Statistics · JEE Main previous year questions

2019 10 questions

1. Q132019 · 12 Apr 2019 · Shift 1

   If the data $x_1,x_2,\dots ,x_{10}$ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

   1. A.$\sqrt{2}$
   2. B.2
   3. C.$2\sqrt{2}$
   4. D.4
   Show answer

   Answer: B

2. Q282019 · 12 Apr 2019 · Shift 1

   Let a random variable X have a binomial distribution with mean 8 and variance 4. If $P(X\le 2)=\frac{k}{2^{16}}$, then k is equal to :

   1. A.17
   2. B.1
   3. C.137
   4. D.121
   Show answer

   Answer: C

3. Q192019 · 10 Apr 2019 · Shift 1

   If for some $x\in \mathrm{R}$, the frequency distribution of the marks obtained by 20 students in a test is : | Marks | 2 | 3 | 5 | 7 | | Frequency | $(x+1{)}^2$ | $2x-5$ | $x^2-3x$ | $x$ | then the mean of the marks is

   1. A.3.0
   2. B.2.8
   3. C.2.5
   4. D.3.2
   Show answer

   Answer: B

4. Q182019 · 10 Apr 2019 · Shift 2

   If both the mean and the standard deviation of 50 observations $x_1,x_2,\dots ,x_{50}$ are equal to 16, then the mean of $(x_1-4{)}^2,(x_2-4{)}^2,\dots ,(x_{50}-4{)}^2$ is :

   1. A.400
   2. B.480
   3. C.380
   4. D.525
   Show answer

   Answer: A

5. Q42019 · 9 Apr 2019 · Shift 1

   If the standard deviation of the numbers –1, 0, 1, k is $\sqrt{5}$ where k > 0, then k is equal to

   1. A.$2\sqrt{6}$
   2. B.$\sqrt{6}$
   3. C.$2\sqrt{\frac{5}{6}}$
   4. D.$2\sqrt{\frac{10}{3}}$
   Show answer

   Answer: A

6. Q182019 · 9 Apr 2019 · Shift 2

   The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then $\frac{y}{x}$ is equal to

   1. A.$\frac{7}{2}$
   2. B.$\frac{8}{3}$
   3. C.$\frac{9}{4}$
   4. D.$\frac{7}{3}$
   Show answer

   Answer: D

7. Q22019 · 8 Apr 2019 · Shift 2

   A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

   1. A.$\frac{100}{\sqrt{3}}$
   2. B.$\frac{10}{\sqrt{3}}$
   3. C.$\frac{10}{3}$
   4. D.$\frac{100}{3}$
   Show answer

   Answer: B

8. Q82019 · 12 Jan 2019 · Shift 1

   If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

   1. A.31
   2. B.50
   3. C.51
   4. D.30
   Show answer

   Answer: A

9. Q182019 · 12 Jan 2019 · Shift 2

   The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

   1. A.1
   2. B.7
   3. C.3
   4. D.5
   Show answer

   Answer: B

10. Q62019 · 9 Jan 2019 · Shift 1

    5 students of a class have an average height $150\text{ cm}$ and variance $18{\text{ cm}}^2$. A new student, whose height is $156\text{ cm}$, joined them. The variance (in $\mathrm{c}{\mathrm{m}}^2$) of the height of these six students is :

    1. A.16
    2. B.22
    3. C.20
    4. D.18
    Show answer

    Answer: C