WB JEE 2022 | Sequence and Series Question 25 | Mathematics

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WB JEE 2022

MCQ (Single Correct Answer)

-0.25

Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

$${a_n} < {b_n}\forall n$$

$${a_n} > {b_n}\forall n$$

$${a_n} = {b_n}$$ for infinitely many n

$${a_n} < {b_n}$$ if n be even and $${a_n} > {b_n}$$ if n be odd

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the value of b is 9, then the value of 'a' must be

$$\root 3 \of {81} $$

$${{27} \over 2}$$

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p) = $${1 \over 2}$$ {h(p + 1) + h(p $$-$$ 1)} for every p = 1, 2 ..... 99. Then the value of h(1) is

5.15

5.5

6.15

WB JEE 2021

MCQ (Single Correct Answer)

-0.25

The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is

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