Pakistan MCQs

An identity matrix has 1s on the main diagonal and 0s elsewhere.
It leaves a compatible matrix unchanged under multiplication.

For independent events, multiply their probabilities.
Thus, 1/2 × 1/3 = 1/6.

A square matrix is invertible only when its determinant is nonzero.
A zero determinant means the matrix is singular.

There are 2 favorable blue balls out of 5 total balls.
The probability is therefore 2/5.

The probability is 4/10 × 3/9.
This simplifies to 12/90 = 2/15.

Three distinct objects can be arranged in 3! ways.
Thus, 3! = 3 × 2 × 1 = 6.

The number of arrangements of 5 distinct objects is 5!.
Thus, 5! = 120.

Selection without order uses combinations.
5C2 = 5 × 4 ÷ 2 = 10.

A set with n elements has 2ⁿ subsets.
For n = 5, this is 2⁵ = 32.

There are 4 choices for the first digit, then 3, then 2.
Thus, 4 × 3 × 2 = 24.

Use n(M ∪ E) = n(M) + n(E) - n(M ∩ E).
Thus, 22 + 18 - 8 = 32.

There are 5 letters with L repeated twice and E repeated twice.
Distinct arrangements = 5!/(2!2!) = 30.