Region is defined as the region in the first quadrant satisfying the condition . Given that a point lies in , what is the probability that ?

1/2 Explanation: Consider the region and let be a point in the first quadrant chosen uniformly from this region. We want to find the probability that The region is a quarter circle of radius . The line divides this quarter circle into two congruent regions of equal area. Therefore, the probability is

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NIMCET 2024 — Mathematics PYQ

NIMCET | Mathematics | 2024

Region $R$ is defined as the region in the first quadrant satisfying the condition $x^2 + y^2 < 4$ . Given that a point $P = (r, s)$ lies in $R$ , what is the probability that $r > s$ ?

Choose the correct answer:

A.
1
B.
0
C.
1/2
(Correct Answer)
D.
1/3

Correct Answer:

1/2

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Explanation

Consider the region
$x^2 + y^2 < 4,$
and let $P = (r, s)$ be a point in the first quadrant chosen uniformly from this region.

We want to find the probability that
$r > s.$

The region is a quarter circle of radius $2$ .
The line $r = s$ divides this quarter circle into two congruent regions of equal area.

Therefore, the probability is
$P (E) = \frac{1}{2} .$

Explanation

Consider the region
$x^2 + y^2 < 4,$
and let $P = (r, s)$ be a point in the first quadrant chosen uniformly from this region.

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