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 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 6.5( Application of derivative) Question 1: Find the maximum and minimum values, if any, of the following functions given by:(class 12 maths ex 6.5 ncert solution) (i) (ii) (iii) (iv) Solution: (i) Given function is: We know that for all Adding 3 both sides, we get The minimum value of is 3 when , … 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 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