UPSC NDA 2 2019 Mathematics Solved Paper

As, sum of first n natural number =

n(n+1)

2

So, sum of first 15 natural number∴ M = Mean of first 15 natural number=

15×8

18

=8
∴M=8
[first 15 natural numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
Now, variance, V=

1

n

‌∑(xi−M)2
=

1

15

[280]=

56

3

∴V+M2=

56

3

+82=

56

3

+64
=

56+192

3

=

248

3