due to vibration of the object reaches the ear drum, the pressure on the outside of the membrane increases and forces the eardrum inward. Similarly, the eardrum moves outward when a rarefaction reaches. In this way the ear drum vibrates. (ii) Middle ear: The vibrations are amplified several times by three bones (the hammer, anvil and stirrup) in the middle ear which act as levers. The middle ear transmits the amplified pressure variations received from the sound wave to the inner ear. (iii) Inner ear: In the inner ear, the pressure variations are turned into electrical signals by the cochlea. These electrical signals are sent to the brain via the auditory nerve, and the brain interprets them as sound.

Electric current : An electric current is defined as the amount of charge flowing through any cross-section of a conductor per unit time, I = . Electric current is a scalar quantity.  Electric current in terms of number of electrons (n) in a conductor, I = , e = charge on an electron = –1.6 × 10–19 C.  In a metallic wire or conductor, the flow of electric current is due to the flow of electrons from one end to the other end of the wire.  Charge carrier in a metallic wire are conduction elements.  6.25 × 1018 electrons make one coulomb of charge.  S.I. unit of electric current is ampere (A).  Ampere (A) : Electric current through a conductor is said to be 1 ampere if one coulomb charge flows through any cross-section of the conductor in one second.  Ammeter is used to measure electric current.  Ammeter is always connected in series in an electric circuit.  Electric potential is defined as work done per unit charge. V =  Electric potential is a scalar quantity.  Electric potential difference is defined as the work done in moving a unit positive charge from one point to another point. dV =  SI unit of electric potential is volt (V).  Voltmeter is used to measure the potential difference between two points in an electric circuit.  Voltmeter is always connected in parallel in an electric circuit.  Ohm's Law : This law states that, "the electric current flowing in a conductor is directly proportional to the potential difference across the ends of the conductor, provided the temperature and other physical conditions of the conductor remain the same".  Resistance (R) : Resistance of a conductor is the ability of the conductor to oppose the flow of charge through it.  Unit of resistance is ohm.  1 Ohm : Resistance of a conductor is said to be 1 ohm if a potential difference of 1 volt across the ends of the conductor produces a current of 1 ampere through it. Resistor is a component (say a metallic wire) in an electric circuit which offers resistance to the flow of electrons constituting the electric current in the electric circuit.  Law of Resistance : (i) Resistance of a conductor depends upon the nature of the material of the conductor. (ii) Resistance of a conductor is directly proportional to the length of the conductor. (iii) Resistance of a conductor is inversely proportional to the each of cross-section of the conductor. (iv) Resistance of metallic conductor increases with the increase of temperature and decreases with the decrease of the temperature.  R =  Resistivity or Specific Resistance () : Resistivity is defined as the resistance of the conductor of unit length and unit area of cross-section.  Unit of Resistivity : In CGS system, unit if resistivity is ohm-cm. In SI system, unit of resistivity is ohm-metre.  Two or more resistors are said to be connected in series if same amount of current flows through these resistors.  The effective resistance of series combination of resistors is the algebraic sum of the individual resistances of the resistors in the combination.  An electric bulb or a heater or a metallic wire acts as a resistor.  If one of the electric bulbs connected in a series is fused, then no electric bulb will glow inspite of the fact that the combination is connected with a source of electric current.  Two or more resistors are said to be connected in parallel if the potential difference across each resistor is equal to the applied potential difference across the combination of the resistors.  The effective resistance of the resistors connected in parallel is less than the minimum resistance of a resistor in the combination.  Resistors are connected in series if the resistance of the electric circuit is to be increased.  Resistors are connected in parallel if the resistance of the electric circuit is to be decreased.  Joule's Law of Heating : The amount of heat produced in a conductor is (i) Directly proportional to the square of the electric current flowing through it. (ii) Directly proportional to the resistance of the conductor. (iii) Directly proportional to the time for which the electric current flows through the conductor. H = I2Rt (joule)  Electric fuse is a safety device used to save the electric appliances from burning.  Electric fuse is a wire made of a material having low melting point.  Electric fuse wire is made of copper or tin-lead alloy.  Electric energy : The work done by a source of electricity to maintain a current in an electric circuit is known as electric energy. E = VIt  Electric power : Electric power is defined as the amount of electric work done in one second. P = VI = I2R = V2 / R  SI unit of power is watt.  Practical unit of power is horse power (h.p.) 1 h.p. = 746 W  Electric energy = Electric power × time  Commercial unit of Energy : kilowatt-hour (kWh)  1 kWh = 3.6 × 106 J

Electric current : An electric current is defined as the amount of charge flowing through any cross-section of a conductor per unit time, I = . Electric current is a scalar quantity.  Electric current in terms of number of electrons (n) in a conductor, I = , e = charge on an electron = –1.6 × 10–19 C.  In a metallic wire or conductor, the flow of electric current is due to the flow of electrons from one end to the other end of the wire.  Charge carrier in a metallic wire are conduction elements.  6.25 × 1018 electrons make one coulomb of charge.  S.I. unit of electric current is ampere (A).  Ampere (A) : Electric current through a conductor is said to be 1 ampere if one coulomb charge flows through any cross-section of the conductor in one second.  Ammeter is used to measure electric current.  Ammeter is always connected in series in an electric circuit.  Electric potential is defined as work done per unit charge. V =  Electric potential is a scalar quantity.  Electric potential difference is defined as the work done in moving a unit positive charge from one point to another point. dV =  SI unit of electric potential is volt (V).  Voltmeter is used to measure the potential difference between two points in an electric circuit.  Voltmeter is always connected in parallel in an electric circuit.  Ohm's Law : This law states that, "the electric current flowing in a conductor is directly proportional to the potential difference across the ends of the conductor, provided the temperature and other physical conditions of the conductor remain the same".  Resistance (R) : Resistance of a conductor is the ability of the conductor to oppose the flow of charge through it.  Unit of resistance is ohm.  1 Ohm : Resistance of a conductor is said to be 1 ohm if a potential difference of 1 volt across the ends of the conductor produces a current of 1 ampere through it. Resistor is a component (say a metallic wire) in an electric circuit which offers resistance to the flow of electrons constituting the electric current in the electric circuit.  Law of Resistance : (i) Resistance of a conductor depends upon the nature of the material of the conductor. (ii) Resistance of a conductor is directly proportional to the length of the conductor. (iii) Resistance of a conductor is inversely proportional to the each of cross-section of the conductor. (iv) Resistance of metallic conductor increases with the increase of temperature and decreases with the decrease of the temperature.  R =  Resistivity or Specific Resistance () : Resistivity is defined as the resistance of the conductor of unit length and unit area of cross-section.  Unit of Resistivity : In CGS system, unit if resistivity is ohm-cm. In SI system, unit of resistivity is ohm-metre.  Two or more resistors are said to be connected in series if same amount of current flows through these resistors.  The effective resistance of series combination of resistors is the algebraic sum of the individual resistances of the resistors in the combination.  An electric bulb or a heater or a metallic wire acts as a resistor.  If one of the electric bulbs connected in a series is fused, then no electric bulb will glow inspite of the fact that the combination is connected with a source of electric current.  Two or more resistors are said to be connected in parallel if the potential difference across each resistor is equal to the applied potential difference across the combination of the resistors.  The effective resistance of the resistors connected in parallel is less than the minimum resistance of a resistor in the combination.  Resistors are connected in series if the resistance of the electric circuit is to be increased.  Resistors are connected in parallel if the resistance of the electric circuit is to be decreased.  Joule's Law of Heating : The amount of heat produced in a conductor is (i) Directly proportional to the square of the electric current flowing through it. (ii) Directly proportional to the resistance of the conductor. (iii) Directly proportional to the time for which the electric current flows through the conductor. H = I2Rt (joule)  Electric fuse is a safety device used to save the electric appliances from burning.  Electric fuse is a wire made of a material having low melting point.  Electric fuse wire is made of copper or tin-lead alloy.  Electric energy : The work done by a source of electricity to maintain a current in an electric circuit is known as electric energy. E = VIt  Electric power : Electric power is defined as the amount of electric work done in one second. P = VI = I2R = V2 / R  SI unit of power is watt.  Practical unit of power is horse power (h.p.) 1 h.p. = 746 W  Electric energy = Electric power × time  Commercial unit of Energy : kilowatt-hour (kWh)  1 kWh = 3.6 × 106 J

