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

Total Questions: 100

11. A two-digit number is 9 more than four times of the number obtained by interchanging its digits. If the product of digits in the two-digit number is 8, then what is the number?

Correct Answer: (a) 81
Solution:Let two digit number = 10x + y



12. If α and β are the roots of the quadratic equation x² + kx - 15 = 0 such that α - β = 8 then what is the positive value of k ?

Correct Answer: (a) 2
Solution:Given quadratic equation,

13. What are the values of p and q respectively, if (x - 1) and (x + 2) divide the polynomial x³ + 4x² + px + q ?

Correct Answer: (a) 1, -6
Solution:Given polynomial is

14. If (x + k) is the HCF of x² + 5x + 6 and x² + 8x + 15 then what is the value of k ?

Correct Answer: (b) 3
Solution:Since, (x + k) is the HCF of

15. If 5ˣ⁺¹ - 5ˣ⁻¹ = 600 then what is the value of 10²ˣ ?

Correct Answer: (d) 1000000
Solution:

16. A number divides 12288, 28200 and 44333 so as to leave the same remainder in each case. What is that number ?

Correct Answer: (c) 221
Solution:Let divisor is x and remainder is r.

17. If x² + 9y² = 6xy, then what is y : x equal to ?

Correct Answer: (a) 1 : 3
Solution:

18. If mand n are positive integers such that mⁿ = 1331 then what is the value of (m - 1)ⁿ⁻¹ ?

Correct Answer: (b) 100
Solution:

19. Answer the following question

Correct Answer: (b) -1
Solution:

20. Solve the following equation

Correct Answer: (b) z < x < y
Solution: