Mathematics (NDA/NA SOLVED PAPER 2022-II) (01 to 50)

Total Questions: 50

11. Find the value?

Correct Answer: (a) 3√c
Solution:

12. What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm?

Correct Answer: (c) 2 + √3 cm
Solution:

13. Let A = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16} and let f : A -> N be defined by f(x) = the highest prime factor of x.

How many elements are there in the range of f?

Correct Answer: (c) 6
Solution:f(x) = the highest prime factor of x,
f(7) = 7, f(8) = 2, f(9) = 3, f(10) = 5, f(11) = 11,
f(12) = 3, f(14) = 7, f(15) = 5, f(16) = 2, f(13) = 13
Range = {2, 3, 5, 7, 11, 13}

14. Let R be a relation from N to N defined by R= {(x, y) : x ,y ∈ N and x² = y³}. Which of the following are not correct?

1. (x, x) ∈ R for all x ∈ N
2. (x,y) ∈ R ⇒ (y, x) ∈ R
3. (x, y) ∈ R and (y,z) ∈ R ⇒ (x, z) ∈ R
Select the correct answer using the code given below:

Correct Answer: (d) 1, 2 and 3
Solution:(d)

15. Consider the following:

1. A ∩ B = A ∩ C ⇒ B = C
2. A ∪ B = A ∪ C ⇒ B = C
Which of the above is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:Let A = {1, 2}, B = {2, 3}, C = {2, 4}
A ∩ B = A ∩ C = {2}
But B ≠ C
So, statement 1 is wrong
Let A = {1, 2}, B = {2, 3}, C = {1, 2, 3}
A U B = A U C = {1, 2, 3}
But B ≠ C.
So, statement 2 is wrong.

16. What is the modulus of z?

Correct Answer: (a)
Solution:

17. What is angle θ such that z is purely real?

Where n is an integer

Correct Answer: (c)
Solution:

18. What is angle θ such that z is purely real?

Where n is an integer

Correct Answer: (b)
Solution:

19. What is the ratio of the first term of A to that of B?

Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B.
Let P : Q = (5n+4): (9n+6)

Correct Answer: (d) 3/5
Solution:

20. What is the ratio of their 10th terms ?

Let P be the sum of first n positive terms of an increasing arithmetic progression A. Let Q be the sum of first n positive terms of another increasing arithmetic progression B.
Let P : Q = (5n+4): (9n+6)

Correct Answer: (c) 33/59
Solution: