1
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $$X$$ and $$Y$$ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then $$n(X \cap Y)$$ is equal to

A
12
B
10
C
8
D
6
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is

A
120
B
78
C
132
D
720
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If three numbers $$a, b, c$$ constitute both an A.P and G.P, then

A
$$ a=b=c $$
B
$$ a=b+c $$
C
$$ a b=c $$
D
$$ a=b-c $$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \cos ^6 A-\sin ^6 A \text { is equal to } $$

A
$$ \cos 2 A\left(1-\frac{1}{4} \sin ^2 2 A\right) $$
B
$$ \cos 2 A\left(1-\frac{3}{4} \sin ^2 2 A\right) $$
C
$$ \cos 2 A\left(1-\frac{1}{2} \sin ^2 2 A\right) $$
D
$$ \cos 2 A\left(1+\frac{1}{4} \sin ^2 2 A\right) $$
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