SOLVED PAPER 2024 (CDS) (I) (Mathematics)

Total Questions: 100

21. Find the value of this -

Correct Answer: (c) 2a
Solution:

22. A plank of wood 4.25 m long and 3.4 m wide is to be cut into square pieces of equal size. How many square pieces of largest size can be cut from the plank, if no wastage is allowed?

Correct Answer: (b) 20
Solution:The length of the plank of wood = 4.25m = 425cm
and breadth = 3.4 m = 340 cm
The square pieces of equal size
after the cutting plank of wood
= HCF of (425, 340)
= HCF of (85 × 5,85 × 4) = 85
∴ The number of square pieces of the largest size
= (340 × 425)/(85 × 85) = 20

23. Find the value of this -

Correct Answer: (a) x - 5y
Solution:

24. If HCF of 768 and x⁶ y² is 32xy for natural numbers x ≥ 2 , y ≥ 2 then what is the value of (x + y) ?

Correct Answer: (a) 5
Solution:

25. What is the smallest natural number n such that (n + 1) × n × (n - 1) × (n - 2) × ...... 3 × 2 × 1 is divisible by 910 ?

Correct Answer: (d) 12
Solution:Given,
Number = (n + 1) × (n) × (n-1) ×..... × 3 × 2 × 1= (n + 1)! ∀ n ∉ N
and the number is completely divisible by 910.
∴ 910 = 13 × 7 × 5 × 2
On putting the value of n = 12
from option (d). (12 + 1)! = 13!
=13 × 12 × 11 × 10 × ..... × 2 × 1
Which is completely divisible by 910.
So, the smallest natural number = 12

26. The expression 555⁷⁷⁷ + 777⁵⁵⁵ is divisible by which of the following?

1.2, 2.3, 3.37

Select the correct answer using the code given below.

Correct Answer: (d) 1, 2 and 3
Solution:

27. Consider the following statements :

1. If (3m³ + 2m² + 5m + n) / m is not an integer, where m and n are integers, then n is not divisible by m.
2. 5(8ᵐ) + 2³ᵐ is divisible by 48 for all whole numbers m.

Which of the statements given above is/are correct?

Correct Answer: (a) 1 only
Solution:

28. The sum of two positive number is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers?

Correct Answer: (c) 24
Solution:

29. 50 men can complete a work in 40 days. They begin the work together but a batch of 5 men left after each period of 10 days. What is the time to complete the work?

Correct Answer: (b) 50 days
Solution:Total work of 50 men in 40 days = 50 x 40 = 2000 units
Since, 5 men left the work after each period of 10 days.
On the first 10 days, the work will be = 50 x 10=500 units
Next 10 days, the work will be = 45 x 10 = 450 units
Similarly, 10 days the work will be = 40 x 10 400 units
10 days the work will be = 35 x 10 = 350 units
So, the last 10 days, the work will be = 30 x 10=300 units
∴ The total time taken to complete the work
= 10 +10 +10 +10 +10 = 50 days

30. which one of the following is correct?

Correct Answer: (a) 0 < x < 0.5
Solution: