Set Theory Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 21

If X= {a, {b}, c}, Y = {{a}, b, c} and Z = {a, b, {c}}, then (X ∩ Y) ∩ Z equals to

a) {Φ}

b) {{a}, {b}, {c}}

c) {a, b, c}

d) Φ

Question : 22

In the quadratic equation $x^2$ + ax + b = 0, a and b can take any value from the set {1, 2, 3, 4}. How many pairs of values of a and b are possible in order that the quadratic equation has real roots?

a) 8

b) 7

c) 6

d) 16

Question : 23

In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics?

a) 150

b) 100

c) 90

d) 160

Question : 24

Let :
P = Set of all integral multiples of 3
Q = Set of all integral multiples of 4
R = Set of all integral multiples of 6
Consider the following relations:
I. P ∪ Q = R
II. P ⊂ R
III. R ⊂ (P ∪ Q)
Which of the relations given above is/are correct?

a) Only III

b) Only II

c) Only I

d) II and III

Question : 25

If A = {x : x is an odd integer} and B = {x : $x^2$ – 8x + 15 = 0}. Then, which one of the following is correct?

a) B ⊆ A

b) A ⊆ B

c) A = B

d) A ⊆ $B^C$