SOLVED PAPER 2020 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

1. x³ + x² + 16 is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is

Correct Answer: (c) 5
Solution:

2. The number of (a, b, c) where a, b, c are positive integers such that abc = 30, is

Correct Answer: (b) 27
Solution:We have,

3. If the roots of the quadratic equation x² - 4x - log₁₀ N = 0 are real, then what is the minimum value of N?

Correct Answer: (d)
Solution:Given equation,

4. The number of different solutions of the equation x + y + z = 12, where each of x, y and z is a positive integer, is

Correct Answer: (c) 55
Solution:We have,

5. If I = a² + b² + c², where a and b are consecutive integers and c = ab, then I is

Correct Answer: (d) square of an odd integer.
Solution:We have, l = a² + b² + c²

6. If the number 23P62971335 is divisible by the smallest odd composite number, then what is the value of P?

Correct Answer: (a) 4
Solution:Given,

7. What is the remainder when the sum 1⁵ + 2⁵ + 3⁵ + 4⁵ + 5⁵ is divided by 4 ?

Correct Answer: (b) 1
Solution:Given number,

8. What is the digit in the unit place of 3⁹⁹ ?

Correct Answer: (c) 7
Solution:Given number,

9. LCM of two numbers is 28 times their HCF. The sum of the HCF and the LCM is 1740. If one of these numbers is 240, then what is the other number?

Correct Answer: (a) 420
Solution:


10. (xⁿ - aⁿ) is divisible by (x - a) where x ≠ a, for every

Correct Answer: (a) natural number n
Solution: