SOLVED PAPER 2021 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

21. For how many real values of k is 6kx² + 12kx - 24x + 16 a perfect square for every integer x ?

Correct Answer: (c) Two
Solution:Let


22. Solve it ?

Correct Answer: (b)
Solution:



23. If the equation 4x² - 2kx + 3k = 0 has equal roots, then what are the values of k ?

Correct Answer: (c) 0, 12
Solution:Given equation,
4x² - 2kx + 3k = 0
ln ax² + bx + c = 0,
condition for equal roots is

D= 0 i.e., b² - 4ac = 0
For the given equation,
a = 4, b = - 2k and c = 3k
Put b² - 4ac = 0

⇒ (- 2k)² - 4(4)(3k) = 0
⇒ 4k² - 48k = 0
⇒ k² - 12k = 0
⇒ k(k - 12) = 0
k = 0 or k = 12
Hence, the required values of k are 0 and 12.

24. If the sum as well as the product of the roots of the equation px²-6x + q = 0 is 6, then what is (p + q) equal to?

Correct Answer: (b) 7
Solution:


25. 4x³ + 12x² - x - 3 is divisible by

Correct Answer: (c) Both (2x + 1) and (2x - 1)
Solution:


26. Which one of the following fractions will have minimum change in its value if 3 is added to both the numerator and the denominator of all the fractions ?

Correct Answer: (d) ⅚
Solution:


27. Let the average score of a class of boys and girls in an examination be p. The ratio of boys and girls in the class is 3 : 1. If the average score of the boys is (p + 1) then what is the average score of the girls?

Correct Answer: (c) (p - 3)
Solution:Let the number of boys be 3a
and number of girls be a.
Let the average score of the girls be N.
Sum of scores of boys = 3a(p + 1)
Sum of scores of girls = Na
Sum of scores of the whole class

= (3a + a)p = 4ap
∴ 3a(p + 1) + Na = 4ap
⇒ 3ap + 3a + Na = 4ap
⇒ a(3 + N) = 4ap - 3ap = ap
⇒ a(3 + N) = ap
⇒ 3 + N = p
⇒ N = p - 3
Hence, the average score of the girls is (p - 3)

28. The income of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's saving is one-fourth of his income, then the ratio of savings of A, B and C is

Correct Answer: (a) 56 : 99 : 69
Solution:


29. A train 200 m long passes a platform 100 m long in 10 sec. What is the speed of the train?

Correct Answer: (b) 30 m/s
Solution:

30. Solve it ?

Correct Answer: (b) 99
Solution: