Class 11 || Mathematics || Relations and Functions : Practice Question - A

 Short Answer Type Questions

Question 1 : If A = {-1, 2, 3 } and B = {1, 3}, then determine
(i) AxB (ii) BxC (c) BxB (iv) AxA

Question 2 : If P = {x : x < 3, x e N}, Q= {x : x≤2,x ∈ W}. Find (P∪ Q) x (P∩ Q), where W is the set of whole numbers.

Question 3 : lfA={x:x∈ W,x < 2}, 5 = {x : x∈N, 1 <.x < 5}, C= {3, 5}. Find
(i) Ax(B∩Q) (ii) Ax(B∪C)

Question 4 : In each of the following cases, find a and b. (2a + b, a – b) = (8, 3) (ii) {a/4, a – 2b) = (0, 6 + b)

Question 5 : Given A = {1,2,3,4, 5}, S= {(x,y) :x∈ A,y∈ A}.Find the ordered pairs which satisfy the conditions given below, (i) x+y = 5 (ii) x+y<5 (iii) x+y>8

Question 6 : Given R = {(x,y) : x,y ∈ W, x2 + y2 = 25}. Find the domain and range of R

Question 7 : If R1 = {(x, y)| y = 2x + 7, where x∈ R and -5 ≤ x ≤ 5} is a relation. Then find the domain and range of R1.

Question 8 : If R2 = {(x, y) | x and y are integers and x2 +y2 = 64} is a relation. Then find R2

Question 9 : If R3 = {(x, |x|) | x is a real number} is a relation. Then find domain and range.

Question 10 : Is the given relation a function? Give reasons for your answer.
(i) h={(4,6), (3,9), (-11,6), (3,11)}
(ii) f = {(x, x) | x is a real number}
(iii) g = {(n, 1 In)| nis a positive integer}
(iv) s= {(n, n2) | n is a positive integer}
(v) t= {(x, 3) | x is a real number}

Question 11 : If f and g are real functions defined byf( x) = x2 + 7 and g(x) = 3x + 5, find each of the following.

Question 12 : Let f and g be real functions defined by f(x) = 2x+ 1 and g(x) = 4x – 7.
(i) For what real numbers x,f(x)= g(x)?
(ii) For what real numbers x,f (x) < g(x)?

Question 13 : If f and g are two real valued ftmctions defined as f(x) = 2x + 1, g(x) = x2 + 1, then find.

Question 14 : Express the following functions as set of ordered pairs and determine their range.
f:X->R,f{x) =  x3 + 1, where X= {-1,0, 3, 9, 7}

Question 15 : Find the values of x for which the functions f(x) = 3x2 -1 and g(x) = 3+ x are equal.

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