NCERT solution class 9 chapter Surface area and volume

Exercise 13.1 Question 1 A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic[…]

Rd sharma solution class 12 chapter 2 functions

Exercise 3.1 Question 1 Give an example of a function (i) which is one-one but not onto Sol : Injectivity : Let x and y be any two elements in the domain (Z) , such that […]

NCERT solution class 10 chapter 2 polynomials

Exercise 2.2 (working) Question 1 Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) Sol : or or Therefore , the zeroes of are 4[…]

NCERT solution class 10 chapter 2 polynomials

Exercise 2.1 Question 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i)   Sol : (i) The[…]

NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1    Exercise 1.2   Exercise 1.3   Exercise 1.4 Exercise 1.4 Question 1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating[…]

NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1    Exercise 1.2   Exercise 1.3   Exercise 1.4 Exercise 1.3 Question 1 Prove that is irrational . Sol : Let is a rational number. Therefore, we can find two integers a , b[…]

NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1    Exercise 1.2   Exercise 1.3   Exercise 1.4 Exercise 1.2 Question 1 Express each number as product of its prime factors: (i) 140 Sol :   (ii) 156 Sol :   (iii) 3825[…]

Rd sharma solution class 12 chapter Relations

Exercise 1.1 Question 1 Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) R =[…]

Rd sharma solution class 12 chapter Differentiation

Exercise 11.2 Question 1 Differentiate  Sol : Let  Differentiating y with respect to x we get, So,     Question 2 Differentiate Sol : Let  which can be written as Differentiating y with respect to[…]

Rd sharma solution class 12 chapter Inverse trigonometric functions

Exercise 4.1 Question 1  Find the principal value of each of the following: (i) Sol :   (ii) Sol :   (iii)  Sol :       (iv)   Sol :        […]

Rd sharma solution class 12 chapter Continuity

Exercise 9.1 Question 1 Test the continuity of the function on at the origin: Sol : Given We observe (LHL at x= 0) =-1   (RHL at x = 0) =1 Hence, is discontinuous at[…]

NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1    Exercise 1.2   Exercise 1.3   Exercise 1.4 Exercise 1.1 Question 1 Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 Sol : (i) 135 and 225 Since 225[…]

Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.2 Question 1

Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.1 Question 1 Evaluate each of the following integrals: (i) Sol :   (ii) Sol :   (iii) Sol :   (iv)  Sol :   (v)  Sol :   (vi)  Sol :   (vii)[…]

RD Sharma solution class 12 chapter 28 Straight line in space

Exercise 28.1 Question 1 Find the vector and cartesian equations of the line through the point and which is parallel to the vector   Sol : We know that the vector equation of a line[…]

NCERT solution class 8 chapter 16 Playing with numbers

Exercise 16.1   Exercise 16.2 Exercise 16.2 Question 1 If 21y5 is a multiple of 9, where y is a digit, what is the value of y? Sol : If a number is a multiple of[…]

NCERT solution class 8 chapter 16 Playing with numbers

Exercise 16.1   Exercise 16.2 Exercise 16.1 Question 1 Find the values of the letters in the following and give reasons for the steps involved. Sol : The addition of A and 5 is giving 2[…]

NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1   Exercise 15.2   Exercise 15.3 Exercise 15.3 Question 1  Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples Number of apples 1 2 3[…]

NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1   Exercise 15.2   Exercise 15.3 Exercise 15.2 Question 1  Plot the following points on a graph sheet. Verify if they lie on a line (a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5) (b)[…]

NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1   Exercise 15.2   Exercise 15.3 Exercise 15.1 Question 1  The following graph shows the temperature of a patient in a hospital, recorded every hour. (a) What was the patient’s temperature at 1 p.m.? (b)[…]

NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1   Exercise 14.2   Exercise 14.3   Exercise 14.4 Exercise 14.4 Question 1  Find and correct the errors in the statement: 4(x − 5) = 4x − 5 Sol : L.H.S. = 4(x − 5) =[…]

NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1   Exercise 14.2   Exercise 14.3   Exercise 14.4 Exercise 14.3 Question 1  Carry out the following divisions. (i) 28×4 ÷ 56x (ii) −36y3 ÷ 9y2 (iii) 66pq2r3 ÷ 11qr2 (iv) 34x3y3z3 ÷ 51xy2z3 (v) 12a8b8[…]

NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1   Exercise 14.2   Exercise 14.3   Exercise 14.4 Exercise 14.2 Question 1  Factorise the following expressions. (i) a2 + 8a + 16 (ii) p2 − 10p + 25 (iii) 25m2 + 30m + 9 (iv)[…]

NCERT solution class 8 chapter 13 Direct and Inverse proportions

Exercise 13.1   Exercise 13.2 Exercise 13.2 Question 1  Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken[…]

NCERT solution class 8 chapter 13 Direct and Inverse proportions

Exercise 13.1   Exercise 13.2 Exercise 13.1 Question 1  Following are the car parking charges near a railway station up to 4 hours Rs 60 8 hours Rs 100 12 hours Rs 140 24 hours Rs[…]

NCERT solution class 8 chapter 12 Exponents and Power

Exercise 12.1   Exercise 12.2 Exercise 12.2 Question 1 Express the following numbers in standard form. (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000 Sol : (i) 0.0000000000085 = 8.5 × 10−12 (ii) 0.00000000000942[…]

NCERT solution class 8 chapter 12 Exponents and Power

Exercise 12.1   Exercise 12.2 Exercise 12.1 Question 1 Evaluate (i) 3−2 (ii) (−4)−2 (iii) Sol : (i) (ii) (iii)     Question 2 Simplify and express the result in power notation with positive exponent. (i)[…]

NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1   Exercise 11.2   Exercise 11.3   Exercise 11.4 Exercise 11.4 Question 1 Given a cylindrical tank, in which situation will you find surface area and in which situation volume. (a) To find how much it[…]

NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1   Exercise 11.2   Exercise 11.3   Exercise 11.4 Exercise 11.3 Question 1 There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make? Sol :[…]

NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1   Exercise 11.2   Exercise 11.3   Exercise 11.4 Exercise 11.2 Question 1 The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and[…]

NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1   Exercise 11.2   Exercise 11.3   Exercise 11.4 Exercise 11.1 Question 1 A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?[…]

NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1  Exercise 10.2  Exercise 10.3 Exercise 10.3 Question 1 Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles? Sol : (i) No, such a polyhedron is[…]

NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1  Exercise 10.2  Exercise 10.3 Exercise 10.2 Question 1 Look at the given map of a city. Answer the following. (a) Colour the map as follows: Blue − water plant, red − fire station, orange −[…]

NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1  Exercise 10.2  Exercise 10.3 Exercise 10.1 Question 1 For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. Sol : The given solids, matched[…]

NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1  Exercise 9.2  Exercise 9.3  Exercise 9.4  Exercise 9.5 Exercise 9.4 Question 1 Multiply the binomials. (i) (2x + 5) and (4x − 3) (ii) (y − 8) and (3y − 4) (iii) (2.5l − 0.5m) and[…]

NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1  Exercise 9.2  Exercise 9.3  Exercise 9.4  Exercise 9.5 Exercise 9.5 Question 1 Use a suitable identity to get each of the following products. (i) (x + 3) (x + 3) (ii) (2y + 5) (2y +[…]

NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1  Exercise 9.2  Exercise 9.3  Exercise 9.4  Exercise 9.5 Exercise 9.3 Question 1 Carry out the multiplication of the expressions in each of the following pairs. (i) 4p, q + r (ii) ab, a − b (iii)[…]

NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1  Exercise 9.2  Exercise 9.3  Exercise 9.4  Exercise 9.5 Exercise 9.2 Question 1 Find the product of the following pairs of monomials. (i) 4, 7p (ii) − 4p, 7p (iii) − 4p, 7pq (iv) 4p3, − 3p[…]

NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1  Exercise 9.2  Exercise 9.3  Exercise 9.4  Exercise 9.5 Exercise 9.1 Question 1 Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 − 3zy (ii) 1 + x + x2 (iii) 4x2y2 −[…]

NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1  Exercise 8.2  Exercise 8.3 Exercise 8.3 Question 1 Calculate the amount and compound interest on (a) Rs 10800 for 3 years at per annum compounded annually. Sol : (a) Principal (P) = Rs[…]

NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1  Exercise 8.2  Exercise 8.3 Exercise 8.2 Question 1 A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary. Sol : Let the original[…]

NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1  Exercise 8.2  Exercise 8.3 Exercise 8.1 Question 1 Find the ratio of the following: (a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b)[…]

NCERT solution class 8 chapter 7 Cube and Cube roots

Exercise 7.1  Exercise 7.2 Exercise 7.2 Question 1 Find the cube root of each of the following numbers by prime factorization method. (i) 64 Sol : (i) Prime factorization of ∴   (ii) 512 Sol[…]

NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1  Exercise 6.2  Exercise 6.3  Exercise 6.4 Exercise 6.3 Question 1 What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001[…]

NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1  Exercise 6.2  Exercise 6.3  Exercise 6.4 Exercise 6.4 Question 1 Find the square root of each of the following numbers by division method. (i) 2304 Sol : (i) The square root of 2304[…]

NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1  Exercise 6.2  Exercise 6.3  Exercise 6.4 Exercise 6.2 Question 1 Find the square of the following numbers (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 Sol : (i) 322[…]

NCERT Solutions for class 8 Maths chapter 5 Data handling

Exercise 5.1  Exercise 5.2 Exercise 5.3 Exercise 5.2   Question 1 A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart[…]

NCERT Solutions for class 8 Maths chapter 5 Data handling

Exercise 5.1  Exercise 5.2 Exercise 5.3 Exercise 5.1 Question 1 For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag.[…]

RD sharma solution class 12 chapter determinants

Determinants Exercise 6.1 Question 1 Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (i) A = Sol : In[…]

NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1  Exercise 4.2  Exercise 4.3  Exercise 4.4  Exercise 4.5 Exercise 4.5 Question 1 Draw the following: The square READ with RE = 5.1 cm Sol : All the sides of a square are of[…]

NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1  Exercise 4.2  Exercise 4.3  Exercise 4.4  Exercise 4.5 Exercise 4.4 Question 1 Construct the following quadrilaterals, (i) Quadrilateral DEAR DE = 4 cm EA = 5 cm AR = 4.5 cm ∠E =[…]

NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1  Exercise 4.2  Exercise 4.3  Exercise 4.4  Exercise 4.5 Exercise 4.3 Question 1 Construct the following quadrilaterals. (i) Quadrilateral MORE MO = 6 cm OR = 4.5 cm ∠M = 60° ∠O = 105°[…]

NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1  Exercise 4.2  Exercise 4.3  Exercise 4.4  Exercise 4.5 Exercise 4.2 Question 1 Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm IF = 3 cm TL = 2.5 cm LF =[…]

NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1  Exercise 4.2  Exercise 4.3  Exercise 4.4  Exercise 4.5 Exercise 4.1 Question 1 Construct the following quadrilaterals. (i) Quadrilateral ABCD AB = 4.5 cm BC = 5.5 cm CD = 4 cm AD =[…]

NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1  Exercise 3.2  Exercise 3.3  Exercise 3.4 Exercise 3.4 Question 1 State whether True or False. (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles.[…]

NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1  Exercise 3.2  Exercise 3.3  Exercise 3.4 Exercise 3.3 Question 1 Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = … (ii) ∠DCB = … (iii)[…]

NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1  Exercise 2.2  Exercise 2.3  Exercise 2.4  Exercise 2.5  Exercise 2.6 Exercise 2.6 Question 1 : Solve : ​$$\dfrac{8x-3}{3x}=2$$​ Sol :  ​$$\dfrac{8x-3}{3x}=2$$​ On multiplying both sides by 3x , we obtain 8x -3 = 6x[…]

NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1  Exercise 2.2  Exercise 2.3  Exercise 2.4  Exercise 2.5  Exercise 2.6 Exercise 2.5  Question 1 : Solve the linear equation  ​$$\dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4}$$​ Sol : ​$$\dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4}$$​ L.C.M of the denominators 2, 3, 4, and 5 is 60[…]

NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1  Exercise 2.2  Exercise 2.3  Exercise 2.4  Exercise 2.5  Exercise 2.6 Exercise 2.4 Question 1: Amina thinks a number and subtracts ​$$\dfrac{5}{2}$$​ from it . She multiplies the result by 8. The result now obtained is 3 times[…]

NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1  Exercise 2.2  Exercise 2.3  Exercise 2.4  Exercise 2.5  Exercise 2.6 EXERCISE 2.1 Question 1 : Solve : x-2=7 sol : x-2=7 On transposing 2 to R.H.S , we obtain  x=7+2=9   Question 2 : Solve : y+3=10 sol[…]