Chapter 2 Miscellaneous(Sets) Class 11 Question 1: The relation f is defined by The relation g is defined by Show that f is a function and g is not a function. Solution: The given relation f is defined as: It is seen that for 0 ≤ x < 3, f(x) = x2 and for 3 < x ≤ 10, f(x) = 3x Also, at x = 3 f(x) = 32 = 9 … Read more
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 2: Miscellaneous Exercise Find the value of the following:(Class 12 ncert solution math chapter 2 Miscellaneous) Question 1: Find the value of . Solution: Question 2: Find the value of . Solution: Question 3: Prove that . Solution: Let Then, Therefore, Thus, Question 4: Prove that . Solution: Let Then, Therefore, Now, let Then, … Read more
EXERCISE 2.2 Prove the following:(Class 12 ncert solution math exercise 2.2) Question 1: Prove . Solution: Let Hence, Now, =L H S Question 2: Prove . Solution: Let Hence, Now, Question 3: Prove . Solution: Since we know that Now, Question 4:Prove . Solution: Since we know that Now, Question 5: … Read more
EXERCISE 2.1 Find the principal values of the following:(Class 12 ncert solution math exercise 2.1) Question 1: Solution : Principal value of Question 2: Solution : Principal value of Question 3: Solution: Principal value of Question 4: Solution: Principal value of Question 5: Solution :Principal value of Question 6: Solution: Principal value of … Read more