# Important Questions for Class 11 Chapter 2 - Relations and Functions

Our team of experienced subject experts have ensured to provide complete step-by-step solutions to help you deal with any question. You can download freely and use the class 11th Important Questions for doing homework, learning concepts or preparing for exams.

Important questions based on NCERT syllabus Class 11 Chapter 2-Relations and Functions:

Question 1: If A=(1,2,3), B=(3,4,5) C=(1,3,5), then write the following sets:
a) (A x B) ∩ (B x A)
b) (A x B) U (B x A)
Solution:
Consider (A x B) = (1,2,3) x (3,4,5) = {(1,3)(1,4)(1,5)(2,3)(2,4)(2,5)(3,3)(3,4)(3,5)}
(B x A) = (3,4,5) x (1,2,3) = {(3,1)(3,2)(3,3)(4,1)(4,2)(4,3)(5,1)(5,2)(5,3)}

Now,

a) (A x B) ∩ (B x A) {(1,3)(1,4)(1,5)(2,3)(2,4)(2,5)(3,3)(3,4)(3,5)} ∩ {(3,1)(3,2)(3,3)(4,1)(4,2)(4,3)(5,1)(5,2)(5,3)}= { {(3,3)}

b) (A x B) U (B x A) = {(1,3)(1,4)(1,5)(2,3)(2,4)(2,5)(3,3)(3,4)(3,5)} U {(3,1)(3,2)(3,3)(4,1)(4,2)(4,3)(5,1)(5,2)(5,3)} = {(1,3)(1,4)(1,5)(2,3)(2,4)(2,5)(3,4)(3,5)(3,1)(3,2)(3,3)(4,1)(4,2)(4,3)(5,1)(5,2)(5,3)}

Question 2: Find the domain and range of following real valued functions:

a) f(x) = (x+1)/(x²-3x+2)
b) f(x) = √x
Solution: Consider (x²-3x+2)

Find the root of the equation (x^2-3x+2) = 0
x^2 - 2x - x + 2
x(x-2)-1(x-2) = 0
(x-2)(x-1) = 0
x = 2, x = 1

Hence the domain of the function R - {1,2}

b) the domain of the function {0, +∞}

Question 3: let R be the relation on z defined by R = {(a,b): a belongs to z and b belongs to z, a^2 =b^2}, Find
i) R
ii) Domain R
iii) Range R

Solution:
i) R = {(a,a): a belongs to z} U {(a,-a): a belongs to z}
ii) Domain = z
iii) Range = z