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UPSC NDA II 2014 Mathematics Paper

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For the next four (04) items that follow:

Consider events A, B, C, D, E of the sample space S = {n : n is an integer such that 10 ≤ n ≤ 20} given by :

A is the set of all even numbers.

B is the set of all prime numbers.

C = 15

D is the set of all integers ≤ 16.

E is the set of all double digit numbers expressible as a power of 2.

S=\{n:n\in Z,10\le n\le 20\}

A=\{10,12,14,16,18,20\}

B=\{11,13,17,19\}

C=\{15\}

D=\{10,11,12,13,14,15,16\}

E=\{16\}

[NDA II 2014]

Question : 109 of 120

Marks: +1, -0

B and C are

[NDA II 2014]

Mutually exclusive events but not exhaustive events
Compound events
Mutually exclusive and exhaustive events
Elementary events

Validate

Solution:

S=\{ n : n \in Z, 10 \le n \le 20 \}

A=\{ 10, 12, 14, 16, 18, 20 \}

B=\{ 11, 13, 17, 19 \}

C=\{ 15 \}

D=\{ 10, 11, 12, 13, 14, 15, 16 \}

E=\{ 16 \}

B and C are mutually exclusive events as they do not have any element in common.But union of B and C does not contain all elements in the sample space. Hence, they are not exhaustive events.

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