Practice Pakistan questions with answers and explanations.
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Matrix order is written as rows by columns.
Therefore, 3 rows and 4 columns give order 3 × 4.
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Matrix addition is performed entry by entry.
Each corresponding pair sums to 5.
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For [[a, b], [c, d]], determinant = ad - bc.
Thus, 2 × 4 - 3 × 1 = 5.
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An identity matrix has 1s on the main diagonal and 0s elsewhere.
It leaves a compatible matrix unchanged under multiplication.
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A square matrix is invertible only when its determinant is nonzero.
A zero determinant means the matrix is singular.
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The increase is 210 - 120 = 90 units.
The percentage increase is 90/120 × 100 = 75%.
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If 55% are girls, then 45% are boys.
Forty-five percent of 480 is 216.
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A full pie chart is 360°.
Thus, 72/360 × 100 = 20%.
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Use inclusion-exclusion: 80 + 60 - 20.
This gives 120 people who prefer at least one.
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The total production is 210 units.
Dividing by 4 gives 52.5 units.
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The sum is 40 and there are 5 values.
The mean is 40 ÷ 5 = 8.
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A fair coin has two equally likely outcomes.
One favorable outcome out of two gives probability 1/2.
