Practice IBA Undergraduate Aptitude questions with answers and explanations.
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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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The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.
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The three interior angles of every Euclidean triangle sum to 180°.
This is a fundamental angle property.
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The quadratic factors as (x - 2)(x - 3) = 0.
Therefore, x is 2 or 3.
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Triangle angles sum to 180°.
The third angle is 180° - 45° - 65° = 70°.
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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.
