SOLVED PAPER 2023 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

81. (Question 81-82) Consider the following data for the questions two questions that follow.

Class0-3030-6060-9090-120
Frequency4574

What is the mode of the distribution?

Correct Answer: (b) 72
Solution:

82. If the median (P) and mode (Q) satisfy the relation 7(Q - P) = 2R, then what is the value of R?

Correct Answer: (a) 6
Solution:

83. (Question 83-84) Consider the following data for the next two questions that follow.

Class40-5050-6060-7070-80
Frequency4574

What is the mean of the distribution?

Correct Answer: (d) 56
Solution:
xxᵢfᵢxᵢfᵢ
40-50454180
50-60553165
60-7065165
70-80752150
∑fᵢ = 10∑xᵢfᵢ = 560

Mean = ∑fx ÷ ∑f
= 560 ÷ 10 = 56

84. If M is the median, then what is the value of 3M?

Correct Answer: (c) 160
Solution:

85. The plinth of a house has an area of 200 m². It is rectangular in shape and its length and breadth are in the ratio 2 : 1. The owner of the house extends the terrace by 1 m on each side. What is the percentage of area that has increased in the terrace relative to the plinth?

Correct Answer: (b) 32%
Solution:Let the length and breadth of the
plinth are 2x and x respectively.
Area of the plinth = 2x × x
200 = 2x² ⇒ x² = 100
⇒ x = 10
∴ Length = 2x = 2 × 10 = 20m
breadth = x = 10m
Now percentage of area that has increased

86. A square sheet of side length 44 cm is rolled along one of its sides to form a cylinder by making opposite edges just to touch each other. What is the volume of the cylinder? (Take π = ²²⁄₇)

Correct Answer: (a) 6776 cm³
Solution:Circumference of cylinder
= Side of square
⇒ 2πr = 44
⇒ 2 × (22÷7) × r = 44 ⇒ r = 7 cm
Now, Volume of cylinder = πr²h
= (22 ÷ 7) × 7 × 7 × 44 = 22 × 7 × 44
= 22 × 308 = 6776 cm³

87. The volume of a cuboid is 3600 cm³ . The areas of two adjacent faces are 225 cm² and 144 cm³ . What is the area of the other adjacent face?

Correct Answer: (a) 400 cm²
Solution:

88. The perimeter and the area of a right-angled triangle are 36 cm and 54 sq cm, respectively. What is the length of the hypotenuse?

Correct Answer: (c) 15 cm
Solution:

89. Let X = { x | x = 2 + 4k where k = 0, 1, 2, 3 ,...24}. Let S be a subset of X such that the sum of no two elements of S is 100. What is the maximum possible number of elements in S?

Correct Answer: (d) 13
Solution:X = { x | x = 2 + 4k}
at K = 0, 1, 2, 3, 4 ,...24
then, X= {2, 6, 10, 14, 18, 22, 26 ,
30, 34, 38, 42,46, 50, 54,58, 62,66,
70, 74, 78, 82, 86, 90, 94, 98}
S = {2, 6, 10, 14, 18, 22, 26, 30,
34 , 38, 42, 46, 50}
[because two element sum ≠ 100]
∴ Number of terms = 13

90. The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. What is the area of the sector?

Correct Answer: (a) 15.6 cm²
Solution: