Question

$\text{Which of the following pair of}$
$\text{events are mutually exclusive events}$
$\text{on rolling a dice once}?$

• A. $\text{Getting an even number}$
  $\text{or getting a perfect number.}$
• B. $\text{Getting an even number}$
  $\text{or getting a perfect square number.}$
• C. $\text{Getting an odd number}$
  $\text{or getting a perfect number}$
• D. $\text{Getting an even prime number}$
  $\text{or getting a perfect number.}$

Answer 1

Answer: (C), (D)

The correct options are
C $\text{Getting an odd number}$
$\text{or getting a perfect number}$
D $\text{Getting an even prime number}$

$\text{or getting a perfect number.}$
When two events (call them "A" and "B") are Mutually Exclusive it is impossible for them to happen together.

'2', '4', '6' are even numbers and '6' is the only perfect number. A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
For instance, 6 has divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number.
So when '6' is obtained, both the events can happen together.

'4' is both a perfect square number and even number so, when '4' is obtained both the events can happen together.

'1', '3', '5' are odd numbers and '6' is the only perfect number. Both of these events cannot happen together.

'2' is the only even prime number and '6' is the only perfect number, therefore both these events can not happen together.