1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

What is $\int^{1}_{-1}(3\sin x-\sin 3x)\cos^2 xdx$ equal to?

A

$\frac{1}{4}$

B

0

C

$\frac{1}{2}$

D

$\frac{1}{4}$

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Let $p=\int_a^b f(x) d x$ and $q=\int_a^b|f(x)| d x$. If $f(x)=e^{-x}$, then which one of the following is correct ?
A

$p=2q$

B

$p=-q$

C

$4p=q$

D

$p=q$

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

What is $\int^{\pi/2}_0 \frac{a+\sin x}{2a+\sin x+\cos x} dx$ equal to?

A

$\frac{\pi}{4}$

B

$\frac{\pi}{2}$

C

1

D

0

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83

Let $f(x)=|x-1|, g(x)=[x]$ and $h(x)=f(x) g(x)$ where [.] is greatest integer function.

What is $\int\limits_{-1}^{0} h(x) dx$ equal to?

A

$-\frac{3}{2}$

B

$-1$

C

$0$

D

$\frac{1}{2}$

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