Mathematics NDA/NA SOLVED PAPER 2021-II (101 to 120)

Total Questions: 20

1. Find the value?

Correct Answer: (b) 33
Solution:

2. 3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?

Correct Answer: (a) 0
Solution:Total 3 digits numbers formed by 1, 3, 7 without repetition = 3 × 2 × 1 = 6 Sum of digits = 1 + 3 + 7 = 11
A number is divisible by 3 when the sum of digits of the number is either divisible by 3 or a multiple of 3 but 11 is neither the multiple of 3 nor divisible by 3.
n(E) = 0 & n(S) = 6
Probability =n(E) / n(S) = 0/6 = 0

3. What is the probability that the roots of the equation x² + x + n = 0 are real, where n ∈ N and n < 4?

Correct Answer: (a) 0
Solution:A quadratic equation has only two roots. Here, x² + x + n = 0 and n ∈ N where n < 4
n = 1 , 2, 3 ⇒ Three equations are possible.
Thus, Total number of Roots, n = 6
→ For equation x² + x + n = 0; D = 1 - 4n D < 0 when n = 1, 2 and 3. Equation will give complex roots not real.
Thus, favourable number of roots, r = 0
Hence, probability = r/n = 0/6 = 0

4. If A and B are two events such that P (not A) = 7/10, P(not B)= 3/10 and P(A | B)= 3/14, then what is P(B | A) equal to?

Correct Answer: (d) 1/2
Solution:

5. Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

Correct Answer: (a) 7/15
Solution:

6. Consider the following statements in respect of(x) = |x| - 1:

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

Correct Answer: (a) 1 only
Solution:

7. If f(x) = |x| / |x| x ≠ 0, where [.] denotes the greatest integer function, what is the right-hand limit f(x) at x = 1?

Correct Answer: (c) 1
Solution:

8. Consider the following statements in respect of the function

1. It is continuous at x = 0, if f(0) = 0.
2. It is continuous at x = 2/√π.
Which of the above statements is/are correct?

Correct Answer: (b) 2 only
Solution:

9. What is the range of the function f(x) = 1 - sin x defined on entire real line?

Correct Answer: (b) [0, 2]
Solution:

10. What is the slope of the tangent of y = cos⁻¹ (cos x) at x = - π/4?

Correct Answer: (c) 1
Solution: