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

31. Find the value?

Let f(x) be a function satisfying f(x + y) = f(x) f(y) for all x, y ∈ N such that
f(1) = 2:

(a) 8
(b) 9
(c) 10
(d) 11

Correct Answer: (c) 10

Solution:

32. Find the value?

Let f(x) be a function satisfying f(x + y) = f(x) f(y) for all x, y ∈ N such that
f(1) = 2

(a) 341
(b) 682
(c) 1023
(d) 1364

Correct Answer: (b) 682

Solution:

33. Find the value?

Let f(x) be a function satisfying f(x + y) = f(x) f(y) for all x, y ∈ N such that
f(1) = 2:

(a) 1365
(b) 2730
(c) 4024
(d) 5460

Correct Answer: (d) 5460

Solution:

34. How many received medals in exactly two of the three sports?

A university awarded medals in basket ball, football and volleyball. Only x students (x < 6) got medal in all the three sports and the medals went to a total of 15x students. It awarded 5x medals in basketball, (4x + 15) medals in football and (x + 25) medals in volleyball.

(a) 30 - 4x
(b) 35 - 7x
(c) 40 - 7x
(d) 45 - 5x

Correct Answer: (c) 40 - 7x

Solution:(c)

35. How many received medals in at least two of three sports?

(a) 30 - 6x
(b) 35 - 6x
(c) 40 - 5x
(d) 40 - 6x

Correct Answer: (d) 40 - 6x

Solution:At least two of three sports
= b + e + f + d = 40 - 7x + x = 40 - 6x

36. How many received medals in exactly one of three sports?

(a) 21x - 40
(b) 21x - 35
(c) 20x - 35
(d) 20x - 25

Correct Answer: (a) 21x - 40

Solution:Exactly one of three sports
= a + c + g = 15x - (40 - 6x)
= 21x - 40

37. What is P equal to?

Correct Answer: (a)

Solution:

38. What is Q equal to?

Correct Answer: (d)

Solution:

39. What is the minimum value of determinant of A?

(a) 1/4
(b) 1/2
(c) 3/4
(d) 1

Correct Answer: (a) 1/4

Solution:

40. What is the height of the lamp post?

ABC is a triangular plot with AB = 16 m; BC = 10 m and CA = 10 m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45° at the vertex B.