NCERT Solutions

Exercise 1.2 1. Which of the following are examples of the null set: (i) Set of odd natural numbers divisible by 2. (ii) Set of even prime numbers. (iii) { is a natural number, and } (iv) { is a point common to any two parallel lines} Ans. (i) Set of odd natural numbers divisible … Read more

Exercise 6.1 1. Solve when: (i) is a natural number (ii) is an integer Ans. Given: Dividing both sides by 24, (i) When is a natural number then values of that make statement true are 1, 2, 3, 4. The solution set of inequality is {1, 2, 3, 4}. (ii) When is an integer then … Read more

Exercise 9.4 Find the sum to terms in each of the series in Exercises 1 to 7. 1. Ans. Given:to terms = [ term of 1, 2, 3, ………..][ term of 2, 3, 4, 5, ………] = = = = = = = = = 2. Ans. Given: to terms = [ term of 1, … Read more

Exercise 1.4 1. Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} and Y = {1, 2, 3} (ii) A = and B = (iii) A = { is a natural number and multiple of 3} and B = { is a natural number less than 6} … Read more

Exercise 6.2 Solve the following inequalities graphically in two dimensional planes: 1. Ans. Given: Table of values satisfying the equation 1 2 4 3 Putting (0, 0) in the given in equation, 0 < 5 which is true. Therefore, Half plane of towards origin. 2. Ans. Given: Table of values satisfying the equation 1 2 … Read more

Miscellaneous Exercise 1. Show that the sum of  and  terms of an A.P. is equal to twice the  terms. Ans. Here,  …..(i) and   …..(ii) To prove: Adding eq. (i) and (ii), we get                  2. If the sum of three numbers in A.P., is 24 and their product is 440. … Read more

Exercise 1.6 1. If X and Y are two sets such that and find Ans. Given: and 2. If X and Y are two sets such that has 18, X has 8 elements and Y has 15 elements; how many elements has ? Ans. Given: and 3. In a group of 400 people, 250 can … Read more

Exercise 6.3 Solve the following systems of inequalities graphically: 1. Ans. Given: Putting (0, 0) in which is false. Half plane of is away from origin. Again Putting (0, 0) in which is false. Half plane of is away from origin. 2. Ans. Given: Table of values satisfying the equation 2 4 3 0 Putting … Read more

17. If  are in G.P., prove that  are in G.P. Ans. Given:  are in G.P. To prove:  are in G.P.    Let       And    Also    Now,         Therefore,  are in G.P. 18. If  and  are the roots  and  are roots of  where  form a G.P. Prove that   Ans. … Read more

Miscellaneous Exercise 1. Decide among the following sets, which sets are subsets of each another: A = { R and satisfies }, B = {2, 4, 6}, C = {2, 4, ,6 , 8…….}, D = {6} Ans. Given: A = { R and satisfies } = { R and satisfies } = {2, 6} … Read more

Miscellaneous Exercise Solve the inequalities: 1. Ans. Given: 2. Ans. Given: 3. Ans. Given: 4. Ans. Given: 5. Ans. Given: 6. Ans. Given: Solve the inequalities in Exercises 7 to 10 and represent the solution graphically on number line: 7. Ans. Given: and and and 8. Ans. Given: and and and and 9. Ans. Given: … Read more

Exercise 10.1 1. Draw a quadrilateral in the Cartesian plane, whose vertices are and Also, find its area. Ans. Area of quadrilateral ABCD = Area of + Area of trapezium ABED = = = 26 + 34.8 = 60.8 sq. units 2. The base of an equilateral triangle with side lies along the axis such … Read more

Exercise 1.3 1. Make correct statements by filling in the symbols or in the blank spaces: (i) {2, 3, 4} _______ {1, 2, 3, 4, 5} (ii) (iii) { is a student of class XI of your school} _______ { student of your school} (iv) { is a circle in the plane} _______ { is … Read more

Exercise 7.1 1. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that: (i) repetition of the digits is allowed (ii) repetition of the digits is not allowed. Ans. (i) The unit place can be filled by any one of the digits 1, 2, 3, 4 and … Read more

Exercise 10.2 In Exercises 1 to 8, find the equations of the line which satisfy the given conditions: 1. Write the equations for the and axis. Ans. Equation for axis is Equation for axis is 2. Passing through the point with slope Ans. Given: and 3. Passing through (0, 0) with slope Ans. Given: and … Read more