Mathmatics NDA/NA Solved Paper 2020-I (51-100)

Total Questions: 50

21. In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers ?

Correct Answer: (c) 2/15
Solution:

Prime number between 1 to 10 are 2,3,5,7.
Now, number of ways of selecting 2 prime number out of 4 prime number = ⁴C₂ = 6.
Number of ways of selecting 2 numbers out of 10 numbers = ¹⁰C₂ = 45.

22. Solve the following equation?

Correct Answer: (b) Y = 1.12X - 5.8
Solution:

23. Consider a random variable X which follows Binomial distribution with parameters n = 10 and p = (1/5). Then Y = 10 - X follows Binomial distribution with parameters n and p respectively given by

Correct Answer: (d) 10 (4/5)
Solution:

24. If A and B are two events such that P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.4, then consider the following statements :


Which of the above statements is/are correct ?

Correct Answer: (d) Neither 1 nor 2
Solution:


Hence, statements (2) is not correct.

25. Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02, 0.03 and 0.05, it fails to rise. In the restaurant where they work, X bakes 50%, Y bakes 30% and Z bakes 20% of cakes. What is the proportion of failures caused by X?

Correct Answer: (b) 10/29
Solution:

26. Consider the following statements for f (x) = e⁻|ˣ|

(1) The function is continuous at x = 0.
(2) The function is differentiable at x = 0.
Which of the above statements is/are correct ?

Correct Answer: (a) 1 only
Solution:

27. What is the maximum value of sin𝓍 . cos𝓍 ?

Correct Answer: (c) 1/2
Solution:

28. Solve the following equation?

Correct Answer: (a) 0
Solution:

29. What is the derivative of tan⁻¹𝓍 with respect to cot⁻¹𝓍 ?

Correct Answer: (a)
Solution:

30. The function u(𝓍, y) = c which satisfies the differential equation

𝓍(d𝓍 - dy) + y(dy - d𝓍) = 0, is

Correct Answer: (b) 𝓍² + y² = 2𝓍y + c
Solution: