JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable

x

to be the number of rotten apples in a draw of two apples, the variance of

x

(1) $\frac{37}{153}$
(2) $\frac{40}{153}$ Official answer
(3) $\frac{47}{153}$
(4) $\frac{57}{153}$

Official answer

Option 2

NTA final key.

Chapter: Probability
Topic: Variance and SD
Idea tested: Variance via Relative Frequencies

Same topic in other shifts

All Variance and SD questions

2 Apr 2026, Shift 1 · Q8If the mean of the data | Class | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | | Frequency | 2 | $k$ | 28 | 54 | $k+1$ | 5 | is $21$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q9The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first $(n - 1)$ observations is 48 and the sum of…EasySingle correct
4 Apr 2026, Shift 2 · Q8For 10 observations $x_1,x_2,\ldots,x_{10}$ , if $\sum_{i=1}^{10}(x_i+2)^2=180$ and $\sum_{i=1}^{10}(x_i-1)^2=90$ , then their standard…MediumSingle correct
6 Apr 2026, Shift 1 · Q9A data consists of 20 observations $x_1, x_2,\ldots, x_{20}$ . If $\sum_{i=1}^{20}(x_i+5)^2=2500$ and $\sum_{i=1}^{20}(x_i-5)^2=100$ , then…MediumSingle correct
6 Apr 2026, Shift 2 · Q8Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$ , $\alpha<\beta$ , be 8 and 16 respectively. Then the…MediumSingle correct
8 Apr 2026, Shift 2 · Q7A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.