WB JEE 2023 | Definite Integration Question 27 | Mathematics

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

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

less than or equal to $${\pi \over 6}$$

greater than or equal to 1

less than $${1 \over 2}$$

greater than $${\pi \over 6}$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

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

A.P.

G.P.

H.P.

no such relation

WB JEE 2023

MCQ (Single Correct Answer)

-0.5

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

$${\pi \over {16}}$$

$${{3\pi } \over {16}}$$

$${{16\pi } \over 3}$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.5

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

$${2 \over \pi }$$

$${3 \over \pi }$$

$${4 \over \pi }$$

$$\pi $$

WB JEE Subjects