1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the distance between the foci is equal to the length of the latus rectum, then the eccentricity of the ellipse is
A
$\frac{\sqrt{5}+1}{2}$
B
$\frac{1-\sqrt{5}}{2}$
C
$\frac{\sqrt{5}-1}{2}$
D
$\frac{1 \pm \sqrt{5}}{2}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
In an entrance test, there are multiple choice questions. There are four possible answers to each question of which only one is correct. The probability that a student knows the answer to a question is $90 \%$. If he gets the correct answer to a question, then the probability that he was guessing is
A
$\frac{36}{37}$
B
$\frac{1}{9}$
C
$\frac{1}{37}$
D
$\frac{37}{40}$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The magnitude of the projection of the vector $-\hat{\imath}+2 \hat{\jmath}-\hat{k}$ on the z -axis is
A
2
B
$\frac{1}{\sqrt6}$
C
1
D
$-\frac{1}{\sqrt6}$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A solid S is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are $x \mathrm{~cm}$. The height of the cylinder is $(20-4 x) \mathrm{cm}$ and the volume of S is $V=\frac{1}{3} \pi y$. Find the maximum value of $y$.
A
480
B
360
C
320
D
160
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