1
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
2
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
$\frac{5}{8}$
3
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
$y \sin x=c$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must have at least one bottle of each variety is
A
150
B
120
C
60
D
90
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