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

Total Questions: 100

21. 20 men are supposed to complete a work in 10 days after working for 5 days they realise that only one fourth of the work is done. How many more men they need to employ to finish the work on time?

Correct Answer: (a) 40
Solution:

22. If x is a negative real number, then which of the following are not correct?

1. There is some natural number k such that kx > 0
2. x² + x > 0 always
3. 2x < x < - x
4. x² is is always a rational number

Select the correct answer using the code given below:

Correct Answer: (b) 1, 2 and 4
Solution:


23. What is the sum of the linear factors (in x and y) of the expression 2x² + xy - 3y² ?

Correct Answer: (c) 3x + 2y
Solution:

24. Which one of the following equations does not have real roots?

Correct Answer: (d) 4x² + 9x + 6 = 0
Solution:


25. The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation?

Correct Answer: (b) x² - 8x + 12 = 0
Solution:


26. For which values of k, does the equation x² - kx + 2 = 0 have real and distinct solutions?

Correct Answer: (d) k 2√2
Solution:

27. If α + β + ϒ = α β + β ϒ + ϒ α then

what is (1 - α) (1 - β) (1 - ϒ) equal to

Correct Answer: (a) 1 - α β ϒ
Solution:

28. If log₁₀ x + log₁₀ x² = 2log₁₀ x + 1 then what is the value of x ?

Correct Answer: (d) 10
Solution:

29. The LCM of two prime numbers p and q is 2231, where p > q . What is the value of p - q ?

Correct Answer: (c) 74
Solution:Given, LCM of two prime
numbers p and q is 2231,
where p > q.

We know, LCM of two prime
numbers = Product of the numbers

⇒ 2231 = pq
⇒ p × q = 2231
⇒ p × q = 23 × 97
∴ p = 97 and q = 23(∴ p > q )
Now, p - q = 97 - 23 = 74
Hence, the value of p - q is 74

30. Three runners are running in a circular track, and they complete one round in 20, 30 and 35 minutes respectively. when will they next meet at the starting point?

Correct Answer: (d) After 7 hour
Solution:The time interval when they will meet
next at the starting point is the LCM
(20, 30 and 35).
Thus, the prime factorisation of 20,
30 and 35 is

20 = 2 × 2 × 5 = (2)² × (5)¹,
30 = 2 × 3 × 5 = (2)¹ × (3)¹ × (5)¹
and 35 = 5 × 7 = (5)¹ × (7)¹
LCM (20, 30, 35)

= (2)² × (3)¹ × (5)¹ × - (7)¹
= 12 × 35
= 420min
= (⁴²⁰⁄₆₀) h = 7h

Hence, all three runners will next
meet after 7 h at the starting point.