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Give me question paper for National Defence Academy mathematics examination organized by UPSC ?

[Arun Vats]

Here I am giving you question paper for National Defence Academy mathematics examination organized by UPSC in a PDF file attached with it so you can get it easily.

1. If A and ~ ' & e subsets of a set X,
then what is (A n (X - B)) u B equal
to? . P
(a) A v B

2. The total number of subsets of a
finite set A has 56 more elements
than the total number of subsets of
another finite set B. What is the
number of elements in the set A?

3. What is the smallest natural
number n such that n! is divisible
by 990 3
(4 9
(4 11
(c) 33

(4 99
4. Which one of the following is correct?
(a) Ax(B-C)=(A-B)x(A-C)
(b) Ax(B-C)=(AxB)-(AXC)
(c) An(BuC)=[AnB)vC
(d) A u ( B n C ) = ( A u B ) n C

5. In an examination out of 100
students, 75 passed in English,
60 passed in Mathematics and
45 passed in both English and
Mathematics, What' is the number
of stude&s passed in exactly one of
the two subjects?

6, Let
R= { X ~ X E N, x is a multiple of 3
and x 5 100)
S = {x lx E N, x is a multiple of 5
and x 5 100)
What is the number of elements in
{Rx S) n(Sx R)?

7. If A = (a, b, c} and R= {(a, a), (a, b),
(b* 4, (b, 4, (G 4, fcY 41 is a
binary relation on A, then which
one of the following is correct?
(a) R is reflexive and symmetric,
but not transitive
(b) R is reflexive and transitive,
but not symmetric
(c) R is reflexive, but neither
symmetric nor transitive,
(d) R is reflexive, symmetric and
transitive