1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is

A
$${{\sin x} \over {x\sin x + \cos x}}$$
B
$${1 \over {{{(x\sin x + \cos x)}^2}}}$$
C
$${{ - x} \over {\cos x(x\sin x + \cos x)}}$$
D
$${1 \over {\sin x(x\cos x + \sin x)}}$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}^4}}}} \right\} + c} $$, then the value of k is

A
4
B
6
C
8
D
12
3
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
$$n-1$$
4
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 $${\pi \over 6}$$
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