WB JEE 2011 | Mathematical Induction Question 5 | Mathematics

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WB JEE 2011

MCQ (Single Correct Answer)

+1

-0.25

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

A

10⁴

B

10⁶

C

10⁸

D

10¹²

2

WB JEE 2023

MCQ (Single Correct Answer)

+1

-0.25

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

A

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

B

there exists prime integer which divides P(n).

C

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

D

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

3

WB JEE 2019

MCQ (Single Correct Answer)

+1

-0.25

7²ⁿ + 16n $$-$$1 (n$$ \in $$ N) is divisible by

A

65

B

63

C

61

D

64

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