SOLVED PAPER 2024 (CDS) (II) (Mathematics)

Total Questions: 100

61. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question : What is the integral value of k for which the expression 4x² - kx + 1 is positive?
Statements :
I. k < - 2
II. k > - 4
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (c) The question can be answered by using both the statements together, but cannot be answered using either statement alone

62. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question : In how many days can A, B and C together finish the work?
Statements
I. A and B together can finish the work in 24 days
II. B and C together can finish the work in 36 days.
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (d) The question cannot be answered even by using both the statements together
Solution:There is no relation defined on A and C. So, insufficient data.

63. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question: Can we have a common solution which is prime?
Statements:
I: x² - 26x + 133 = 0
II. x² - 44x + 475 = 0
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (c) The question can be answered by using both the statements together, but cannot be answered using either statement alone
Solution:Statement I. x² - 26x + 133 = 0
x² - 19x - 7x + 133 = 0
(x - 19)(x - 7) = 0
x = 19, 7
Statement II. x² - 44x + 475 = 0
x² - 25x - 19x + 475 = 0
(x - 25)(x - 19) = 0
x = 25, 19
⇒ Common solution is x = 19 which is prime.
So, (c) is the correct option.

64. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question: Is 327" + 173" divisible by 500?

Statements:
I. n is odd natural number
II. n is a positive integer
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (a) The question can be answered by using one of the statement alone, but cannot be answered using the other statements alone
Solution:327ⁿ + 173ⁿ We know that
(aⁿ + bⁿ)/(a + b) if n is odd.
Take n = 1 then 327 + 173 = 500
which is divisible by 500
⇒ Statement I correct.
Take n = 2
(327)² + (173)² = 136858 which is not divisible by 500.
So, Statement II is incorrect.
∴ (a) is the correct option.

65. A question is given followed by two Statements I and II. Consider the question and the Statements and mark the correct option.

Question: If the price of petrol goes up by 20%, by what percentage should the consumption be reduced, so that the expenditure remains the same?
Statements:
I. Price of petrol per liter was ₹90.
II. Consumption was 24 L before price hike.
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (d) The question cannot be answered even without using any of the statements
Solution:Price of petrol increase 20% ↑
Price: 5 → 6
Quantity: 6 → 5
Expenditure same same
Quantity decrease 1/6 × 100 = (16⅔)%
So, we do not use any statement.
∴ (d) is the correct option.

66. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question: The ratio of P's salary to Q's salary is 6: 5. How much is P's expenditure?
Statements:
I. The ratio of P's saving to Q's saving is 3 : 2.
II. The ratio of P's expenditure to Q's expenditure is 1 : 1.
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (d) The question cannot be answered even by using both the statements together.

67. A question is given followed by two Statements I and II. Consider the question and the statements and mark the correct option.

Question: The largest of five different integers is 8 and least is 2. What is the average of these integers?
Statements:
I. The sum of all the 5 integers is a multiple of 5
II. The number of odd integers is odd.
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (a) The question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

68. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question: There are three different weights. All the weights are integers and their sum is a prime number. What are the weights?
Statements:
I. One of the weights is twice the another weight
II. One of the weights is thrice the another weight
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (c) The question can be answered by using both the statements together, but cannot be answered using either statement alone.
Solution:a + b + c = Prime no.
Given that one of the weights is twice other and one of the weight is thrice the another weight.
i.e., a = 2b
⇒ a/b = 2/1 and b = 3c
⇒ b/c = 3/1
⇒ a/c = 3/1
From given relation we can't find exact value of a, b and c we can always find ratio of a, b, c.

69. A question is given followed by two statements I and II. Consider the question and the statements and mark the correct option.

Question: What is the amount at the end of 10 yr?
Statements:
I. The principal amount is ₹100000
II. Rate of interest is 10% per annum
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (d) The question cannot be answered even by using both the statements together
Solution:Time period = 10 years
Principal amount = 100000
Rate of interest = 10% per annum
But it is not say about to find compound interest or simple interest.

70. A question is given followed by two Statements I and II. Consider the question and the statements and mark the correct option.

Question: Is p² + pq + q² odd where p, q are integers?
Statements:
I. p + q is even
II. pq is odd.
Which one of the following is correct in respect of the above question and the statements?

Correct Answer: (a) The question can be answered by using one of the statements alone, but cannot be answered using the other statements alone
Solution:p² + pq + q² odd where p/q are integer.
p + q = even
⇒ p and q are both even or both odd.
If p, q are even then P² + pq + q² is even so this case is incorrect.
Statement I is incorrect.
pq is odd P ⇒ odd and q = odd
⇒ p² + pq + q² is odd.
So statement II is correct.
∴ (a) is the correct option.