MHT-CET

11. Binomial Theorem & Mathematical Induction question bank (Mathematics)

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Q1.

If $^nC_0 + \frac{1}{2} ^nC_1 + \frac{1}{3} ^nC_2 + \dots + \frac{1}{n+1} ^nC_n = \frac{1023}{10}$, then $n =$ ?

(A)

$7$

(B)

$8$

(C)

$9$

(D)

$10$

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Q2.

GATE Technical Standard: In computational modeling of 'Principle of Mathematical Induction', 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 (Principle of Mathematical Induction)

(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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