Electric current : An electric current is defined as the amount of charge flowing through any cross-section of a conductor per unit time, I = . Electric current is a scalar quantity.  Electric current in terms of number of electrons (n) in a conductor, I = , e = charge on an electron = –1.6 × 10–19 C.  In a metallic wire or conductor, the flow of electric current is due to the flow of electrons from one end to the other end of the wire.  Charge carrier in a metallic wire are conduction elements.  6.25 × 1018 electrons make one coulomb of charge.  S.I. unit of electric current is ampere (A).  Ampere (A) : Electric current through a conductor is said to be 1 ampere if one coulomb charge flows through any cross-section of the conductor in one second.  Ammeter is used to measure electric current.  Ammeter is always connected in series in an electric circuit.  Electric potential is defined as work done per unit charge. V =  Electric potential is a scalar quantity.  Electric potential difference is defined as the work done in moving a unit positive charge from one point to another point. dV =  SI unit of electric potential is volt (V).  Voltmeter is used to measure the potential difference between two points in an electric circuit.  Voltmeter is always connected in parallel in an electric circuit.  Ohm's Law : This law states that, "the electric current flowing in a conductor is directly proportional to the potential difference across the ends of the conductor, provided the temperature and other physical conditions of the conductor remain the same".  Resistance (R) : Resistance of a conductor is the ability of the conductor to oppose the flow of charge through it.  Unit of resistance is ohm.  1 Ohm : Resistance of a conductor is said to be 1 ohm if a potential difference of 1 volt across the ends of the conductor produces a current of 1 ampere through it. Resistor is a component (say a metallic wire) in an electric circuit which offers resistance to the flow of electrons constituting the electric current in the electric circuit.  Law of Resistance : (i) Resistance of a conductor depends upon the nature of the material of the conductor. (ii) Resistance of a conductor is directly proportional to the length of the conductor. (iii) Resistance of a conductor is inversely proportional to the each of cross-section of the conductor. (iv) Resistance of metallic conductor increases with the increase of temperature and decreases with the decrease of the temperature.  R =  Resistivity or Specific Resistance () : Resistivity is defined as the resistance of the conductor of unit length and unit area of cross-section.  Unit of Resistivity : In CGS system, unit if resistivity is ohm-cm. In SI system, unit of resistivity is ohm-metre.  Two or more resistors are said to be connected in series if same amount of current flows through these resistors.  The effective resistance of series combination of resistors is the algebraic sum of the individual resistances of the resistors in the combination.  An electric bulb or a heater or a metallic wire acts as a resistor.  If one of the electric bulbs connected in a series is fused, then no electric bulb will glow inspite of the fact that the combination is connected with a source of electric current.  Two or more resistors are said to be connected in parallel if the potential difference across each resistor is equal to the applied potential difference across the combination of the resistors.  The effective resistance of the resistors connected in parallel is less than the minimum resistance of a resistor in the combination.  Resistors are connected in series if the resistance of the electric circuit is to be increased.  Resistors are connected in parallel if the resistance of the electric circuit is to be decreased.  Joule's Law of Heating : The amount of heat produced in a conductor is (i) Directly proportional to the square of the electric current flowing through it. (ii) Directly proportional to the resistance of the conductor. (iii) Directly proportional to the time for which the electric current flows through the conductor. H = I2Rt (joule)  Electric fuse is a safety device used to save the electric appliances from burning.  Electric fuse is a wire made of a material having low melting point.  Electric fuse wire is made of copper or tin-lead alloy.  Electric energy : The work done by a source of electricity to maintain a current in an electric circuit is known as electric energy. E = VIt  Electric power : Electric power is defined as the amount of electric work done in one second. P = VI = I2R = V2 / R  SI unit of power is watt.  Practical unit of power is horse power (h.p.) 1 h.p. = 746 W  Electric energy = Electric power × time  Commercial unit of Energy : kilowatt-hour (kWh)  1 kWh = 3.6 × 106 J

