1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The range of $x$ for which the equation $\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)=2 \tan ^{-1} x$ holds true
A
$|x| \leq 1$
B
$\forall x \in R$
C
$x \geq 0$
D
$|x| \geq 1$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A spherical snowball is melting such that its volume is decreasing at the rate of $1 \mathrm{~cm}^3 / \mathrm{min}$. The rate at which the diameter is decreasing when the diameter is 10 cm is
A
$\frac{11}{75 \pi} \mathrm{~cm} / \mathrm{min}$
B
$\frac{1}{50 \pi} \mathrm{~cm} / \mathrm{min}$
C
$\frac{2}{75 \pi} \mathrm{~cm} / \mathrm{min}$
D
$\frac{1}{25 \pi} \mathrm{~cm} / \mathrm{min}$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0

For a given Linear Programming problem, the objective function is

$$z=3 x+2 y$$

Subject to constraints are

$$\begin{aligned} & 4 x+3 y \leq 60 \\ & x \geq 3 \\ & y \leq 2 x \\ & y \geq 0 \end{aligned}$$

P is one of the corner points of the feasible region for the given Linear Programming problem. Then the coordinate of P is

A
$(3,6)$
B
$(0,20)$
C
$(0,0)$
D
$(12,6)$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The curve $a x^3+b x^2+c x+d$ has a point of minima at $x=1$, then
A
$3 a+b<0$
B
$3 a+b>0$
C
$3 a+b=0$
D
$a+3 b>0$
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