1
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 $${\pi \over 6}$$
2
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
3
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

$$\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta } $$ is equal to

A
$${\pi \over {16}}$$
B
$${{3\pi } \over {16}}$$
C
$${{16\pi } \over 3}$$
D
0
4
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

The average ordinate of $$y = \sin x$$ over $$[0,\pi ]$$ is :

A
$${2 \over \pi }$$
B
$${3 \over \pi }$$
C
$${4 \over \pi }$$
D
$$\pi $$
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