1
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The difference between the distance of any point on the hyperbola from the two foci is $\mathbf{1 6}$ and the eccentricity is $\mathbf{2}$. Then the equation of the hyperbola is

A

$\frac{x^2}{64}-\frac{y^2}{64}=1$

B

$\frac{x^2}{64}-\frac{y^2}{256}=1$

C

$\frac{x^2}{64}-\frac{y^2}{192}=1$

D

$\frac{x^2}{192}-\frac{y^2}{64}=1$

2
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } x=a(\theta-\sin \theta) \text { and } y=a(1-\cos \theta) \text {, then } \frac{\left(\mathbf{1}+\boldsymbol{y}_{\mathbf{1}}{ }^{\mathbf{2}}\right)^{\mathbf{3} / \mathbf{2}}}{\boldsymbol{y}_{\mathbf{2}}}= $$

A

$$ -4 a \sin \left(\frac{\theta}{2}\right) $$

B

$$ -\frac{1}{2 \sin ^2\left(\frac{\theta}{2}\right)} $$

C

$$ 4 a \operatorname{cosec}^2\left(\frac{\theta}{2}\right) $$

D

$$ -\frac{1}{4 a} \sin \left(\frac{\theta}{2}\right) $$

3
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The area of the region in the first quadrant enclosed by the $x$-axis, the line $x=\sqrt{3} y$ and the circle $x^2+y^2=4$ is

A

$\frac{\pi}{6}$ sq units

B

$\frac{2 \pi}{3}$ sq units

C

$\pi$ sq units

D

$\frac{\pi}{3}$ sq units

4
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Which of the following is the simplest form of the expression $\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}}\left(\frac{\sqrt{\mathbf{1 + x ^ { \mathbf { 2 } }}}-\mathbf{1}}{\boldsymbol{x}}\right)$ where $x \neq 0$

A

$2 \tan ^{-1} x$

B

$\tan ^{-1} \frac{x}{2}$

C

$\frac{1}{2} \tan ^{-1} x$

D

$\tan ^{-1} x$