SOLVED PAPER 2022 (CDS) (I) (Elementary Mathematics)

1. What is the ratio of interior angle to exterior angle of a regular polygon of n sides?

Correct Answer: (c)

Solution:

2. 41⁴³ + 43⁴³ is divisible by

(a) 80
(b) 84
(c) 86
(d) 88

Correct Answer: (b) 84

Solution:

3. Solved

(a) 1
(b) 2
(c) 3
(d) 4

Correct Answer: (d) 4

Solution:

4. 4⁶¹+ 4⁶² + 4⁶³ + 4⁶⁴ is divisible by

(a) 7
(b) 9
(c) 11
(d) 17

Correct Answer: (d) 17

Solution:We have,
4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴
= 4⁶¹ [1 + 4 + 4 ^ 2 + 4 ^ 3]
= 4⁶¹ × 85
= 4⁶¹ × 5 × 17
Hence, it is divisible by 17.

5. Suppose p and q are the LCM and HCF respectively of two positive numbers. If p : q = 14 : 1 and pq = 1134 then what is the difference between the two numbers?

(a) 27
(b) 35
(c) 45
(d) Cannot be determined due to insufficient data

Correct Answer: (c) 45

Solution:Given, p and q are the LCM
and HCF of two positive numbers.
p : q = 14 : 1, pq = 1134

We know that,
HCF × LCM= Product of two numbers
Let the value of p and q be 14x and
x, respectively.
According to the question,
pq = 1134
⇒ 14 × 𝓍 = 1134
⇒ x² = 1134/14 = 81
∴ x = 9
So, p = 14 × 9 = 126
and q = 1 × 9 = 9
Since, p and q are the LCM and
HCF of two numbers.
Then, we can let two numbers are
9m and 9n [since, 9 is the HCF of
two numbers]
Now, according to the formula,
LCM × HCF = Product of two
numbers
⇒ 126 × 9 = 9m × 9n
∴ mn = 14
So, the possible value of m and n is
(14, 1) and (7, 2).

Case I :- When we take m = 7 and
n = 2 we get
Numbers are ( 9 × 7 =) 63 and
( 9 × 2 =) 18.
So, the difference between the
numbers = 63-18 = 45

Case II :- When we take m = 14and
n = 1 we get
Numbers are ( 9 × 14 =) 126 and
( 9 × 1 =)9
So, the difference between the
numbers = 126-9 = 117
Hence, according to the options,
difference = 45