Statistics · JEE Main previous year questions

2025 8 questions

1. Q122025 · 4 Apr 2025 · Shift 1

   A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

   1. A.$\frac{11}{15}$
   2. B.$\frac{2}{15}$
   3. C.$\frac{3}{5}$
   4. D.$\frac{28}{75}$
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   Answer: D

2. Q32025 · 4 Apr 2025 · Shift 2

   Let the mean and the standard deviation of the observation $2,3,3,4,5,7,a,b$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is :

   1. A.$\frac{1}{2}$
   2. B.$\frac{3}{4}$
   3. C.1
   4. D.2
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   Answer: C

3. Q122025 · 3 Apr 2025 · Shift 2

   Let the Mean and Variance of five observations $x_1=1,x_2=3,x_3=a,x_4=7$ and $x_5=b,a>b$, be $5$ and $10$ respectively. Then the Variance of the observations $n+x_n,n=1,2,\dots ,5$ is

   1. A.$17$
   2. B.$16$
   3. C.$16.4$
   4. D.$17.4$
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   Answer: B

4. Q12025 · 2 Apr 2025 · Shift 2

   If the mean and the variance of $6,4,a,8,b,12,10,13$ are 9 and 9.25 respectively, then $a+b+ab$ is equal to :

   1. A.103
   2. B.106
   3. C.100
   4. D.105
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   Answer: A

5. Q112025 · 28 Jan 2025 · Shift 1

   Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denotes the number of defective oranges, then the variance of $x$ is

   1. A.$26/75$
   2. B.$14/25$
   3. C.$18/25$
   4. D.$28/75$
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   Answer: D

6. Q172025 · 24 Jan 2025 · Shift 1

   For a statistical data $x_1,x_2,\dots ,x_{10}$ of $10$ values, a student obtained the mean as $5.5$ and ${\sum }_{i=1}^{10}{x}_i^2=371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$ , instead of the correct values $6$ and $8$ , respectively. The variance of the corrected data is

   1. A.$5$
   2. B.$7$
   3. C.$9$
   4. D.$4$
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   Answer: B

7. Q252025 · 23 Jan 2025 · Shift 2· Numerical answer

   The variance of the numbers $8,21,34,47,\dots ,320$ is _________.

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   Answer: 8788

8. Q112025 · 22 Jan 2025 · Shift 1

   A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and ${\sigma }^2$ denote the mean and variance of $X$, then the value of $64\left(\mu +{\sigma }^2\right)$ is:

   1. A.64
   2. B.32
   3. C.51
   4. D.48
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   Answer: D