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NDA (II) 2023 · Mathematics

A full Mathematics paper in the UPSC NDA pattern. 120 questions in 150 minutes, with a third of the marks deducted for every wrong answer.

120questions

300marks

+2.5 / −0.83per question

28/66/26easy / medium / hard

Sections and topics

One 120-question Mathematics paper covering algebra, trigonometry, calculus, geometry, vectors, statistics and probability.

Sets · medium

Let

A\subset B

with

n(A)=3

and

n(B)=6

. The number of sets

C

such that

A\subseteq C\subseteq B

Show answer and solution

Answer: C
Every such

C

contains all 3 elements of

A

and any subset of the remaining

6-3=3

elements of

B

. Hence the count is

2^3=8

. The trap is to use

2^6=64

(all subsets of

B

) or to exclude

C=A

C=B

, which are both allowed because the inclusions are not strict.