WB JEE 2023 | Mathematical Induction and Binomial Theorem Question 20 | Mathematics

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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 $$n \in N$$.

WB JEE 2022

MCQ (Single Correct Answer)

-0.25

The number of zeros at the end of $$\left| \!{\underline {\, {100} \,}} \right. $$ is

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i}\,.\,{x^i}} $$, then a₁₇ is equal to

$${{2016!} \over {17!1999!}}$$

$${{2016!} \over {16!}}$$

$${{2017!} \over {2000!}}$$

$${{2017!} \over {17!2000!}}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.5

The coefficient of a³b⁴c⁵ in the expansion of (bc + ca + ab)⁶ is

$${{12!} \over {3!4!5!}}$$

$${{6!} \over {3!}}$$

$$3\,.\,\left( {{{6!} \over {3!3!}}} \right)$$

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