CDS Exam (II)- 2022 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2022 - Elementary Mathematics

CDS Exam (II)- 2022 - Elementary Mathematics Defence Questions

21.
Consider the number \( N = 12^{6} \times 3^{8} \times 5^{3} \). Which of the following statements is/are correct?
1. The number of odd factors of N is 60.
2. The number of even factors of N is 720.
Select the correct answer using the code given below:
A.
Only 1
B.
Only 2
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
C. Both 1 and 2
22.
If \( \frac{\log_{10} a}{b - c} = \frac{\log_{10} b}{c - a} = \frac{\log_{10} c}{a - b} \), \( (a \neq b \neq c) \), then what is the value of abc?
A.
-1
B.
0
C.
1
D.
3
😑 View Answer Error
ANSWER :
C. 1
23.
What is the angle between the hour hand and the minute hand of a clock when the clock shows 4 hours 40 minutes?
A.
\( 80^{\circ} \)
B.
\( 100^{\circ} \)
C.
\( 120^{\circ} \)
D.
\( 220^{\circ} \)
😑 View Answer Error
ANSWER :
B. \( 100^{\circ} \)
24.
If \( \log_{10}\left(995 + \sqrt{x^{2} - 12x + 60}\right) = 3 \), then what is the sum of the roots of the equation?
A.
12
B.
11
C.
10
D.
9
😑 View Answer Error
ANSWER :
A. 12
25.
How many of the following values of x would satisfy the equation \( qx^{2} - 2px + q = 0 \)?
1. \( x = \frac{\sqrt{p + q} + \sqrt{p - q}}{\sqrt{p + q} - \sqrt{p - q}} \), where \( p > q \)
2. \( x = \frac{p + \sqrt{p^{2} - q^{2}}}{q} \), where \( p > q \)
3. \( x = \frac{\sqrt{p + q}}{\sqrt{p - q}} \), where \( p > q \)
Select the correct answer using the code given below:
A.
Only one value
B.
Only two values
C.
All three values
D.
None
😑 View Answer Error
ANSWER :
B. Only two values
26.
Let \( p(x) = x^{4} + x^{2} + 1 \), \( q(x) = x^{4} - 2x^{3} + 3x^{2} - 2x + 1 \). If GCD of p(x) and q(x) is \( x^{2} - x + 1 \), then what is their LCM?
A.
\( (x^{2} + x + 1)(x^{2} - x + 1)^{2} \)
B.
\( (x^{4} + x^{2} + 1)^{2}(x^{2} - x + 1) \)
C.
\( (x^{4} + x^{2} + 1)(x^{2} + x + 1)^{2} \)
D.
\( (x^{4} + x^{2} + 1)(x^{2} - x + 1)^{2} \)
😑 View Answer Error
ANSWER :
A. \( (x^{2} + x + 1)(x^{2} - x + 1)^{2} \)
27.
Consider the question and two statements given below:
A 2-digit number is added to the number formed by reversing the digits of the 2-digit number.
Question: What is the 2-digit number?
Statement-1: The sum is divisible by 9.
Statement-2: The sum is divisible by 2.
Which one of the following is correct in respect of the question and the statements?
A.
Statement-1 alone is sufficient to answer the question
B.
Statement-2 alone is sufficient to answer the question
C.
Both Statement-1 and Statement-2 are sufficient to answer the question
D.
Both Statement-1 and Statement-2 are not sufficient to answer the question
😑 View Answer Error
ANSWER :
C. Both Statement-1 and Statement-2 are sufficient to answer the question
28.
Consider the question and two statements given below:
LCM of two numbers x and y is 481 where \( x > y \).
Question: What is the value of (3x - 2y)?
Statement-1: \( y > 1 \).
Statement-2: HCF of x and y is 1.
Which one of the following is correct in respect of the question and the statements?
A.
Statement-1 alone is sufficient to answer the question
B.
Statement-2 alone is sufficient to answer the question
C.
Both Statement-1 and Statement-2 are sufficient to answer the question
D.
Both Statement-1 and Statement-2 are not sufficient to answer the question
😑 View Answer Error
ANSWER :
C. Both Statement-1 and Statement-2 are sufficient to answer the question
29.
Consider the question and two statements given below:
Question: Is \( (x^{n} + y^{n}) \) divisible by (x + y)?
Statement-1: n is a natural number.
Statement-2: n is an even natural number.
Which one of the following is correct in respect of the question and the statements?
A.
Statement-1 alone is sufficient to answer the question
B.
Statement-2 alone is sufficient to answer the question
C.
Both Statement-1 and Statement-2 are sufficient to answer the question
D.
Both Statement-1 and Statement-2 are not sufficient to answer the question
😑 View Answer Error
ANSWER :
B. Statement-2 alone is sufficient to answer the question
30.
Consider the question and two statements given below:
Let x and y be two real numbers.
Question: Is \( xy > 0 \)?
Statement-1: \( x^{8}y^{9} < 0 \).
Statement-2: \( x^{9}y^{10} < 0 \).
Which one of the following is correct in respect of the question and the statements?
A.
Statement-1 alone is sufficient to answer the question
B.
Statement-2 alone is sufficient to answer the question
C.
Both Statement-1 and Statement-2 are sufficient to answer the question
D.
Both Statement-1 and Statement-2 are not sufficient to answer the question
😑 View Answer Error
ANSWER :
C. Both Statement-1 and Statement-2 are sufficient to answer the question
Prev Next page