Practice Pakistan questions with answers and explanations.
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Set x - 3 equal to 5 and -5.
The resulting solutions are x = 8 and x = -2.
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Square the equation: x² + 2 + 1/x² = 25.
Subtracting 2 gives x² + 1/x² = 23.
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Use a² + b² = (a + b)² - 2ab.
Thus, 144 - 70 = 74.
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Add the geometric terms directly.
Their total is 31.
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The first term is 8 and common ratio is 1/2.
The sum is a/(1-r) = 8/(1/2) = 16.
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For ax² + bx + c = 0, the sum of roots is -b/a.
Here, -(-9)/1 = 9.
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For ax² + bx + c = 0, the product of roots is c/a.
Here, 20/1 = 20.
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Substitute x = -4 into the expression.
Then y = 3(-4) - 2 = -14.
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Slope-intercept form is y = mx + c.
With m = 2 and c = 3, the equation is y = 2x + 3.
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A point with x = 0 gives the y-intercept 4.
Using y = mx + c with m = -1 gives y = -x + 4.
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The sum of the roots is 6.
Their average is 6/2 = 3.
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The total population is 100,000.
The largest town has 45,000, so the fraction is 45/100 = 9/20.
