1
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
$a+3 b>0$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . . \tan 88^{\circ} \tan y^{\circ}=1$ then $\cot (x+y)=$
A
0
B
1
C
$\frac{1}{2}$
D
Undefined
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Vasant and Jothi play a game with a coin. Vasant stakes ₹ 1 and throw the coins four times. If he throws four heads, he gets his stake and ₹3 from Jothi. If he throws only three heads and they are consecutive, he gets his stake and ₹2 from Jothi. If he throws only two heads and they are consecutive, he gets his stake and ₹1 from Jothi. In all other cases Jothi takes the stake money. Find the expectation of Vasant's gain.
A
$-\frac{5}{8}$
B
0
C
1
D
$\frac{5}{8}$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The solution of the differential equation $\frac{d y}{d x}+y \log y \cot x=0$ is
A
$\cos x \log y=c$
B
$\log y=c \sin x$
C
$\sin x \log y=c$
D
$y \sin x=c$
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