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

Total Questions: 100

11. If 17²⁰²⁰ is divided by 18, then what is the remainder?

Correct Answer: (a) 1
Solution:

12. What is the value of

Correct Answer: (c) 9
Solution:Given,

13. Solve the following equation

Correct Answer: (a)
Solution:We have,

14. The sum of all possible products taken two at a time out of the numbers ±1, ±2, ±3, ±4, ±5 is

Correct Answer: (c) - 55
Solution:Given number, ±1, ±2, ±3, ±4, ±5

15. A train of length 110 m is moving at a uniform speed of 132 km/h. The time required to cross a bridge of length 165 m is

Correct Answer: (c) 7.5 s
Solution:Length of train = 110 m

16. The simple interest on a certain sum is one-fourth of the sum. If the number of years and the rate of annual interest are numerically equal, then the number of years is

Correct Answer: (d) 5
Solution:

17. A 60-page book has n lines per page. If the number of lines were reduced by 3 in each page, the number of pages would have to be increased by 10 to give the same writing space. What is the value of n ?

Correct Answer: (b) 21
Solution:Total number of line in 60 page = 60n .....(i)
Total number of line when number of line were reduced 3 in each page and number of pages increased by
10 = (n - 3)(70) .....(ii)
From Equations (i) and (ii)
60n = (n - 3) 70
60n = 70n - 210
n= 21

18. If x men working x hours per day can do x units of work in x days, then y men working y hours per day in y days would be able to do k units of work. What is the value of k ?

Correct Answer: (d) y³ x⁻²
Solution:Given,

19. Let d(n) denote the number of positive divisors of a positive integer n. Which of the following are correct?

1. d(5) = d(11)
2. d(5) ⋅ d(11) = d(55)
3. d(5) + d(11) = d(16)

Select the correct answer using the code given below:

Correct Answer: (b) 1 and 2
Solution:Here, d(n), denotes the number of positive divisors of a positive integer n.

20. If Aₙ = Pₙ + 1 where Pₙ is the product of the first n prime numbers, then consider the following statements :

1. Aₙ is always a composite number.
2. Aₙ + 2 is always an odd number.
3. Aₙ + 1 is always an even number.

Which of the above statements is/are correct?

Correct Answer: (d) 2 and 3
Solution: