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

Let $y_1(x)$ and $y_2(x)$ be two solutions of the differential equation $\frac{dy}{dx} = x$. If $y_1(0) = 0$ and $y_2(0) = 4$, then what is the number of points of intersection of the curves $y_1(x)$ and $y_2(x)$?

A

No point

B

One point

C

Two points

D

More than two points

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

The differential equation, representing the curve $y = e^{x}(a\cos{x} + b\sin{x})$ where $a$ and $b$ are arbitrary constants, is

A

$\frac{d^2y}{dx^2} + 2y = 0$

B

$\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + 2y = 0$

C

$\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0$

D

$\frac{d^2y}{dx^2} + y = 0$

3
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

4
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

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