1
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the third ball drawn is black is

A
$$\frac{17}{30}$$
B
$$\frac{37}{60}$$
C
$$\frac{31}{60}$$
D
$$\frac{23}{30}$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is

A
$$x+y \pm 5 \sqrt{2}=0$$
B
$$x-y \pm 2 \sqrt{5}=0$$
C
$$x+y \pm 2 \sqrt{5}=0$$
D
$$x-y \pm 5 \sqrt{2}=0$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

Given $$a, b, c$$ are three unequal numbers such that $$\mathrm{b}$$ is arithmetic mean of $$a$$ and $$c$$ and $$(b-a),(c-b), a$$ are in geometric progression. Then $$a: b: c$$ is

A
$$2: 3: 5$$
B
$$1: 2: 4$$
C
$$1: 2: 3$$
D
$$1: 3: 5$$
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to } $$

A
$$ -\frac{2}{x^2} $$
B
$$ -\frac{1}{x} $$
C
$$ -\frac{1}{x^2} $$
D
$$ \frac{2}{x^2} $$
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