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

$$ \begin{aligned} &\text { Consider two skew lines in 3D space. }\\ &M_1: \frac{x-1}{1}=\frac{2-y}{1}=\frac{z-5}{1} \text { and } M_2: \frac{x+3}{1}=\frac{y-7}{2}=\frac{z+4}{1} \end{aligned} $$

Let $L_1$ be the line of shortest distance (common perpendicular) between $M_1$ and $M_2$

If $L_2$ is a line parallel to the vector $\vec{b}=\hat{\jmath}+\hat{k}$,

Then the acute angle $\boldsymbol{\theta}$ between the lines $L_1$ and $L_2$ is:

A

$30^{\circ}$

B

$45^{\circ}$

C

$\cos ^{-1}\left(\frac{1}{3}\right)$

D

$60^{\circ}$

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

$$ \int \frac{d x}{x \sqrt{x^2+4}}= $$

A

$$ \frac{1}{4} \log \left|\frac{\sqrt{x^2+4}-2}{\sqrt{x^2+4}+2}\right|+C $$

B

$$ \frac{1}{4} \log \left|\frac{\sqrt{x^2+4}+2}{\sqrt{x^2+4}-2}\right|+C $$

C

$$ \frac{1}{2} \log \left|\frac{\sqrt{x^2+4}+2}{\sqrt{x^2+4}-2}\right|+C $$

D

$$ \frac{1}{2} \log \left|\frac{\sqrt{x^2+4}-2}{\sqrt{x^2+4}+2}\right|+C $$

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

Let $A$ and $B$ be two subsets of $\xi=\{\mathbf{1}, \mathbf{2}, \mathbf{3},-------, \mathbf{4 4}, \mathbf{4 5}\}$ such that

$A=\{x: x$ is divisible by 3 and 4$\}$

$B=\{x: x$ is a perfect square number $\}$

Then $n(B-A)$ equals

A

2

B

9

C

5

D

1

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

If $P(A \cup B)=0.85, P(B)=0.50$ and $P(A \cap B)=0.30$. Then $P\left(A \cap B^{\prime}\right)=$

A

0.65

B

0.55

C

0.35

D

0.2