CDS Exam (I)- 2023 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2023 - Elementary Mathematics

CDS Exam (I)- 2023 - Elementary Mathematics Defence Questions

41.
What is the difference between simple interest and compound interest on ₹ 10,000 for two years at 20% per annum compounded half-yearly?
A.
₹ 842
B.
₹ 756
C.
₹ 641
D.
₹ 542
😑 View Answer Error
ANSWER :
C. ₹ 641
42.
Consider the following statements in respect of the polynomial \( a(b - c)(x - b)(x - c) + b(c - a)(x - c)(x - a) + c(a - b)(x - a)(x - b) \):
1. The coefficient of \( x^{2} \) is 0.
2. The coefficient of x is \( (a - b)(b - c)(c - a) \).
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. 1 only
43.
Consider the following statements in respect of the polynomial \( 1 - x - x^{n} + x^{n+1} \), where n is a natural number:
1. It is divisible by \( 1 - 2x + x^{2} \).
2. It is divisible by \( 1 - x^{n} \).
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
C. Both 1 and 2
44.
For what values of m, is \( mx^{2} + mx + 8x + 9 \) a perfect square?
A.
1, 4
B.
4, 9
C.
9, 16
D.
4, 16
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ANSWER :
D. 4, 16
45.
If \( x = a + b + \frac{(a - b)^{2}}{4a + 4b} \) and \( y = \frac{a + b}{4} + \frac{ab}{a + b} \), then what is the value of \( (x - a)^{2} - (y - b)^{2} \)?
A.
\( a^{2} \)
B.
\( b^{2} \)
C.
ab
D.
\( a^{2}b^{2} \)
😑 View Answer Error
ANSWER :
B. \( b^{2} \)
46.
Consider the following:
1. \( \cos^{4} \theta - \sin^{4} \theta = \frac{2 \tan \theta}{1 - \tan^{2} \theta}, 0 < \theta < \frac{\pi}{2} \)
2. \( \mathrm{cosec} \theta + \cot \theta = \frac{1}{\mathrm{cosec} \theta - \cot \theta}, 0 < \theta < \frac{\pi}{2} \)
3. \( \cos^{2} \theta - \sin^{2} \theta = \frac{1 - \tan^{2} \theta}{1 + \tan^{2} \theta}, 0 < \theta < \frac{\pi}{2} \)
Which of the above equations are identities?
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
B. 2 and 3 only
47.
If \( \sin \theta = \frac{12}{13} \), then what is the value of \( (\tan \theta + \sec \theta)^{2} (\mathrm{cosec} \theta - \cot \theta)^{-2}, 0 < \theta < \frac{\pi}{2} \)?
A.
\( \frac{121}{4} \)
B.
\( \frac{169}{9} \)
C.
\( \frac{196}{9} \)
D.
\( \frac{225}{4} \)
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ANSWER :
D. \( \frac{225}{4} \)
48.
If \( \tan^{8} \theta + \cot^{8} \theta = m \), then what is the value of \( \tan \theta + \cot \theta \)?
A.
\( \sqrt{\sqrt{m + 2} + 2} \)
B.
\( \sqrt{\sqrt{\sqrt{m + 4} + 2}} \)
C.
\( \sqrt{\sqrt{\sqrt{m + 2} + 2} + 2} \)
D.
\( \sqrt{\sqrt{\sqrt{m + 4} + 2} + 2} \)
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ANSWER :
C. \( \sqrt{\sqrt{\sqrt{m + 2} + 2} + 2} \)
49.
What is the minimum value of \( 6 - 4 \sin \theta, 0 \leq \theta \leq \frac{\pi}{2} \)?
A.
1
B.
2
C.
4
D.
6
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ANSWER :
B. 2
50.
What is the value of x that satisfies \( 4 \cos^{2} 30^{\circ} + 2x \sin 30^{\circ} - \cot^{2} 30^{\circ} - 6 \tan 15^{\circ} \tan 75^{\circ} = 0 \)?
A.
1
B.
2
C.
3
D.
6
😑 View Answer Error
ANSWER :
D. 6
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