CDS Exam (II)- 2026 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2026 - Elementary Mathematics

CDS Exam (II)- 2026 - Elementary Mathematics Defence Questions

31.
Consider the following statements:
I. The set of all birds living on the Earth is an infinite set.
II. The set of all real numbers between 0 and 10 is a finite set.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
D. Neither I nor II
32.
Consider the following sets:
I. The set of even prime numbers
II. \( \left\{ x \in \mathbb{R} : x^{3} + 1 = 0 \right\} \)
III. \( \left\{ n : n^{2} < 1 \right\} \), where n is an integer
How many of the above are null sets?
A.
None
B.
One
C.
Two
D.
All the three
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ANSWER :
A. None
33.
Consider the following statements:
I. If A is a subset of U and U is the Universal set, then the complement of the set A is also a subset of U.
II. The complement of a Universal set is a singleton set.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
A. I only
34.
What should be added to \( \frac{x^{2} - 1}{x^{2} + 1} \) to get \( \frac{2x^{3} + 3x^{2} - 1}{(x + 2)(x^{2} + 1)} \)?
A.
\( \frac{x^{2} - 1}{(x + 2)(x^{2} + 1)} \)
B.
\( \frac{x^{2} + 2}{(x + 2)(x^{2} + 1)} \)
C.
\( \frac{x + 1}{x + 2} \)
D.
\( \frac{x - 1}{x + 2} \)
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ANSWER :
C. \( \frac{x + 1}{x + 2} \)
35.
If x + y + z = 0, then what is \( x(y + z)^{2} + y(z + x)^{2} + z(x + y)^{2} \) equal to?
A.
xyz
B.
2xyz
C.
3xyz
D.
6xyz
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ANSWER :
C. 3xyz
36.
If \( \tan 6\theta \cdot \tan 3\theta = 1 \), where \( 0 < \theta < 30^{\circ} \), then what is \( \theta \) equal to?
A.
\( 5^{\circ} \)
B.
\( 10^{\circ} \)
C.
\( 15^{\circ} \)
D.
No such value exists
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ANSWER :
B. \( 10^{\circ} \)
37.
If \( \frac{1 - \tan x}{1 + \tan x} = 1 - \frac{2\tan x}{1 + \tan^{2} x} \), \( 0 \leq x < \frac{\pi}{2} \), \( x \neq \frac{\pi}{4} \), then what is \( (\sin x + \cos x) \) equal to?
A.
\( \frac{1}{2} \)
B.
\( \frac{3}{4} \)
C.
1
D.
\( \sqrt{2} \)
😑 View Answer Error
ANSWER :
C. 1
38.
If \( \cos^{2} x + \cos^{4} x = 1 \), where \( 0 < x < \frac{\pi}{2} \), then what is \( (\sin^{2} x + \sin^{3} x) + (\sin^{3} x + \sin^{4} x) \) equal to?
A.
\( \frac{21 + 12\sqrt{3}}{16} \)
B.
\( \frac{3 + 2\sqrt{2}}{4} \)
C.
\( \frac{9}{8} \)
D.
1
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ANSWER :
D. 1
39.
If \( \sin^{4} x + \cos^{4} x = 1 \), where \( 0 \leq x \leq \frac{\pi}{2} \), then what is \( \sin x \cdot \cos x \) equal to?
A.
0
B.
\( \frac{1}{2} \)
C.
\( \frac{3}{4} \)
D.
1
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ANSWER :
A. 0
40.
If \( 3\cos \theta + 4\sin \theta = 4 \), where \( 0 \leq \theta < \frac{\pi}{2} \), then what is \( 4\cos \theta + 3\sin \theta \) equal to?
A.
\( \frac{117}{25} \)
B.
3
C.
\( \frac{107}{25} \)
D.
4
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ANSWER :
A. \( \frac{117}{25} \)
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