1
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0

The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx} $$ is

A
$${{100!} \over {{{(100)}^{100}}}}$$
B
$${1 \over {100}}$$
C
0
D
$${\pi \over {100}}$$
2
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0

OA and OB are two roads enclosing an angle of 120$$^\circ$$. X and Y start from O at the same time. X travels along OA with a speed of 4 km/h and Y travels along OB with a speed of 3 km/h. The rate at which the shortest distance between X and Y is increasing after 1 hour is

COMEDK 2020 Mathematics - Application of Derivatives Question 20 English

A
37 km/h
B
$$\sqrt{37}$$ km/h
C
$$\sqrt{13}$$ km/h
D
13 km/h
3
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0

If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} } $$, then the value of $$k$$ is

A
3
B
9
C
1/3
D
1/9
4
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0

The value of $$\int {{1 \over {1 + \cos 8x}}dx} $$ is

A
$${{\tan 8x} \over 8} + C$$
B
$${{\tan 2x} \over 8} + C$$
C
$${{\tan 4x} \over 8} + C$$
D
$${{\tan 4x} \over 4} + C$$
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