MHT-CET

Basic of Logarithms question bank (Mathematics)

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Q1.

If $x, y, z$ are the sides of a right-angled triangle, where $z$ is the hypotenuse (largest side), then find the value of $\frac{1}{\log_{x+z} y} + \frac{1}{\log_{z-x} y}$.

(A)

$1$

(B)

$2$

(C)

$3$

(D)

$4$

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Q2.

GATE Technical Standard: In computational modeling of 'Mix Examples-Logarithms, Indices and Surds, Partial Fractions', what constitutes the primary performance trade-off regarding asymptotic efficiency and resource conservation?

(A)

Minimizing peak algorithmic runtime and memory latency through optimal dynamic constraints (Mix Examples-Logarithms, Indices and Surds, Partial Fractions)

(B)

Maximizing redundant register transfers to force artificial synchronization

(C)

Arbitrary thread serialization without mutex coordination or race mitigation

(D)

Unbounded stack consumption with circular recursive invocation

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