NDA Statistics Past Papers PDF

# Unacademy NDA & CDS Mock Tests and Courses ## NDA-I (2024) ### Question 1 From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y = a + bx, then what is the value of 2a + 15b? * (a) 6 * (b) 11 * (c) 17 * (d) 21 ### Question 2 Let x + 2y + 1 = 0 and 2x +...

# Unacademy NDA & CDS Mock Tests and Courses ## NDA-I (2024) ### Question 1 From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y = a + bx, then what is the value of 2a + 15b? * (a) 6 * (b) 11 * (c) 17 * (d) 21 ### Question 2 Let x + 2y + 1 = 0 and 2x + 3y + 4 = 0 are two lines of regression computed from some bivariate data. If O is the acute angle between them, then what is the value of 488tan30? * (a) 191 * (b) 161 * (c) 131 * (d) 121 ### Question 3 If two random variables X and Y are connected by relation $2X-3Y/5X+4Y$ = 4 and X follows Binomial distribution with parameters n = 10 and $p = 1/2$ , then what is the variance of Y? * (a) 810/361 * (b) 9/19 * (c) 21/361 * (d) 121/361 ### Question 4 An edible oil is sold at the rates 150, 200, 250, 300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year during these years, what is the average price of oil in rupees (approximately) per litre? * (a) 210 * (b) 220 * (c) 230 * (d) 240 ### Question 5-7 Consider the following for the next two items: | Xi | 1 | 2 | 3 | ... | n | |---|---|---|---|---|---| | fi | 1 | 2⁻¹ | 2⁻² | ... | 2⁻⁽ⁿ⁻¹⁾ | * What is Σxifi equal to? * (a) 2ⁿ⁺¹-n+2 / 2ⁿ⁻¹ * (b) 2ⁿ⁺¹-n-2 / 2ⁿ⁻¹ * (c) 2ⁿ⁺¹+n+2 / 2ⁿ⁻¹ * (d) 2ⁿ⁺¹-n-2 / 2ⁿ * What is the mean of the distribution? * (a) 2ⁿ⁺¹-n+2 / 2ⁿ⁻¹ * (b) 2ⁿ⁺¹-n-2 / 2ⁿ⁻¹ * (c) 2ⁿ⁺¹-n-2 / 2ⁿ⁻¹ * (d) 2ⁿ⁺¹-n+2 / 2ⁿ * The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50, and 41. What is the mean deviation of the largest five observations? * (a) 4.8 * (b) 5.5 * (c) 6 * (d) 7.5 ### Question 8 The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50, and 41. What is the variance of the largest five observations? * (a) 14.6 * (b) 21.8 * (c) 25.2 * (d) 46.8 ## NDA-II (2023) ### Question 9 If H is the Harmonic Mean of three numbers ¹⁰C₄, ¹⁰C₅, and ¹⁰C₆, then what is the value of 270/H? * (a) 1 * (b) 14/17 * (c) 17/14 * (d) 1/31 ### Question 10 If r is the coefficient of correlation between x and y, them what is the correlation coefficient between (3x + 4) and (-3y + 3)? * (a) -r * (b) r * (c) √3r * (d) -√3r ### Question 11 What is the mean of the numbers 1, 2, 3, …, 10 with frequencies ⁹C₀, ⁹C₁, ⁹C₂, …, ⁹C₉ respectively? * (a) 1.1 x 2⁸ * (b) 1.2 x 7⁴ * (c) 5.5 * (d) 0.55 ### Question 12 If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation? * (a) 16 * (b) 6 * (c) 5 * (d) 4 ### Question 13 If X = 20 is the mean of 10 observations X₁, X₂, …, X₁₀; then what is the value of Σ¹⁰ᵢ₌₁ (3xᵢ - 4)/5)? * (a) 0 * (b) 12 * (c) 112 * (d) 1012 ### Question 14 The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (pq)² = 10000, then what is the value of n? * (a) 10 * (b) 20 * (c) 50 * (d) 100 ## NDA-I (2023) ### Question 15 A die is thrown 10 times and obtained the following outputs: 1, 2, 1, 1, 2, 1, 4, 6, 5, 4. What will be the mode of data so obtained? * (a) 6 * (b) 4 * (c) 2 * (d) 1 ### Question 16 A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x? * (a) x - 4y + 5 = 0 * (b) 3x + 2y - 1 = 0 * (c) x + 4y + 1 = 0 * (d) 5x - 4y + 1 = 0 ### Question 17 The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to? * (a) 10 * (b) 12 * (c) 17 * (d) 21 ### Question 18 The central angles p, q, r, and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. What is the value of 4p-q? * (a) 12 * (b) 24 * (c) 30 * (d) 36 ### Question 19 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? * (a) -13 * (b) -5 * (c) 5 * (d) 7 ### Question 20 Let X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and p = ⁴/₅, what is the variance of Y? * (a) 1 * (b) ¹/₂ * (c) 16 * (d) ¹/₁₆ ### Question 21 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. * (a) 8 and 15 * (b) 9 and 14 * (c) 10 and 13 * (d) 11 and 12 ## NDA-II (2022) ### Question 22-24 Consider the following for the next three items. Consider the following grouped frequency distribution. | Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | |---|---|---|---|---|---|---| | Frequency | 1 | 2 | 4 | 6 | 4 | 3 | * What is the median of the distribution? * (a) 34 * (b) 34.5 *(c) 35* * (d) 35.5 * What is the mean deviation about the median? * (a) 11.4 * (b) 11.1 * (c) 10.8 * (d) 10.5 * What is the mean deviation about the mean? * (a) 10.15 * (b) 10.65 * (c) 11.15 * (d) 11.65 ### Question 25-27 Consider the following for the next two items. The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below: | Subject | Mathematics | Physics | Chemistry | Biology | |---|---|---|---|---| | Mean Marks | 40 | 28 | 38 | 36 | | SD | 15 | 12 | 14 | 16 | * Which one of the following subjects shows highest variability of marks? * (a) Mathematics * (b) Physics * (c) Chemistry * (d) Biology * What is the coefficient of variation of marks in Mathematics? * (a) 37.5% * (b) 38.0% * (c) 38.5% * (d) 39.0% ### Question 28 Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If $x/y = 55/42$, then what is the value of n? * (a) 24 * (b) 25 * (c) 27 * (d) 30 ### Question 29-31 Consider the following frequency distribution for the next three items. | Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | |---|---|---|---|---|---| | Frequency | 17 | p + q | 32 | p - 3q | 19 | The total frequency is 120. The mean is 50. * What is the value of p? * (a) 25 * (b) 26 * (c) 27 * (d) 28 * What is the value of q? * (a) 1 * (b) 2 * (c) 3 * (d) 4 * If the frequency of each class is doubled, then what would be the mean? * (a) 25 * (b) 50 * (c) 75 * (d) 100 ### Question 32-34 Consider the following data for the next three items: The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3. * What is the mean of the marks? * (a) 67 * (b) 71 * (c) 75 * (d) 79 * What is the median of the marks? * (a) 79.5 * (b) 79 * (c) 78.5 * (d) 77 * What is the sum of the deviations measured from the median? * (a) - 1 * (b) 0 * (c) 1 * (d) 2 ## Unacademy Courses The images you provided also display advertisements for Unacademy courses. **Unacademy offers the following courses:** * **AGNI Complete Batch for NDA 2025** (starts August 29, 2024) * **VEER Batch for CDS 2025** (starts August 30, 2025) * **VIRAAT Batch for CAPF 2025** (starts August 15, 2025) * **YODHA Batch for AFCAT 2025** (starts August 15, 2025) * **MISSION SSB Complete Batch** (starts July 25, 2024) **Unacademy also provides the following:** * **Free UPSC NDA & CDS Milestone 2024 batch** with a weekly schedule. * **VIJAY MOCK TEST SERIES** for NDA, CDS, AFCAT, CAPF * A **telegram group** where you can join to get further updates. 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