Team Gmath EXERCISE 2.3 (Class 11) 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, … Read more
EXERCISE 2.2 (Class 11) 1. Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range. Solution: The relation R from A to A is given as: R = {(x, y): 3x – y = 0, … Read more
EXERCISE 2.1(Class 11) 1. If , find the values of x and y. Solution: Given, As the ordered pairs are equal, the corresponding elements should also be equal. Thus, x/3 + 1 = 5/3 and y – 2/3 = 1/3 Solving, x + 3 = 5 and 3y – 2 = 1 [Taking L.C.M. and … Read more
Chapter 1(Miscellaneous) Class 11 1. Decide, among the following sets, which sets are subsets of one and another. A= {x: x ∈ R and x satisfy x2 – 8x + 12 = 0} B = {2, 4, 6} C = {2, 4, 6, 8…} D = {6} Solution: According to the question, We have, A = … Read more
EXERCISE 6.3 Question 1: Find the slope of the tangent to the curve at . Solution: The slope of tangent to the curve If , then slope Question 2: Find the slope of the tangent to the curve at . Solution: The slope of tangent to the curve If , then … Read more
EXERCISE 1.6 Ex 1.6 sets ncert maths solution class 11 1. If X and Y are two sets, such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y). Solution: Given, n (X) = 17, n (Y) = 23, n (X U Y) = 38 We know that n (X … Read more
EXERCISE 1.5 (Ex 1.5 sets ncert maths solution class 11) 1. Let U = {1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, and C = {3, 4, 5, 6}. Find (i) A’ (ii) B’ (iii) (A U … Read more
Prove that root 2 is an irrational number Solution:- Let us assume that on the contrary that √2 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒ Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 2 then also divisible … Read more
EXERCISE 1.4 1. Find the union of each of the following pairs of sets:(Ex 1.4 sets ncert maths solution class 11) (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = {a, e, i, o, u} B = {a, b, c} (iii) A = {x: x is a natural number and multiple of 3} B = {x: x is a natural … Read more
Exercise 6.2 class 12 maths ex 6.2 ncert solution Question 1: Show that the function given by is strictly increasing on . Solution: Therefore, the function is strictly increasing on . Question 2: Show that the function given by is strictly increasing on . Solution: , For all Therefore, the … Read more