WB JEE 2011 | Mathematical Induction and Binomial Theorem Question 17 | Mathematics

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The number (101)¹⁰⁰ $$-$$ 1 is divisible by

10⁴

10⁶

10⁸

10¹²

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

If A and B are coefficients of xⁿ in the expansions of (1 + x)²ⁿ and (1 + x)^{2n $$-$$ 1} respectively, then A/B is equal to

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

If n > 1 is an integer and x $$\ne$$ 0, then (1 + x)ⁿ $$-$$ nx $$-$$ 1 is divisible by

nx³

n³x

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then

P(n) is not divisible by any prime integer.

there exists prime integer which divides P(n).

P(n) is divisible by 5 for all $$n \in N$$.

P(n) is divisible by 3 for all $$n \in N$$.

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