Important Questions for Class 11 Chapter 2 - Relations and Functions

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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