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

Let $\vec{a}$ and $\vec{b}$ be two vectors of magnitude 4 inclined at an angle $\frac{\pi}{3}$, then what is the angle between $\vec{a}$ and $\vec{a} - \vec{b}$?

A

$\frac{\pi}{2}$

B

$\frac{\pi}{3}$

C

$\frac{\pi}{4}$

D

$\frac{\pi}{6}$

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

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

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

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

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

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

If $f(x)=ax-b$ and $g(x)=cx+d$ are such that $f(g(x))=g(f(x))$, then which one of the following holds?

A

$f(d) = g(b)$

B

$f(b)+g(d)=0$

C

$f(a)+g(c)=2a$

D

$f(d)+g(b)=2d$

EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12