1
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

$p=q$

2
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

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

The non-negative values of $b$ for which the function $\frac{16x^3}{3} - 4bx^2 + x$ has neither maximum nor minimum in the range $x>0$ is

A

0 < b < 1

B

1 < b < 2

C

b > 2

D

0 <= b < 1

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

Which one of the following is correct in respect of $f(x) = \frac{1}{\sqrt{|x| - x}}$ and $g(x) = \frac{1}{\sqrt{x - |x|}}$?

A

$f(x)$ has some domain and $g(x)$ has no domain

B

$f(x)$ has no domain and $g(x)$ has some domain

C

$f(x)$ and $g(x)$ have the same domain

D

$f(x)$ and $g(x)$ do not have any domain

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