Practice Pakistan questions with answers and explanations.
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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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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.
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Travel time is 210 ÷ 70 = 3 hours.
Three hours after 8:00 a.m. is 11:00 a.m.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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Their closing speed is 20 + 25 = 45 km/h.
Time = 90 ÷ 45 = 2 hours.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
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When multiplying powers with the same base, add the exponents.
Thus, a³ × a⁵ = a⁸.
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The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
