1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-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
A.P.
B
G.P.
C
H.P.
D
no such relation
2
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5

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

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

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

A
$${2 \over \pi }$$
B
$${3 \over \pi }$$
C
$${4 \over \pi }$$
D
$$\pi$$
4
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25

Let f be derivable in [0, 1], then

A
there exists $$c \in (0,1)$$ such that $$\int\limits_0^c {f(x)dx = (1 - c)f(c)}$$
B
there does not exist any point $$d \in (0,1)$$ for which $$\int\limits_0^d {f(x)dx = (1 - d)f(d)}$$
C
$$\int\limits_0^c {f(x)dx}$$ does not exist, for any $$c \in (0,1)$$
D
$$\int\limits_0^c {f(x)dx}$$ is independent of $$c,c \in (0,1)$$
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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