1
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

$\frac{9}{2}$

2
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

3
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

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

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

$$ \int \frac{e^{\log \left(1+\frac{1}{x^2}\right)}}{x^2+\frac{1}{x^2}} d x= $$

A

$$ \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^2+1}{x \sqrt{2}}\right)+C $$

B

$$ \frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{x^2-1}{\sqrt{2} x}\right)+C $$

C

$$ -\frac{1}{\sqrt{2}} \tan ^{-1}\left(x-\frac{1}{x}\right)+C $$

D

$$ \frac{1}{\sqrt{2}} \tan ^{-1}\left(x-\frac{1}{x}\right)+C $$