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

Total Questions: 100

1. The number 2 × 3 × 5 × 7 × 11 + 1 is

Correct Answer: (a) a prime number
Solution:Given, number 2 × 3 × 5 × 7 × 11 + 1 = 2310 + 1 = 2311
Which is a prime number.

2. Two unequal pairs of numbers satisfy the following conditions

(i) The product of the two numbers in each pair is 2160.
(ii) The HCF of the two numbers in each pair is 12.

If x is the mean of the numbers in the first pair and y is the mean of the numbers in the second pair, then what is the mean of x and y?

Correct Answer: (b) 72
Solution:Let two unequal pairs of numbers are (12a, 12b) and (12c 12d).

3. How many digits are there in (54)¹⁰ ? (Given that log₁₀ 2 = 0.301 and log₁₀ 3 = 0.477

Correct Answer: (b) 18
Solution:Let x = (54)¹⁰

4. Simplify the equation

Correct Answer: (a) {1, n²}
Solution:


5. In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics?

Correct Answer: (d) 160
Solution:Total number of students have registered = 250
Students have registered for Physics = 50
Students have registered for Mathematics = 75
And students have registered for both Mathematics and Physics = 35

∴ Number of students who registered for atleast one subject
= (50 - 35) + (75 - 35) + 35
= 15 + 40 + 35 = 90

∴ The number of students who have registered neither for Physics nor for Mathematics = 250-90 = 160

6. If the sum of the digits of a number 10ⁿ - 1, where n is a natural number, is equal to 3798, then what is the value of n ?

Correct Answer: (b) 422
Solution:

7. Which one of the following is the largest number among 2222², 222²², 22²²², 2²²²² ?

Correct Answer: (a) 2²²²²
Solution:


8. If m is the number of prime numbers between 0 and 50 ; and n is the number of prime numbers between 50 and 100, then what is (m - n) equal to?

Correct Answer: (b) 5
Solution:

9. Answer the following question

Correct Answer: (b) ¾
Solution:



10. Which one of the following is the largest divisor of 3ˣ + 3ˣ⁺¹ + 3ˣ⁺², if x is any natural number?

Correct Answer: (c) 39
Solution: