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

Total Questions: 100

31. If α and β are the roots of the

quadratic equation x² + αx + β = 0
where β ≠ 0, then what is the value
of α - β  ?

Correct Answer: (b) 3
Solution:

32. A shopkeeper marks the price of an article at 200. After allowing a discount of 10%, he still gains 20% on the cost price. What is the cost price of the article?

Correct Answer: (c) ₹150
Solution:

33. A person borrowed ₹ 9000 at 7%,

₹ 12000 at 8% and ₹ 15000 at 9% on
simple interest per annum. He had
to pay ₹ 50700 at the end of n year.
What is the value of n?

Correct Answer: (c) 5
Solution:

34. Consider the following statements :

1. The sum of the cubes of three consecutive natural numbers is divisible by 9.
2. Every even power of every odd number (> 1) when divided by 8 gives 1 as remainder.

Which of the above statements is/are correct?

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


35. What is the number of divisors of 1000 (excluding 1 and 1000)?

Correct Answer: (c) 14
Solution:

36. If the sum of the roots of the

equation x² - k² x + 30kx
- 161x - 64 = 0 is zero, then what
is the difference of the roots?

Correct Answer: (b) 16
Solution:

37. A piece of cloth costs ₹ 10000. If a 2 m longer piece of the same cloth is purchased for the same amount, it would cost ₹ 250 less per metre. What is the original length of the piece of cloth?

Correct Answer: (a) 8 m
Solution:

38. What is the condition that the roots of the equation ax² + bx + c = 0 are in the ratio c : 1 ?

Correct Answer: (a) b² = a (c + 1)²
Solution:


39. Two sides of a triangle forming a right angle are 6x² and (2x² - 1) If the area of the triangle is 84 square units, then what is the perimeter of the triangle?

Correct Answer: (c) 56 units
Solution:

40. A train X takes 2 h less than a train Y to cover a distance of 192 km between two cities. Their average speeds differ by 16 km/h. How long does the faster train take to cover the journey?

Correct Answer: (b) 4 h
Solution: