JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 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 JEE Mathematics questions?

JEE 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 JEE previous year papers available for free?

Yes. Mathem Solvex provides free access to JEE 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

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

If the variance of the frequency distribution

is 3, then a is equal to

Choose the correct answer:

Explanation

Solution

Step 1: Mean $(\bar{x})$ aur Variance $(\sigma^2)$ ka formula

Variance ka formula hota hai:

\sigma^2 = \frac{\sum f_i x_i^2}{\sum f_i} - \left( \frac{\sum f_i x_i}{\sum f_i} \right)^2

Step 2: Table calculation

Maana $\sum f_i = N = 3 + 6 + 16 + \alpha + 9 + 5 + 6 = 45 + \alpha$ .

Ab $\sum f_i x_i$ nikalte hain:

\sum f_i x_i = (2 \times 3) + (3 \times 6) + (4 \times 16) + (5 \times \alpha) + (6 \times 9) + (7 \times 5) + (8 \times 6)

\sum f_i x_i = 6 + 18 + 64 + 5\alpha + 54 + 35 + 48 = 225 + 5\alpha

Ab Mean $(\bar{x})$ nikalte hain:

\bar{x} = \frac{225 + 5\alpha}{45 + \alpha} = \frac{5(45 + \alpha)}{45 + \alpha} = 5

Step 3: $\sum f_i x_i^2$ ki calculation

\sum f_i x_i^2 = (2^2 \times 3) + (3^2 \times 6) + (4^2 \times 16) + (5^2 \times \alpha) + (6^2 \times 9) + (7^2 \times 5) + (8^2 \times 6)

\sum f_i x_i^2 = 12 + 54 + 256 + 25\alpha + 324 + 245 + 384 = 1275 + 25\alpha

Step 4: Variance formula mein value rakhne par

Diya gaya hai ki $\sigma^2 = 3$ :

3 = \frac{1275 + 25\alpha}{45 + \alpha} - (5)^2

3 + 25 = \frac{1275 + 25\alpha}{45 + \alpha}

28 = \frac{1275 + 25\alpha}{45 + \alpha}

Ab cross-multiplication karein:

28(45 + \alpha) = 1275 + 25\alpha

1260 + 28\alpha = 1275 + 25\alpha

28\alpha - 25\alpha = 1275 - 1260

3\alpha = 15

\alpha = 5

Ans: $\alpha = 5$

Choose the correct answer:

Explore More