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

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CDS Exam (I)- 2024- Elementary Mathematics

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

1.
If a : b : c : d = \( \sqrt{4} : \sqrt{3} : \sqrt{2} : \sqrt{1} \), then what is the value of \( \frac{\left(-a^{2} + b^{2} + c^{2} + d^{2}\right)}{\left(a^{2} - b^{2} + c^{2} - d^{2}\right)} \)?
A.
1
B.
2
C.
3
D.
6
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ANSWER :
A. 1
2.
The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where x, u, t are real numbers. What is the value of x?
A.
8
B.
6
C.
5
D.
2
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ANSWER :
B. 6
3.
If m : n = 1 : 2 and p : q = 3 : 4, then what is (2m + 4p) : (n + 3q) equal to?
A.
1 : 1
B.
1 : 3
C.
2 : 1
D.
2 : 3
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ANSWER :
A. 1 : 1
4.
If the rate of interest is 5%, then what would be the difference between compound interest and simple interest received on ₹ 10,000 (each) after 3 years from now?
A.
₹ 175.25
B.
₹ 152.25
C.
₹ 76.25
D.
₹ 24.25
😑 View Answer Error
ANSWER :
C. ₹ 76.25
5.
A person bought a book at 3/4th of its listed price and sold it at 50% more than its listed price. What is the percentage of gain in the transaction?
A.
20%
B.
40%
C.
75%
D.
100%
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ANSWER :
D. 100%
6.
If the difference between the interior and exterior angles of a regular polygon is \( 144^{\circ} \), then what is the number of sides of the polygon?
A.
12
B.
16
C.
18
D.
20
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ANSWER :
D. 20
7.
If the sum and product of the roots of a quadratic equation are 2 and -100 respectively, then which one of the following is correct?
A.
There are infinitely many such equations having different roots.
B.
There is only one such equation which is \( x^{2} + 2x - 100 = 0 \).
C.
There is only one such equation which is \( x^{2} - 2x - 100 = 0 \).
D.
There is no such equation.
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ANSWER :
C. There is only one such equation which is \( x^{2} - 2x - 100 = 0 \).
8.
If 2 is a zero of the polynomial
\( p(x) = x^{3} + 3x^{2} - 6x - a \), then what is the sum of the squares of the other zeros of the polynomial?
A.
10
B.
17
C.
21
D.
37
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ANSWER :
B. 17
9.
If t = \( \cos 79^{\circ} \), then what is
\( \mathrm{cosec} 79^{\circ} \left(1 - \cos 79^{\circ}\right) \) equal to?
A.
\( \sqrt{\frac{1 + t}{1 - t}} \)
B.
\( \frac{t}{\sqrt{1 - t^{2}}} \)
C.
\( \frac{\sqrt{1 - t^{2}}}{t} \)
D.
\( \sqrt{\frac{1 - t}{1 + t}} \)
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ANSWER :
D. \( \sqrt{\frac{1 - t}{1 + t}} \)
10.
Suppose \( p(x) = x^{4} + a_{3}x^{3} + a_{2}x^{2} + a_{1}x + a_{0} \) and \( q(x) = x^{4} + b_{3}x^{3} + b_{2}x^{2} + b_{1}x + b_{0} \) are the polynomials. If \( \alpha, \beta, \gamma, \delta \) are zeros of p(x) and \( \alpha, \beta, \gamma, \lambda \) are zeros of q(x), then what is \( \frac{p(x) - q(x)}{(x - \alpha)(x - \beta)(x - \gamma)} \) equal to?
A.
\( -\lambda + \delta \)
B.
\( \lambda - \delta \)
C.
\( \lambda + \delta \)
D.
\( -\lambda - \delta \)
😑 View Answer Error
ANSWER :
B. \( \lambda - \delta \)
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