NIMCET 2013 — Mathematics PYQ

Q: How do I solve NIMCET 2013 Mathematics questions?

Practice NIMCET 2013 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2013 — Mathematics PYQ

NIMCET | Mathematics | 2013

A random variable X has the distribution law as given below:

The variance of the distribution is:

Choose the correct answer:

Explanation

Solution

Step 1: Calculate the Mean (Expected Value), $E(X)$

$E(X) = \sum x_i P(x_i)$

$E(X) = (1 \times 0.3) + (2 \times 0.4) + (3 \times 0.3)$

$E(X) = 0.3 + 0.8 + 0.9$

$E(X) = 2.0$

Step 2: Calculate $E(X^2)$

$E(X^2) = \sum x_i^2 P(x_i)$

$E(X^2) = (1^2 \times 0.3) + (2^2 \times 0.4) + (3^2 \times 0.3)$

$E(X^2) = (1 \times 0.3) + (4 \times 0.4) + (9 \times 0.3)$

$E(X^2) = 0.3 + 1.6 + 2.7$

$E(X^2) = 4.6$

Step 3: Calculate the Variance, $Var(X)$

$Var(X) = E(X^2) - [E(X)]^2$

$Var(X) = 4.6 - (2.0)^2$

$Var(X) = 4.6 - 4.0$

$Var(X) = 0.6$

Final Answer:

The variance of the distribution is $0.6$ , which corresponds to Option 2.