Practice Pakistan questions with answers and explanations.
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Since 32 = 2⁵, the exponents must be equal.
Therefore, x = 5.
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The logarithm asks what power of 10 gives 1,000.
Since 10³ = 1,000, the answer is 3.
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The logarithmic equation means x = 2⁶.
Thus, x = 64.
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The common difference is 4.
Adding 4 to 19 gives 23.
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The nth term is a + (n - 1)d.
Thus, 3 + 9 × 4 = 39.
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Each term is multiplied by 2.
Thus, 24 × 2 = 48.
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The common ratio is 3, so a₆ = 2 × 3⁵.
This equals 2 × 243 = 486.
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Substitute x = 5 into the function.
Then f(5) = 2(5) + 1 = 11.
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Time is inversely proportional to speed.
The decrease is 1 - 50/60 = 1/6 = 16 2/3%.
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The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.
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Let total distance be 3d; time is d/30 + 2d/60 = d/15.
Average speed is 3d ÷ (d/15) = 45 km/h.
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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
