1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What are the order and degree respectively of the differential equation $$ \left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{0-6}=\frac{d^2 y}{d x^2} ? $$
A

2, 2

B

2, 3

C

5, 2

D

2, 5

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If $\frac{dy}{dx} = 2e^xy^3$, $y(0)= \frac{1}{2}$ then what is $4y^2(2-e^x)$ equal to?

A

1

B

2

C

3

D

4

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

$p=q$

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

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

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