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

Total Questions: 100

41. (Questions 41 and 42) Consider the following for the next two items that follow.

A line segment AB is bisected at C and semi-circles S₁, S₂ and S₃ are drawn respectively on AB, AC and CB as diameters such that they all lie on same side of AB. A circle S is drawn touching internally S₁ and externally S₂ and S₃.

If r is the radius of S and R is the radius of S₂, then which one of the following is correct?

Correct Answer: (d) 2R = 3r
Solution:

42. If m is the area of the circle S and n is the area of semi-circle S₁ then which one of the following is correct?

Correct Answer: (a) 9m = 2n
Solution:

43. (Questions 43 and 44) Consider the following for the next two items that follow:

Correct Answer: (d) 1/m
Solution:

44. What is x equal to ?

Correct Answer: (a)
Solution:

45. (Questions 45 and 46) Consider the following for the next two items that follow.

The total monthly electricity bill for a house consists of the sum of two parts, one part is proportional to number of rooms and the other part is proportional to number of units consumed. ₹ 400 is the monthly electricity bill for a house with 8 rooms and consuming 240 units and ₹ 320 is the monthly electricity bill for a house with 6 rooms and consuming 200 units.

What is the monthly electricity bill for a house with m rooms and consuming n units?

Correct Answer: (b) ₹ (20m + n)
Solution:Let per room charge be ₹ x and per unit charge be ₹ y.
According to the question,
8x + 240y = 400 ..... (i)
6x + 200y = 320 ..... (ii)
Solving Equation (i) and (ii),we get
x = 20 y = 1
∴ Required bill = ₹ (20m + n)

46. What is the monthly electricity bill. for a house with 7 rooms consuming 300 units?

Correct Answer: (b) ₹ 440
Solution:∴ Required bill = ₹ (20 × 7 + 300)
= ₹ (140 + 300)
= ₹ 440

47. (Quetions 47 and 48) Consider the following for the next two items that follow:

A grouped frequency distribution is given below.

Weekly wages in Rupees (₹)Number of workers
2050-25505
2550-305010
3050-3550k
3550-40508
4050-45502
4550-505010

If average weekly wages earned by a worker is ₹ 3520, then what is the value of k?

Correct Answer: (c) 15
Solution:
Weekly wages (₹)xᵢfᵢxᵢfᵢ
2050-25502300511500
2550-305028001028000
3050-35503300k3300K
3550-40503800830400
4050-4550430028600
4550-505048001048000
Total35+k126500 +3300k

48. What is the median (approximate value) of the distribution?

Correct Answer: (b) ₹ 3383
Solution:
Weekly wages (₹)fᵢcf
2050-255055
2550-30501015
3050-35501530
3550-4050838
4050-4550240
4550-505010n=50

49. (Questions 49 and 50) Consider the following for the next two items that follow.

A quadratic equation is given by
(a + b + c) x² - (2a + 2b) x + (a + b - c) = 0
where a, b and c are real and distinct.

What are the roots of the equation?

Correct Answer: (a)
Solution:

50. Consider the following statements.

I. One of the roots of the equation is always less than 1, if a, b and c are all positive.
II. One of the roots of the equation is always negative if a, band c are all negative.

Which of the statements given above is/are correct?

Correct Answer: (a) Only I
Solution: