1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

$$\lim _\limits{n \rightarrow \infty} \frac{1}{n^{k+1}}[2^k+4^k+6^k+\ldots .+(2 n)^k]=$$

A
$$\frac{2^k}{k}$$
B
$$\frac{2^{k+1}}{k+1}$$
C
$$\frac{2^k}{k+1}$$
D
$$\frac{2^{\mathrm{k}}}{\mathrm{k}-1}$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

the expression $${{\int\limits_0^n {[x]dx} } \over {\int\limits_0^n {\{ x\} dx} }}$$, where $$[x]$$ and $$\{ x\} $$ are respectively integral and fractional part of $$x$$ and $$n \in N$$, is equal to

A
$${1 \over {n - 1}}$$
B
$${1 \over n}$$
C
$$n$$
D
$$n-1$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The value $$\int\limits_0^{1/2} {{{dx} \over {\sqrt {1 - {x^{2n}}} }}} $$ is $$(n \in N)$$

A
less than or equal to $${\pi \over 6}$$
B
greater than or equal to 1
C
less than $${1 \over 2}$$
D
greater than $${\pi \over 6}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $${I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx} $$, then I$$_1$$, I$$_2$$, I$$_3$$ ... are in

A
A.P.
B
G.P.
C
H.P.
D
no such relation
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