Practice IBA Mathematics questions with answers and explanations.
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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 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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The required numbers multiply to 6 and add to 5.
Those numbers are 2 and 3.
