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

Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ internally and externally in the ratio 2:3 respectively, then $\overrightarrow{O R}$ and $\overrightarrow{O S}$ are perpendicular when

A

$4|\vec{p}|^2=9|\vec{q}|^2$

B

$9|\vec{p}|=4|\vec{q}|^2$

C

$9|\vec{p}|^2=4|\vec{q}|^2$

D

$4|\vec{p}|^2=9|\vec{q}|$

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

The length of the latus rectum of the curve represented by $x=3(\cos t+\sin t)$ and $y=4(\cos t-\sin t)$ is:

A

$\frac{32 \sqrt{2}}{3}$

B

$9 \sqrt{2}$

C

$\frac{9}{\sqrt{2}}$

D

$\frac{9}{2}$

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

If the function $f(x)=x^4-31 x^2+\boldsymbol{a} x+5$ has a turning point at $x=1$, then the value of ' $\boldsymbol{a}$ ' is $\_\_\_\_$ and the function attains a $\_\_\_\_$ at $x=1$

A

$a=50$, local minima

B

$a=58$, local maxima

C

$a=58$, local minima

D

$a=-50$, local maxima

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

Advika chooses one of three scarves every morning: Red, Blue, or Green.

  • The probability she chooses Red is $20 \%$.

  • The probability she chooses Blue is twice the probability of choosing Red.

  • On the remaining days she wears a Green scarf.

Once a scarf is chosen, she decides whether to wear a Hat (H) and Sunglasses (S).

These choices are independent of each other but depend on the scarf colour:

$$ \begin{array}{|l|l|l|} \hline \text { Scarf colour } & \mathbf{P ( H )} & \mathbf{P ( S )} \\ \hline \text { Red } & 0.5 & 0.8 \\ \hline \text { Blue } & 0.4 & 0.5 \\ \hline \text { Green } & 0.1 & 0.5 \\ \hline \end{array} $$

Advika is spotted outdoors wearing both a Hat and Sunglasses.

What is the probability that she is wearing the Red scarf?

A

$$ \frac{13}{313} $$

B

$$ \frac{8}{21} $$

C

$$ \frac{4}{9} $$

D

$$ \frac{8}{13} $$