Set Theory Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

From option (a),

A = {x is a real number : x > 1 and x < 1}.

So, there is no element which is greater or less than 1.

So, A is a null set.

From option (b),

B = {x : x + 3 = 3} = {0}

= Singleton set

From option (c):

C = {Φ} = Singleton set

From option (d),

D = {x is a real number : x ≥ 1 and x ≤ 1}

= {1} = Singleton set

Answer: (d)

Let the total number of students be 100%

Number of students failed in Hindi = 35%

Number of students failed in English = 45%

Number of students failed in both the subjects = 20%

Total number of students failed = (35 + 45 – 20)% = 60%

Number of students passing in both the subjects = (100 – 60)% = 40%

Answer: (b)

A = {7, 8, 9, 10, 11, 12}; B = {7, 10, 14, 15}

(A – B) = {8, 9, 11, 12} (B – A) = {14, 15}

n (A – B) = 4; n (B – A) = 2

Answer: (a)

A and B are non-empty subsets of E.

∴ A ∪ (A ∩ B) = A ∪ (Shaded portion) = A

Answer: (a)

Here, n(A ∩ B) = 2n

∴ n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

= 2n + 4n – 2n = 4n

Hence, minimum number of elements of A ∪ B is 4n.

Answer: (a)

Since numbers which and leave 4 as Remainder when devided by 12 are

16, 28, 40, 52, 64, 76, 88, 100 and 124

16 = 2 × 8, 8 × 2

28 = 4 × 7, 7 × 4

40 = 4 × 10, 10 × 4, 5 × 5, 8 × 5

All remaining numbers doesn't meet the requirement

Answer is 8.