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UPSC NDA I and II 2020 Math Solved Paper

Question Numbers: 1-3

Directions: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by

n(Z)

. which is equal to 90.

Question : 3 of 120

Marks: +1, -0

Solution:

Concept:

The complement of set

X

U - n(X)

, where

U

is the universal set.

Explanation:

Let

n(U)

be the total number of elements.

Elements not in

X

Y

, or

Z

are

p

, so

n(U) - n(X \cup Y \cup Z) = p

From the Venn diagram,

n(X \cup Y \cup Z) = a + b + 106

Thus

n(U) = p + a + b + 106

Now

n(X)

includes the regions:

a

(only

X

), plus intersections:

16

18

12

n(X) = a + 16 + 18 + 12 = a + 46

The complement of

X

n(U) - n(X) = (p + a + b + 106) - (a + 46)

Simplify:

p + a + b + 106 - a - 46 = p + b + 60

Answer:

p + b + 60

(Option A).

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