Mathematics NDA/NA SOLVED PAPER 2018 (I) (101 to 120)

Total Questions: 20

1. In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?

Correct Answer: (a) 80/243
Solution:

2. Consider the following statements:

I. P(Ā ∪ B̄) = P(Ā)
= P(B̄) − P(Ā ∩ B̄)
II. P(A ∩ B̄) = P(B̄) − P(A ∩ B)
III. P(A ∩ B) = P(B) P(A | B)
Which of the above statements are correct?

Correct Answer: (b) I and III
Solution:

3. If the correlation coefficient between x and y is 0.6, covariance is 27 and variance of y is 25, then what is the variance of x?

Correct Answer: (d) 81
Solution:

4. The probabilities that a student will solve Question A and Questions B are 0.4 and 0.5 respectively. What is the probability that he solves atleast one of the two questions?

Correct Answer: (b) 0.7
Solution:

5. Let x̄ be the mean of x₁, x₂, x₃, …..., xₙ. If xᵢ = a + c yᵢ for some constants a and c, then what will be the mean of y₁, y₂, y₃,...…, yₙ?

Correct Answer: (d)
Solution:

6. Consider the following statements:

Correct Answer: (d) Neither I nor II
Solution:

7. If 4x − 5y + 33 = 0 and 20x − 9y = 107 are two lines of regression, then what are the values of x̄ and ȳ respectively?

Correct Answer: (c) 13 and 17
Solution:

8. Consider the following statements:

I. Mean is independent of change in scale and change in origin.
II. Variance is independent of change in scale but not in origin.
Which of the above statements is/are correct?

Correct Answer: (d) Neither I nor II
Solution:

Since, mean changes with changes in origin. So, Statement I is wrong. And variance is independent to the choice of origin. So, Statement II is also wrong. Hence, both statements are wrong.

9. Consider the following statements:

I. The sum of deviations from mean is always zero.
II. The sum of absolute deviations is minimum when taken around median.
Which of the above statements is/are correct.

Correct Answer: (c) Both I and II
Solution:

By the property of deviation both statement are correct.

10. What is the median of the numbers 4.6, 0, 9.3, -4.8, 7.6 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2?

Correct Answer: (b) 4.9
Solution: