CDS Exam (II)- 2024- Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2024- Elementary Mathematics

CDS Exam (II)- 2024- Elementary Mathematics Defence Questions

31.
A 4-digit number N has exactly 15 distinct divisors. What is the total number of distinct divisors of \( N^{2} \)?
A.
16
B.
30
C.
45
D.
225
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ANSWER :
C. 45
32.
If \( p \), \( q \) and \( r \) are the lengths (in cm) of the sides of a right-angled triangle, then \( (p - q - r)(q - r - p)(r - p - q) \) is
A.
positive only
B.
negative only
C.
non-positive only
D.
non-negative only
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ANSWER :
B. negative only
33.
What is the minimum value of \( \frac{(a^{8} + a^{4} + 1)(b^{8} + b^{4} + 1)}{a^{4}b^{4}} \) where \( a > 0 \), \( b > 0 \)?
A.
1
B.
4
C.
9
D.
16
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ANSWER :
C. 9
34.
In a class containing 200 students, \( n \) students prefer both tea and coffee; \( 2n \) students prefer coffee; \( 3n \) students prefer tea; \( 4n \) students prefer neither tea nor coffee. What is the value of \( n \)?
A.
20
B.
25
C.
30
D.
35
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ANSWER :
B. 25
35.
Let ABC be a triangle with area 36 square cm. If AB = 9 cm, BC = 12 cm and \( \angle ABC = \theta \), what is \( \cos\theta \) equal to?
A.
\( \frac{\sqrt{5}}{3} \)
B.
\( \frac{\sqrt{5}}{4} \)
C.
\( \frac{1}{3} \)
D.
\( \frac{2}{3} \)
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ANSWER :
A. \( \frac{\sqrt{5}}{3} \)
36.
Let \( n \) be a natural number. The HCF of \( n \), and \( (n + 10) \) is 10. If the LCM is \( x \) (a 2-digit number), then how many values of \( x \) are possible?
A.
Only one
B.
Only two
C.
Only three
D.
More than three
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ANSWER :
B. Only two
37.
What is HCF of \( a^{4} + 2a^{3} + 3a^{2} + 2a + 1 \) and \( a^{6} - 2a^{3} + 1 \)?
A.
\( a^{3} + 3a^{2} + 2a + 1 \)
B.
\( a^{3} + a^{2} + a + 1 \)
C.
\( (a^{2} + a + 1)^{2} \)
D.
\( (a^{2} - a + 1)^{2} \)
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ANSWER :
C. \( (a^{2} + a + 1)^{2} \)
38.
If the roots of the equation \( x^{2} - (k - 2)x + (k + 1) = 0 \) are equal, then what are the values of \( k \)?
A.
0, 4
B.
0, 8
C.
4, 4
D.
2, 6
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ANSWER :
B. 0, 8
39.
What is \( \left(\frac{\cos\theta - \sin\theta + 1}{\cos\theta + \sin\theta - 1}\right)(\cot\theta - \mathrm{cosec}\theta) \) equal to?
A.
-1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
A. -1
40.
What is \( \frac{\sin\theta - 2\sin^{3}\theta}{2\cos^{3}\theta - \cos\theta} \) equal to?
A.
\( \sin^{2}\theta \)
B.
\( \cos^{2}\theta \)
C.
\( \cot\theta \)
D.
\( \tan\theta \)
😑 View Answer Error
ANSWER :
D. \( \tan\theta \)
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