 Hans Christian oersted discovered a relationship between electricity and magnetism.  A current carrying wire behaves as a magnet.  When a current passes through a wire, a magnetic field is set up around the wire. This effect of current is called magnetic effect of current.  Like magnetic poles repel each other and unlike magnetic poles attract each other.  Magnetic field is space or region around a current carrying wire or a magnet within which its influence is felt by another magnet.  Magnetic field line : The path along which a free unit north pole moves in a magnetic field is called magnetic field line. The tangent at any point on a magnetic field line gives the direction of the magnetic field at that point.  Two magnetic field lines can't intersect or cross each other.  Magnetic field lines are crowded in a region of strong magnetic field.  Magnetic field lines are far apart in a region of weak magnetic field.  When current passes through a straight wire or conductor, a magnetic field is set up around the wire or conductor.  Magnetic field around a current carrying wire or conductor is represented by concentric circles centred at the wire or the conductor.  The direction of magnetic field around the current carrying conductor is determined by Right Hand Thumb Rule.  Magnetic field around a current carrying wire increases with the increase in the current passing through the wire.  Magnetic field around a current carrying wire or conductor is represented by concentric circles centred at the wire or the conductor.  The direction of magnetic field around the current carrying conductor is determined by Right Hand Thumb Rule.  Magnetic field around a current carrying wire increases with the increase in the current passing through the wire.  Magnetic field around a current carrying wire decreases as we go away from the wire.  Magnetic field due to a very long wire like a power transmission line carrying current I and at a distance r from the wire is given by B = ; where, µ0 = 4 × 10–7 TmA–1  Two parallel wires or conductors carrying current in the same directs attract each other.  Two parallel wires or conductors carrying current in the opposite directions repel each other.  The magnetic field around a straight current carrying conductor or wire can be increased by bending it into a circular loop.  The strength of magnetic field produced at the centre of a circular loop of a wire is (i) directly proportional to the amount of current passing through the loop of the wire. (ii) directly proportional to the number of turns of the circular loop of the wire. (iii) inversely proportional to the radius of the circular loop of the wire.  Magnetic field produced by a current carrying circular wire or loop decreases on both sides along the axis of the circular wire.  A solenoid is a coil of many turns of an insulated copper wire closely wound in the shape of a tight spring.  Magnetic field inside a current carrying solenoid is uniform magnetic field.  A solenoid carrying current behaves like a bar magnet.  A soft iron rod placed in a current carrying solenoid is known as electromagnet.  A current carrying conductor placed perpendicular to the magnetic field experience a force.  The force acting on a current carrying conductor placed perpendicular to the magnetic field B is given by F = BIl  Direction of force experienced by a current carrying conductor placed in a magnetic field is determined by Fleming’s Left Hand Rule.  No Force acts on a current carrying conductor when placed parallel to the magnetic field.  SI unit of magnetic field is tesla (T).  Force acts on a charge moving perpendicular to the magnetic field. This force is called Lorentz force.  Force acting on a charge Q moving with velocity v perpendicular to the magnetic field B is given by F = BQV  No force acts on a charge moving parallel to the magnetic field B.  Direction of force experienced by a moving charge in a magnetic field is determined by Right Hand Rule.  Electric motor is a device which converts electrical energy into mechanical energy.  Principle of electric motor : Electric motor works on the principle that a current carrying conductor placed perpendicular to a magnetic field experiences a force.  The phenomenon of producing induced current in a closed circuit due to the change in magnetic field in the circuit is known as electromagnetic induction.  More induced current flows through a closed coil if a bar magnet is brought towards or away from the coil with large speed.  No induced current flows through a closed coil if magnetic field linked with it does not change.  Direction of induced current in a conductor is determined by Fleming’s Right hand rule.  Direct current is an electric current whose magnitude is either constant or variable but the direction of flow in a conductor remains the same.  Frequency of direct current is zero.  Alternating current is an electric current whose magnitude changes with time and direction reverse periodically.  In India, frequency of A.C. is 50 Hz.  A.C. is more dangerous than D.C.  Electric generator is a device used to convert mechanical energy into electrical energy.  Electric generator works on the principle of electromagnetic induction.  To supply electric power from one place to another place, three wires known as phase wire (or live wire), neutral wire and earth wire are used.  The potential difference between the live wire and neutral wire in a household supply of electric power is 220 V.  Current rating of a fuse is the maximum amount of electric current that can be passed through the fuse wire without melting it.  Current rating of a fuse wire in a circuit having bulbs and tubes is 5A.  Current rating of a fuse wire in a circuit having heating appliances is 15A.  Electric fuse is a safety device used to save the electrical appliances from burning when large current flows in the circuit.  Electric fuse is made of a material of low melting point.  Material used for making a fuse wire is made of copper / aluminium / tin-lead alloy.  Short Circuiting : When live wire and neutral wire come in direct contact, the resistance of the circuit becomes very small. Hence huge current flows through the circuit. This huge current produces large amount of heat in the circuit and the circuit catches fire. This is known as short circuiting.

 Hans Christian oersted discovered a relationship between electricity and magnetism.  A current carrying wire behaves as a magnet.  When a current passes through a wire, a magnetic field is set up around the wire. This effect of current is called magnetic effect of current.  Like magnetic poles repel each other and unlike magnetic poles attract each other.  Magnetic field is space or region around a current carrying wire or a magnet within which its influence is felt by another magnet.  Magnetic field line : The path along which a free unit north pole moves in a magnetic field is called magnetic field line. The tangent at any point on a magnetic field line gives the direction of the magnetic field at that point.  Two magnetic field lines can't intersect or cross each other.  Magnetic field lines are crowded in a region of strong magnetic field.  Magnetic field lines are far apart in a region of weak magnetic field.  When current passes through a straight wire or conductor, a magnetic field is set up around the wire or conductor.  Magnetic field around a current carrying wire or conductor is represented by concentric circles centred at the wire or the conductor.  The direction of magnetic field around the current carrying conductor is determined by Right Hand Thumb Rule.  Magnetic field around a current carrying wire increases with the increase in the current passing through the wire.  Magnetic field around a current carrying wire or conductor is represented by concentric circles centred at the wire or the conductor.  The direction of magnetic field around the current carrying conductor is determined by Right Hand Thumb Rule.  Magnetic field around a current carrying wire increases with the increase in the current passing through the wire.  Magnetic field around a current carrying wire decreases as we go away from the wire.  Magnetic field due to a very long wire like a power transmission line carrying current I and at a distance r from the wire is given by B = ; where, µ0 = 4 × 10–7 TmA–1  Two parallel wires or conductors carrying current in the same directs attract each other.  Two parallel wires or conductors carrying current in the opposite directions repel each other.  The magnetic field around a straight current carrying conductor or wire can be increased by bending it into a circular loop.  The strength of magnetic field produced at the centre of a circular loop of a wire is (i) directly proportional to the amount of current passing through the loop of the wire. (ii) directly proportional to the number of turns of the circular loop of the wire. (iii) inversely proportional to the radius of the circular loop of the wire.  Magnetic field produced by a current carrying circular wire or loop decreases on both sides along the axis of the circular wire.  A solenoid is a coil of many turns of an insulated copper wire closely wound in the shape of a tight spring.  Magnetic field inside a current carrying solenoid is uniform magnetic field.  A solenoid carrying current behaves like a bar magnet.  A soft iron rod placed in a current carrying solenoid is known as electromagnet.  A current carrying conductor placed perpendicular to the magnetic field experience a force.  The force acting on a current carrying conductor placed perpendicular to the magnetic field B is given by F = BIl  Direction of force experienced by a current carrying conductor placed in a magnetic field is determined by Fleming’s Left Hand Rule.  No Force acts on a current carrying conductor when placed parallel to the magnetic field.  SI unit of magnetic field is tesla (T).  Force acts on a charge moving perpendicular to the magnetic field. This force is called Lorentz force.  Force acting on a charge Q moving with velocity v perpendicular to the magnetic field B is given by F = BQV  No force acts on a charge moving parallel to the magnetic field B.  Direction of force experienced by a moving charge in a magnetic field is determined by Right Hand Rule.  Electric motor is a device which converts electrical energy into mechanical energy.  Principle of electric motor : Electric motor works on the principle that a current carrying conductor placed perpendicular to a magnetic field experiences a force.  The phenomenon of producing induced current in a closed circuit due to the change in magnetic field in the circuit is known as electromagnetic induction.  More induced current flows through a closed coil if a bar magnet is brought towards or away from the coil with large speed.  No induced current flows through a closed coil if magnetic field linked with it does not change.  Direction of induced current in a conductor is determined by Fleming’s Right hand rule.  Direct current is an electric current whose magnitude is either constant or variable but the direction of flow in a conductor remains the same.  Frequency of direct current is zero.  Alternating current is an electric current whose magnitude changes with time and direction reverse periodically.  In India, frequency of A.C. is 50 Hz.  A.C. is more dangerous than D.C.  Electric generator is a device used to convert mechanical energy into electrical energy.  Electric generator works on the principle of electromagnetic induction.  To supply electric power from one place to another place, three wires known as phase wire (or live wire), neutral wire and earth wire are used.  The potential difference between the live wire and neutral wire in a household supply of electric power is 220 V.  Current rating of a fuse is the maximum amount of electric current that can be passed through the fuse wire without melting it.  Current rating of a fuse wire in a circuit having bulbs and tubes is 5A.  Current rating of a fuse wire in a circuit having heating appliances is 15A.  Electric fuse is a safety device used to save the electrical appliances from burning when large current flows in the circuit.  Electric fuse is made of a material of low melting point.  Material used for making a fuse wire is made of copper / aluminium / tin-lead alloy.  Short Circuiting : When live wire and neutral wire come in direct contact, the resistance of the circuit becomes very small. Hence huge current flows through the circuit. This huge current produces large amount of heat in the circuit and the circuit catches fire. This is known as short circuiting.

 Energy is the essential requirement for each and every activity in our life.  The various sources of energy are the sun, the wind, water, fossil fuels etc.  The sun is the ultimate source of all forms of energy.  A good source of energy is one which supplies large amount of useful energy, easily available, economical and cause minimum environmental pollution. .  Thermal power plant generates electricity by burning fossil fuel like coal and oil.  LPG is a petroleum gas liquefied under pressure. Its full form is liquefied Petroleum Gas.  CNG is compressed Natural Gas.  Main constituents of CNG is methane.  Electricity produced by flowing water is known as hydro - electric power.  A plant used to produce hydro -electric power is known as hydro -electric power plant.  Potential energy of water stored in a dam is converted into kinetic energy of the falling water. This kinetic energy of falling water is converted into the kinetic energy of the armature of the generator which in turn is converted into electric energy.  Biomass is material which contains carbon and other combustible material.  Plants, wood animals and plants waster are the examples of biomass.  Gobar gas or bio-gas is the example of a bio - mass energy source.  Main constituent of a biogas or gobar gas is a methane gas.  Biogas plant is of two types: (a) Fixed-dome type, (b) Floating gas holder type.  Kinetic energy of wind is known as wind energy.  Wind energy is used to produce electricity.  The region where large number of wind mills are erected to produce electricity is called wind energy farm.  The minimum speed of wind to operate generator to produce electricity is about 15 km/h.  Constant and rapid use of conventional sources of energy would ultimately exhaust these sources and hence a need for tapping energy from alternate or non-conventional sources of energy is seriously felt.  Solar energy is the energy emitted by the sun in the form of heat and light.  Solar constant is defined as the energy received from the sun in one second by a unit square metre area of the outer edge of earth's atmosphere exposed perpendicular to the radiation of the sun at an average distance between the sun and the earth.  Value of solar constant = 1.4 k W/m2.  Solar devices like solar cooker, solar furnace, solar water heater, solar panels and solar cells are used to harness solar energy.  Water due to its high specific heat capacity (4200 J kg–1°C–1) is a store house of heat energy.  Energy from sea or ocean water is available in the form of (i) energy of sea waves (ii) Tidal energy and (iii) Ocean thermal energy (OTE).  The heat energy obtained from the conversion of nuclear mass is known as nuclear energy.  Nuclear energy is obtained by two processes known as nuclear fission and nuclear fusion.  Nuclear energy is expressed in electron - volt(eV) 1 eV = 1.6  10–19J 1 MeV = 106 eV = 1.6 –13J  Nuclear Fission is the process of splitting a heavy nucleus (say Uranium) into two comparatively lower nuclei along with the release of large amount energy when bombarded with thermal neutron.  Nuclear reactor is a device used to carry out controlled chain reaction.  Nuclear fusion is the process of fusing or combining together two small nuclei to form a comparatively big nucleus with the release of large energy.  Nuclear fusion reactions occur at very high temperature (107K).  Nuclear fusion reactions occurring in the interior of the sun are responsible for the energy of the sun. In other words, nuclear fusion reactions are the sources of energy of the sun.  Sources of energy are classified into two categories (i) conventional or non-renewable sources of energy and (ii) Non-conventional or renewable sources of energy.  Extraction and transportation of energy from various sources of energy cause environmental pollution.  The energy from various sources of energy must be used effectively to conserve energy.

 Light is a form of energy which produces the sensation of sight.  Speed of light in vacuum / air = 3 × 108 ms–1  Ray of light : A line drawn in the direction of propagation of light is called ray of light.  Beam of light : A group of parallel rays light emitted by a source of light is called beam of light.  Reflection of light : The phenomenon of returning of light in the same medium after striking a surface is called reflection of light.  Laws of reflection : The reflection of light from a surface obeys certain laws called laws of reflection. (i) incident angle is equal to reflected angle i.e. i = r. (ii) Incident ray, reflected ray and normal to the reflecting surface at the point on incident lie in the same plane.  Concave mirror : concave mirror is a part of a hollow sphere whose outer part is silvered and the inner part is reflecting surface.  Convex mirror : convex mirror is a part of a hollow sphere whose outer part is reflecting surface and inner part is silvered.  Centre of curvature : The centre of a hollow sphere of which the spherical mirror forms a part is called centre of curvature. It is denoted by C  Radius of curvature : The radius of a hollow sphere of which the spherical mirror forms a part is called radius of curvature. It is denoted by R  Pole : The mid point of a spherical mirror is called its pole. It is denoted by P  Aperture: The part of spherical mirror exposed to the incident light is called the aperture of the mirror.  Principal Axis: A line joining the centre of curvature (C) and pole (P) of a spherical mirror and extend on either side is called principal axis of the spherical mirror.  Principal Focus : A point on the principal axis of a spherical mirror where the rays of light parallel to the principal axis meet or appears to meet after reflection from the spherical mirror is called principal focus. It is denoted by F.  Focal Plane : A plane normal or perpendicular to the principal axis and passing through the principal focus (F) of the spherical mirror is called focal plane of the spherical mirror.  Focal length (f): The distance between the pole (P) and the principal focus (F) of a spherical mirror is called the focal length of the spherical mirror.  f = , Where R is the radius of the curvature of the mirror.  Focal length and radius of curvature of a concave mirror are negative.  Focal length and radius of curvature of a convex mirror are positive.  Sign Conventions for reflection by spherical mirrors (1) All distance are measured from the pole of a spherical mirror. (2) Distance measured in the direction of incident light are taken as positive. Distance measured in the direction opposite to that of the incident light are taken negative. (3) The upward distance perpendicular to the principal axis are taken as positive, while the downward distance perpendicular to the principal axis are taken as negative.  Radius of curvature plane mirror =  ( infinite)  Focal length of a plane mirror =   Mirror Formula : The relation between u, v, and focal length (f) of a spherical mirror is known as mirror formula. That is  Linear magnification : Linear magnification produced by a mirror is defined as the ratio of the size ( or height) of the image to the size of the object . It is denoted by m. That is  Power of mirror (P) = =  Linear magnification produced by a plane mirror = + 1.  Refraction of light: The bending of light rays when they pass obsessively from one medium to the other medium is called refraction of light .  A transparent medium through which light travels fast is known as optically rarer medium.  A transparent medium through which light travels slow is known as optically denser medium.  Laws of refraction (i) The incident ray, the refracted ray and the normal to the surface separating two media all lie in the same plane. (ii) The ratio of the sine of the incident angle (i) to the sine of the refracted angle (r) is constant i.e. sin i/ sin r = constant This constant is known as the refractive index of second medium w.r.t the first medium.  Absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v) i.e. n = c / v  Relative refractive index of medium. 2 w.r.t. the medium 1 is defined as the ratio of the speed of light in medium 1 (v1) to the speed of light in medium 2 (v2). i.e. n21= v2 / v1

 Light is a form of energy which produces the sensation of sight.  Speed of light in vacuum / air = 3 × 108 ms–1  Ray of light : A line drawn in the direction of propagation of light is called ray of light.  Beam of light : A group of parallel rays light emitted by a source of light is called beam of light.  Reflection of light : The phenomenon of returning of light in the same medium after striking a surface is called reflection of light.  Laws of reflection : The reflection of light from a surface obeys certain laws called laws of reflection. (i) incident angle is equal to reflected angle i.e. i = r. (ii) Incident ray, reflected ray and normal to the reflecting surface at the point on incident lie in the same plane.  Concave mirror : concave mirror is a part of a hollow sphere whose outer part is silvered and the inner part is reflecting surface.  Convex mirror : convex mirror is a part of a hollow sphere whose outer part is reflecting surface and inner part is silvered.  Centre of curvature : The centre of a hollow sphere of which the spherical mirror forms a part is called centre of curvature. It is denoted by C  Radius of curvature : The radius of a hollow sphere of which the spherical mirror forms a part is called radius of curvature. It is denoted by R  Pole : The mid point of a spherical mirror is called its pole. It is denoted by P  Aperture: The part of spherical mirror exposed to the incident light is called the aperture of the mirror.  Principal Axis: A line joining the centre of curvature (C) and pole (P) of a spherical mirror and extend on either side is called principal axis of the spherical mirror.  Principal Focus : A point on the principal axis of a spherical mirror where the rays of light parallel to the principal axis meet or appears to meet after reflection from the spherical mirror is called principal focus. It is denoted by F.  Focal Plane : A plane normal or perpendicular to the principal axis and passing through the principal focus (F) of the spherical mirror is called focal plane of the spherical mirror.  Focal length (f): The distance between the pole (P) and the principal focus (F) of a spherical mirror is called the focal length of the spherical mirror.  f = , Where R is the radius of the curvature of the mirror.  Focal length and radius of curvature of a concave mirror are negative.  Focal length and radius of curvature of a convex mirror are positive.  Sign Conventions for reflection by spherical mirrors (1) All distance are measured from the pole of a spherical mirror. (2) Distance measured in the direction of incident light are taken as positive. Distance measured in the direction opposite to that of the incident light are taken negative. (3) The upward distance perpendicular to the principal axis are taken as positive, while the downward distance perpendicular to the principal axis are taken as negative.  Radius of curvature plane mirror =  ( infinite)  Focal length of a plane mirror =   Mirror Formula : The relation between u, v, and focal length (f) of a spherical mirror is known as mirror formula. That is  Linear magnification : Linear magnification produced by a mirror is defined as the ratio of the size ( or height) of the image to the size of the object . It is denoted by m. That is  Power of mirror (P) = =  Linear magnification produced by a plane mirror = + 1.  Refraction of light: The bending of light rays when they pass obsessively from one medium to the other medium is called refraction of light .  A transparent medium through which light travels fast is known as optically rarer medium.  A transparent medium through which light travels slow is known as optically denser medium.  Laws of refraction (i) The incident ray, the refracted ray and the normal to the surface separating two media all lie in the same plane. (ii) The ratio of the sine of the incident angle (i) to the sine of the refracted angle (r) is constant i.e. sin i/ sin r = constant This constant is known as the refractive index of second medium w.r.t the first medium.  Absolute refractive index of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v) i.e. n = c / v  Relative refractive index of medium. 2 w.r.t. the medium 1 is defined as the ratio of the speed of light in medium 1 (v1) to the speed of light in medium 2 (v2). i.e. n21= v2 / v1

STRUCTURE OF ATOM - In this chapter we will learn the composition atom and how molecules are made up with atoms. These are the topics (Electrons, protons and neutrons, valency, chemical formula of common compounds. Isotopes and Isobars) that will be discussed in the lectures.

STRUCTURE OF ATOM - In this chapter we will learn the composition atom and how molecules are made up with atoms. These are the topics (Electrons, protons and neutrons, valency, chemical formula of common compounds. Isotopes and Isobars) that will be discussed in the lectures.

STRUCTURE OF ATOM - In this chapter we will learn the composition atom and how molecules are made up with atoms. These are the topics (Electrons, protons and neutrons, valency, chemical formula of common compounds. Isotopes and Isobars) that will be discussed in the lectures.

STRUCTURE OF ATOM - In this chapter we will learn the composition atom and how molecules are made up with atoms. These are the topics (Electrons, protons and neutrons, valency, chemical formula of common compounds. Isotopes and Isobars) that will be discussed in the lectures.

CHEMICAL REACTIONS - In this Chapter we will learn the following topics which includes Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction.

CHEMICAL REACTIONS - In this Chapter we will learn the following topics which includes Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction.

CHEMICAL REACTIONS - In this Chapter we will learn the following topics which includes Chemical equation, Balanced chemical equation, implications of a balanced chemical equation, types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction.

ACIDS , BASES AND SALTS - In this topic we will learn what is acid and base and their uses. The lectures will cover the following topic which includes the definitions of acids and bases in terms of furnishing of H+ and OH– ions, General properties, examples and uses, concept of pH scale (Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of Sodium Hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris

ACIDS , BASES AND SALTS - In this topic we will learn what is acid and base and their uses. The lectures will cover the following topic which includes the definitions of acids and bases in terms of furnishing of H+ and OH– ions, General properties, examples and uses, concept of pH scale (Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of Sodium Hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris

ACIDS , BASES AND SALTS - In this topic we will learn what is acid and base and their uses. The lectures will cover the following topic which includes the definitions of acids and bases in terms of furnishing of H+ and OH– ions, General properties, examples and uses, concept of pH scale (Definition relating to logarithm not required), importance of pH in everyday life; preparation and uses of Sodium Hydroxide, Bleaching powder, Baking soda, Washing soda and Plaster of Paris

METALS AND NON METALS - In this topic we will discuss the following topics which includes Properties of metals and non-metals; Reactivity series; Formation and properties of ionic compounds; Basic metallurgical processes; Corrosion and its prevention.

METALS AND NON METALS - In this topic we will discuss the following topics which includes Properties of metals and non-metals; Reactivity series; Formation and properties of ionic compounds; Basic metallurgical processes; Corrosion and its prevention.