SOLVED PAPER 2024 (CDS) (I) (Mathematics)

Total Questions: 100

31. A bottle contains spirit and water in the ratio 1 : 4 and another identical bottle contains spirit and water in the ratio 4: 1. In what ratio should the mixtures in the two bottles be mixed to get a new mixture in which the ratio of spirit to water is 1 : 3?

Correct Answer: (d) 11 : 1
Solution:

32. If 3sinθ + 5cosθ = 5 then what is the value of 5sinθ - 3cosθ?

Correct Answer: (a) -3
Solution:

33. Consider the following in respect of the polynomial

x⁴ᵏ + x⁴ᵏ⁺² + x⁴ᵏ⁺⁴ + x⁴ᵏ⁺⁶

1. The remainder is zero when the polynomial is divided by x² + 1
2. The remainder is zero when the polynomial is divided by x² + 1

Which of the statements given above is/are correct?

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

34. What is the minimum value of for

Correct Answer: (c) 7
Solution:

35. Find the value of this -

Correct Answer: (a) 1
Solution:

36. Find the value of this -

Correct Answer: (a) 720
Solution:

On comparing L.H.S. and R.H.S, we get
a = 2, b = 3, c = 4, d = 5, and e = 6
Then, a × b × c × d × e
= 2 × 3 × 4 × 5 × 6 = 720

37. A cube whose edge is 14 cm long has on each of its faces a circle of 7 cm radius painted yellow. What is the total area of unpainted surface? (Take π = 22/7)

Correct Answer: (c) 252cm²
Solution:

38. From a circular metal plate of radius 7 cm and thickness 0.16 mm, a sector is cut off containing an angle 150°. The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm?

Correct Answer: (b) 0.7
Solution:

39. The chord AB of a circle with centre at O is 2√3 times the height of the minor segment. If P is the area of the sector OAB and Q is the area of the minor segment of the circle, then what is the approximate value of P/Q ?

(Take, √3 = 1.7 and π = 3.14 )

Correct Answer: (b) 1.7
Solution:According to the given information.
Let OA = OB = r cm
⇒ OD = (r - x) cm

40. What is the area of the region between two concentric circles, if the length of a chord of the outer circle touching the inner circle at a particular point of its circumference is 14 cm? (Take, π = 22/7)

Correct Answer: (a) 154cm²
Solution: