Class 11 Maths Chapter 1: Sets MCQs with answers

Answer: (b) whether a student is 'tall' depends on the person judging, so membership cannot be decided definitely

A set must be a well-defined collection: for any student we must be able to decide definitely whether the student belongs. 'More than 150 cm' can be decided by measuring; 'tall' varies from person to person.

Answer: (a) 4

In a set the letters are taken as distinct and are not repeated: M = {M, I, S, P}, so n(M) = 4. 11 counts the letters of the word with repetition.

Answer: (c) {0, 1, 2}

−2 < 2x ≤ 5 gives −1 < x ≤ 2.5. The integers in this range are 0, 1 and 2. x = −1 fails since 2x = −2 is not greater than −2; x = 3 gives 2x = 6 > 5.

Answer: (c) {x : x = n² − 1, n ∈ N and 2 ≤ n ≤ 6}

3 = 2² − 1, 8 = 3² − 1, 15 = 4² − 1, 24 = 5² − 1, 35 = 6² − 1, so x = n² − 1 with n from 2 to 6. Option (a) would start at 0 and stop at 24.

Answer: (d) {x : x ∈ Z and x² + 1 = 0}

x² + 1 = 0 gives x² = −1, which no integer satisfies, so the set has no element. The others are {3}, {2} and {0}.

Answer: (b) The set of points on a line segment 1 cm long

A line segment, however short, contains infinitely many points. The other three sets are very large but have a definite number of elements, so they are finite.

Answer: (a) {x : x ∈ R and x³ = 27}

The only real number whose cube is 27 is 3, so the set is {3}, with one element. The others are {−3, 3}, φ and {1, 3, 9}.

Answer: (a) 256

The primes less than 20 are 2, 3, 5, 7, 11, 13, 17, 19: eight elements. The number of subsets is 2⁸ = 256 (255 is the number of proper subsets).

Answer: (b) 6

A set with m elements has 2^m − 1 non-empty subsets. 2^m − 1 = 63 gives 2^m = 64, so m = 6.

Answer: (c) 11

Let n(A) = a and n(B) = b. Then 2^a − 2^b = 112, i.e. 2^b(2^{a − b} − 1) = 16 × 7. Since 2^{a − b} − 1 is odd, 2^b = 16 and 2^{a − b} − 1 = 7, so b = 4, a = 7 and a + b = 11.