Set Theory Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16

In an examination, 35% students failed in Hindi, 45% students failed in English and 20% students failed in both the subjects. What is the percentage of students passing in both the subjects?

a) 30

b) 20

c) 0

d) 40

Question : 17

Let A = {7, 8, 9, 10, 11, 12} and B = {7, 10, 14, 15}. What is the number of elements in (A–B) and (B–A) respectively ?

a) 2 and 2

b) 4 and 2

c) 2 and 4

d) 4 and 4

Question : 18

In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects?

a) 23%

b) 21%

c) 18%

d) 25%

Question : 19

Let A and B be finite non-empty sets with the number of elements in A = m and number of elements in B = n. Let m > n. If for some integer k ≥ 1, the number of nonempty subsets of A = $2^k$ + the number of non-empty subsets of B, then which one of the following is correct?

a) m = n + p for some odd prime number p

b) m = n + 1

c) m = n + 2

d) m = n + t for some composite number t

Question : 20

If A = (x : x is a multiple of 7),
B = (x : x is a multiple of 5) and
C = (X : x is a multiple of 35),
then which one of the following is a null set ?

a) (A ∩ B) ∩ C

b) (A– B) – C

c) (A – B) ∪ C

d) (A ∩ B) – C