SOLVED PAPER 2022 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

61. Solved

Correct Answer: (d)
Solution:

62. What are the values of k for which the polynomial (k - 3) x² - kx - 1 has no real linear factors?

Correct Answer: (b) - 6 < k < 2
Solution:

63. If bc + cd = 2bd and a + c = 2b then which one of the following is correct?

Correct Answer: (c) ad - bc = 0
Solution:If bc + cd = 2bd and
a + c = 2b
⇒ bc + cd = d(a + c)
⇒ bc + cd = ad + cd,   [∵ using 2b = a + c ]
⇒ bc - ad = 0
⇒ ad - bc = 0

64. In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/h and time of flight increased by 30 min. What was the original average speed of the aircraft?

Correct Answer: (b) 750 km/h
Solution:

65. If x = b + c, y = c + a, z = a + b, then what is (x + y + z)³ - 24xyz equal to?

Correct Answer: (c) 8(a³ + b³ + c³)
Solution:

66. A person X starts from a place A and another person Y starts simultaneously from another place B which is d km away from A. They walk in the same direction. X walks at an average speed of u km/h and Y walks at an average speed of v km/h. How far will X have walked before he overtakes Y?

Correct Answer: (a)
Solution:

67. If p is the difference between a number and its reciprocal and q is the difference between the square of the same number and the square of its reciprocal, then what is p⁴ + 4p² equal to ?

Correct Answer: (d) q²
Solution:

68. Solved

Correct Answer: (c)
Solution:

69. X takes 3 h longer than Y to walk 30 km. If X doubles his speed, he takes 2 h less than Y. What is the speed of Y?

Correct Answer: (c) 4 ²⁄₇ km/h
Solution:

70. If C is the compound interest on ₹ 10000 for one year at 4% per annum when compounded quarterly, then which one of the following is correct?

Correct Answer: (d) C > ₹ 400
Solution: