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

Total Questions: 100

81. Consider the following statements:

1. x⁴ (y - z) + y⁴ (z - x) + z⁴ (x - y) is positive if x > y > z
2. x⁴ (y - z) + y⁴ (z - x) + z⁴ (x - y) is negative if x < y < z

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:

82. Solved

Correct Answer: (a) x²
Solution:

83. X and Y can do a piece of work in 45 days and 40 days respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to ?

Correct Answer: (b) 9
Solution:

84. 480 persons working 10 h per day complete one-fourth of a work in 10 days. How many additional persons are to be employed in order to complete the remaining work in 20 days, working 8 h per day?

Correct Answer: (b) 420
Solution:

85. 12 women and 16 men can do a piece of work in 5 days. 13 women and 24 men can do it in 4 days. How long will 25 women and 50 men take to do it.

Correct Answer: (b) 2 days
Solution:

86. There are two stations X and Y, 1320 km apart. A train starts from station X at 6 am and moves at an average speed of 60 km/h. At 2 pm another train starts from Y towards X and moves at an average speed of 80 km/h. When do they meet?

Correct Answer: (c) 8 pm
Solution:

87. Two glasses of equal volume are filled with a mixture of alcohol and water in the ratio 3 : 2 and 4 : 1, respectively. These glasses are emptied into a third glass. What is the ratio of alcohol and water in the third glass?

Correct Answer: (c) 7 : 3
Solution:

88. If x is the HCF and y is the LCM of ⅗, ⁶⁄₂₅, ⁹⁄₂₀, ²⁷⁄₅₀ then which one of the following is correct?

Correct Answer: (d) y = 360x
Solution:

89. There are two natural numbers x and y, where x > y When x is divided by 6, it leaves the remainder 2 and when y is divided by 6, it leaves the remainder 3. What is the remainder when (x - y) is divided by 6?

Correct Answer: (c) 5
Solution:According to the question,
x = 6k₁ + 2
y = 6k₂ + 3
x - y = 6k₁ + 2 - 6k₂ - 3
= 6(k₁ - k₂) - 1
x - y = 6(k₁ - k₂ - 1) + 6 - 1
= 6m + 5
∵  When x - y is divided by 6,
then remainder is 5.

90. The value of a 2-digit number is 5 times the sum of the digits. What is the product of the digits?

Correct Answer: (c) 20
Solution: