Statistics · NDA previous year questions

2023 14 questions

1. Q1022023 · 3 Sept 2023

   If $\bar{X}=20$ is the mean of 10 observations $x_1,x_2,\dots x_{10}$; then what is the value of ${\sum }_{i=1}^{10}\left(\frac{3x_i-4}{5}\right)$?

   1. A.0
   2. B.12
   3. C.112
   4. D.1012
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   Answer: C

2. Q1032023 · 3 Sept 2023

   If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

   1. A.16
   2. B.6
   3. C.5
   4. D.4
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   Answer: D

3. Q1082023 · 3 Sept 2023

   What is the mean of the numbers 1, 2, 3, ... 10 with frequencies ${}^9{C}_0,{}^9{C}_1,{}^9{C}_2\dots ,{}^9{C}_9$, respectively?

   1. A.$1.1\times 2^8$
   2. B.$1.2\times 7^4$
   3. C.5.5
   4. D.0.55
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   Answer: C

4. Q1112023 · 3 Sept 2023

   If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?

   1. A.-r
   2. B.r
   3. C.√3 r
   4. D.-√3r
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   Answer: A

5. Q1132023 · 3 Sept 2023

   If H is the Harmonic Mean of three numbers ${}^{10}{C}_4$, ${}^{10}{C}_5$, and ${}^{10}{C}_6$, then what is the value of $\frac{270}{H}$ ?

   1. A.1
   2. B.$\frac{14}{17}$
   3. C.$\frac{17}{14}$
   4. D.$\frac{1}{31}$
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   Answer: C

6. Q1012023 · 16 Apr 2023

   The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?

   1. A.8 and 15
   2. B.9 and 14
   3. C.10 and 13
   4. D.11 and 12
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   Answer: C

7. Q1062023 · 16 Apr 2023

   If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?

   1. A.-13
   2. B.-5
   3. C.5
   4. D.7
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   Answer: C

8. Q1092023 · 16 Apr 2023

   A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

   1. A.x - 4y + 5 = 0
   2. B.3x + 2y - 1 = 0
   3. C.x + 4y + 1 = 0
   4. D.5x - 4y + 1 = 0
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   Answer: A

9. Q1112023 · 16 Apr 2023

   Consider the following frequency distribution : $$\begin{array}{ccccc}x& 1& 2& 3& 5\\ f& 4& 6& 9& 7\end{array}$$ What is the value of median of the distribution ?

   1. A.1
   2. B.2
   3. C.3
   4. D.3.5
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   Answer: C

10. Q1122023 · 16 Apr 2023

    For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five observations, then what is the value of 4M - N ?

    1. A.7
    2. B.4
    3. C.1
    4. D.0
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    Answer: D

11. Q1132023 · 16 Apr 2023

    Let P, Q, R represent mean, median and mode. If for some distribution $5P=4Q=\frac{R}{2}$ then what is $\frac{P+Q}{2P+0.7R}$ equal to ?

    1. A.$\frac{1}{12}$
    2. B.$\frac{1}{7}$
    3. C.$\frac{2}{9}$
    4. D.$\frac{1}{4}$
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    Answer: D

12. Q1142023 · 16 Apr 2023

    If G is the geometric mean of numbers $1,2,2^2,2^3,\dots ,2^{n-1}$, then what is the value of $1+2{\log }_{2}G$ ?

    1. A.1
    2. B.4
    3. C.n - 1
    4. D.n
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    Answer: D

13. Q1152023 · 16 Apr 2023

    If H is the harmonic mean of numbers $1,2,2^2,2^3,\dots ,2^{n-1}$ what is n/H equal to ?

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

14. Q1162023 · 16 Apr 2023

    Let P be the median, Q be the mean and R be the mode of observations $x_1,x_2,x_3,\dots ,x_n$. Let $S={\sum }_{i=1}^n(2x_i-a{)}^2$ S takes minimum value, when a is equal to

    1. A.P
    2. B.Q/2
    3. C.2Q
    4. D.R
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    Answer: C