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

Total Questions: 100

21. If log(x) = 1.25 and y = xˡᵒᵍˣ, then what is log(y) equal to ?

Correct Answer: (c) 1.5625
Solution:

22. If f(x) is divided by (x - α) (x - β), where α ≠ ẞ, then what is the remainder ?

Correct Answer: (c)
Solution:Given, f(x) is divided by (x - α) (x - β).


23. If the area of a square is 2401x⁴ + 196x² + 4, then what is its side length ?

Correct Answer: (c) 49x² + 2
Solution:

24. If x varies as yz, then y varies inversely as

Correct Answer: (c)
Solution:

25. Simplify the equation

Correct Answer: (a)
Solution:

26. What is the point on the xy-plane satisfying 5x + 2y = 7xy and 10x + 3y = 8xy ?

Correct Answer: (b)
Solution:Given, 5x + 2y = 7xy,

27. The price of an article X increases by 20% every year and price of article Y increases by 10% every year. In the year 2010, the price of article X was ₹ 5000 and price of article Y was ₹ 2000. In which year the difference in their prices exceeded ₹ 5000 for the first time ?

Correct Answer: (b) 2013
Solution:In year 2010, Price of article X is ₹5000 and price of article Y is ₹2000.


28. The ratio of speeds of X and Y is 5 : 6. If Y allows X a start of 70 m in a 1.2 km race, then who will win the race and by what distance?

Correct Answer: (c) Y wins the race by 130 m
Solution:Speed of X = 5k and speed of Y = 6k

29. A train takes two hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. What is its usual speed ?

Correct Answer: (d) 25 km/h
Solution:


30. If 6 men and 8 women can do a piece of work in 10 days, and 13 men and 24 women can do the same work in 4 days, then what is the ratio of daily work done by a man to that of a woman ?

Correct Answer: (a) 2 : 1
Solution:Let a man’s one day work = x unit and a woman’s one day work = y unit