NIMCET 2024 — Reasoning PYQ

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Question

NIMCET 2024 — Reasoning PYQ

NIMCET | Reasoning | 2024

In a reality show, two judges independently provided marks base do the performance of the participants. If the marks provided by the second judge are given by Y = 10.5 + 2x, where X is the marks provided by the first judge. If the variance of the marks provided by the second judge is 100, then the variance of the marks provided by the first judge is:

Choose the correct answer:

Explanation

To find the variance of the marks provided by the first judge ( $X$ ), given the relationship $Y = 10.5 + 2 X$ and $Var (Y) = 100$ :

Recall the variance transformation formula: For a linear transformation $Y = a X + b$ , the variance of $Y$ is $Var (Y) = a^{2} \times Var (X)$ .

Identify the constant $a$ : In the equation $Y = 10.5 + 2 X$ , the value of $a$ is $2$ .

Substitute the known values into the formula: Given $Var (Y) = 100$ and $a = 2$ , then
$100 = 2^{2} \times Var (X)$ .

Solve for $Var (X)$ :
$100 = 4 \times Var (X) \Rightarrow Var (X) = \frac{100}{4} = 25$ .

Therefore, the variance of the marks provided by the first judge is $25$ .