Statistics · NDA previous year questions

2026 9 questions

1. Q242026 · 12 Apr 2026

   Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^2-2bx+c^2=0$ where $b,c$ are positive real numbers. Let $A$ be the arithmetic mean of $\alpha$ and $\beta$; and $G$ be the geometric mean of $\alpha$ and $\beta$. What are the roots of the quadratic equation $x^2-(b+c)x+bc=0$ ?

   1. A.$A,G$
   2. B.$2A,G$
   3. C.$A,2G$
   4. D.$2A,2G$
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   Answer: A

2. Q432026 · 12 Apr 2026

   If $p,g_1,g_2$ and $q$ are in GP and $m$ is the arithmetic mean of $p$ and $q$, then $\frac{g_1^2}{g_2}+\frac{g_2^2}{g_1}$ is equal to

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

3. Q552026 · 12 Apr 2026

   Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : $$\begin{array}{lllll}\text{Marks}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40\\ \text{No. of students}& 10& 20& f& 40\end{array}$$ Question: What is the standard deviation ?

   1. A.$8\cdot 5$
   2. B.9
   3. C.$9\cdot 5$
   4. D.10
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   Answer: D

4. Q562026 · 12 Apr 2026

   Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : $$\begin{array}{lllll}\text{Marks}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40\\ \text{No. of students}& 10& 20& f& 40\end{array}$$ Question: What is the mean deviation about the arithmetic mean ?

   1. A.$5\cdot 5$
   2. B.6
   3. C.$6\cdot 5$
   4. D.8
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   Answer: D

5. Q582026 · 12 Apr 2026

   The standard deviation of 100 observations is 10. If 5 is multiplied to each of the observations, then what is the new standard deviation ?

   1. A.20
   2. B.25
   3. C.40
   4. D.50
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   Answer: D

6. Q592026 · 12 Apr 2026

   If the mean of 20 observations, namely $x_1,x_2,x_3,\dots ,x_{20}$ is $1\cdot 414$, then what is the value of ${\sum }_{i=1}^{20}100(2x_i+4)$ ?

   1. A.24168
   2. B.20828
   3. C.15248
   4. D.13656
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   Answer: D

7. Q602026 · 12 Apr 2026

   Let two lines of regression be $x+y+11=0$ and $2x+3y+4=0$ for some data. What is the value of correlation coefficient between $x$ and $y$ ?

   1. A.$-\sqrt{\frac{2}{3}}$
   2. B.$-\sqrt{\frac{1}{6}}$
   3. C.$\sqrt{\frac{2}{3}}$
   4. D.$\sqrt{\frac{1}{6}}$
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   Answer: A

8. Q1062026 · 12 Apr 2026

   Passage: The equation of the sphere $S$ is $x^2+y^2+z^2-4x-6y-12z+k=0$. Question: What is the radius of the sphere passing through origin and concentric with the sphere $S$ ?

   1. A.$\frac{7}{2}$
   2. B.5
   3. C.7
   4. D.Cannot be determined due to insufficient data
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   Answer: C

9. Q1122026 · 12 Apr 2026

   For a Binomial distribution with mean 6 and standard deviation $\sqrt{2}$, what is the value of $P(X=0)$ ?

   1. A.${\left(\frac{1}{3}\right)}^9$
   2. B.${\left(\frac{2}{3}\right)}^9$
   3. C.$\frac{1}{3}{\left(\frac{2}{3}\right)}^8$
   4. D.$\frac{2}{3}{\left(\frac{1}{3}\right)}^8$
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   Answer: A