MHT-CET

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

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Q1.

If ${ }^{n} C_0+\frac{1}{2}{ }^{n} C_1+\frac{1}{3}{ }^{n} C_2+\ldots+\frac{1}{n+1}{ }^{n} C_{n}=\frac{1023}{10}$,then $n=$

(A)

$7$

(B)

$8$

(C)

$9$

(D)

$10$

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Q2.

Engineering Analysis & Principles: In technical analysis of 'Principle of Mathematical Induction' within 11. Binomial Theorem & Mathematical Induction, which governing relationship or mathematical model determines optimal system response under equilibrium conditions?

(A)

First-order linear differential operator with boundary conditions matching system eigenvalues (Principle of Mathematical Induction)

(B)

Zero-order static algebraic summation neglecting non-linear feedback

(C)

Unconstrained stochastic random walk without conservation criteria

(D)

Non-convergent divergence theorem with unbounded parameter drift

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