CDS Exam (I)- 2021 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2021 - Elementary Mathematics

CDS Exam (I)- 2021 - Elementary Mathematics Defence Questions

41.
What is \( \log_{10} 31.25 \) equal to?
A.
\( 3 - 5\log_{10} 2 \)
B.
\( 3 - 2\log_{10} 2 \)
C.
\( 5 - 5\log_{10} 2 \)
D.
\( 5 - 3\log_{10} 2 \)
😑 View Answer Error
ANSWER :
A. \( 3 - 5\log_{10} 2 \)
42.
What is the square root of \( 15 - 4\sqrt{14} \)?
A.
\( 2\sqrt{2} - \sqrt{7} \)
B.
\( 3\sqrt{2} - 2\sqrt{7} \)
C.
\( \sqrt{15} - \sqrt{7} \)
D.
\( \sqrt{5} - \sqrt{3} \)
😑 View Answer Error
ANSWER :
A. \( 2\sqrt{2} - \sqrt{7} \)
43.
The sum of the reciprocals of two alternate natural numbers is \( \frac{7}{24} \). What is the sum of the numbers?
A.
12
B.
13
C.
14
D.
16
😑 View Answer Error
ANSWER :
C. 14
44.
If \( n \) is any natural number, then \( 5^{2n} - 1 \) is always divisible by how many natural numbers?
A.
One
B.
Four
C.
Six
D.
Eight
😑 View Answer Error
ANSWER :
D. Eight
45.
If \( 5^{x - 3} = 8 \), then what is \( x \) equal to?
A.
\( \frac{3}{1 - \log_{10} 2} \)
B.
\( \frac{3}{1 + \log_{10} 2} \)
C.
\( \frac{2}{1 - \log_{10} 2} \)
D.
\( \frac{5}{1 - \log_{10} 2} \)
😑 View Answer Error
ANSWER :
A. \( \frac{3}{1 - \log_{10} 2} \)
46.
What is the least value of \( 3\sin^{2} \theta + 4\cos^{2} \theta \)?
A.
5
B.
4
C.
3
D.
2
😑 View Answer Error
ANSWER :
C. 3
47.
If \( \sin \theta \cos \theta = k \), where \( 0 \leq \theta \leq \frac{\pi}{2} \), then which one of the following is correct?
A.
\( -1 \leq k < 0 \)
B.
\( 0 \leq k \leq 0.5 \) only
C.
\( 0.5 \leq k \leq 1 \) only
D.
\( 0 < k < 1 \)
😑 View Answer Error
ANSWER :
B. \( 0 \leq k \leq 0.5 \) only
48.
If \( p = \sin^{2} \theta + \cos^{4} \theta \) for \( 0 \leq \theta \leq \frac{\pi}{2} \), then consider the following statements:
1. \( p \) can be less than \( \frac{3}{4} \).
2. \( p \) can be more than 1.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
D. Neither 1 nor 2
49.
What is the ratio of the greatest to the smallest value of \( 2 - 2\sin x - \sin^{2} x \), \( 0 \leq x \leq \frac{\pi}{2} \)?
A.
-3
B.
-2
C.
1
D.
3
😑 View Answer Error
ANSWER :
B. -2
50.
If the equation \( x^{2} + y^{2} - 2xy\sin^{2} \theta = 0 \) contains real solution for \( x \) and \( y \), then
A.
\( x = y \)
B.
\( x = -y \)
C.
\( x = 2y \)
D.
\( 2x = y \)
😑 View Answer Error
ANSWER :
A. \( x = y \)
Prev Next page