Mathematics (NDA/NA SOLVED PAPER 2023-I) (101 to 120)

Total Questions: 20

1. 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?

Correct Answer: (c) 10 and 13
Solution:

2. Let A and B be two independent events such that

What is the value of k?

Correct Answer: (c) 2/7
Solution:

3. A biased coin with the probability of getting head equal to 1/4 is tossed five times. What is the probability of getting tail in all the first four tosses followed by head?

Correct Answer: (b) 81/1024
Solution:

4. A coin is biased so that heads comes up thrice as likely as tails. In four independent tossess of the coin, what is probability of getting exactly three heads?

Correct Answer: (b) 27/64
Solution:Heads comes up thrice as likely as tails
⇒ P(H) = 3P(T)
and P(H) + P(T) = 1
P(H) = 3/4
P(T) = 1/4
P (3 head and 1 tail) = 4c₃
3/4 × 3/4 × 3/4 × 1/4 = 27/64.

5. 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?

Correct Answer: (c) 16
Solution:Var(X) = npq = 100 × 4/5 × 1/5 = 16
Var(Y) = var(100 - X) = var(X) = 16

6. 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 ?

Correct Answer: (c) 5
Solution:x + 4y + 1 = 0        ...(1)
4x + 9y + 7 = 0      ...(2)
Putting y = - 3 in (1) and (2)
From (1), x = 11 which is not in option
From (2), x = 5

7. The central angies 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?

Correct Answer: (d) 36
Solution:

8. 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?

Correct Answer: (a) 10
Solution:

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

Correct Answer: (a) x - 4y + 5 = 0
Solution:For line of regression of y on x, the line will be one which satisfy both points.
Clearly, x - 4y + 5 = 0 satisfy (-1, 1) and (3, 2) both.
Hence line is x - 4y + 5 = 0.

10. 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?

Correct Answer: (d) 1
Solution:Mode Data observations with maximum frequency
Mode = 1.