Practice Pakistan questions with answers and explanations.
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The common ratio is 3, so a₆ = 2 × 3⁵.
This equals 2 × 243 = 486.
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The expression is a difference of squares: x² - 3².
Thus, it factors as (x - 3)(x + 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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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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When multiplying powers with the same base, add the exponents.
Thus, a³ × a⁵ = a⁸.
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When dividing powers with the same base, subtract the exponents.
Thus, x⁷ ÷ x³ = x⁴.
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Square the coefficient and multiply the exponent by 2.
This gives 2²a⁶ = 4a⁶.
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An exponent of 1/2 represents a square root.
Thus, 16^(1/2) = √16 = 4.
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Since 32 = 2⁵, the exponents must be equal.
Therefore, x = 5.
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The train covers its length plus the platform length: 300 meters.
Speed = 300 ÷ 20 = 15 m/s.
