1
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
2
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If $$x = \sin \theta $$ and $$y = \sin k\theta $$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$

A
k
B
$$-$$k
C
$$-$$k$$^2$$
D
k$$^2$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

A
never changes sign.
B
changes sign only once.
C
changes sign more than once but finitely many times.
D
changes sign infinitely many times.
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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