CDS Exam (II)- 2022 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2022 - Elementary Mathematics

CDS Exam (II)- 2022 - Elementary Mathematics Defence Questions

1.
If \( x^{2} - 20 = \sqrt{20 + \sqrt{20 + \sqrt{20 + \sqrt{20 + \ldots}}}} \) infinite terms, then what is x equal to?
A.
4
B.
5
C.
\( \sqrt{5} \)
D.
\( 2\sqrt{5} \)
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ANSWER :
B. 5
2.
If \( \frac{a + b}{b + c} = \frac{c + d}{d + a} \) where \( a \neq c \), then which one of the following is correct?
A.
a + b = c + d
B.
a + c = b + d
C.
a - b - c + d = 0
D.
a + b + c + d = 0
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ANSWER :
D. a + b + c + d = 0
3.
If \( (a^{3} + b^{3}) \) is proportional to \( (a^{2} - b^{2}) \), then \( (a^{2} - ab + b^{2}) \) is proportional to
A.
(a - b)
B.
(a + b)
C.
(a + ab + b)
D.
\( (a^{3} - b^{3}) \)
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ANSWER :
A. (a - b)
4.
If \( \frac{\sqrt{x + 20} + \sqrt{x - 1}}{\sqrt{x + 20} - \sqrt{x - 1}} = \frac{7}{3} \), then what is the value of \( \sqrt{(x + 20)(x - 1)} \)?
A.
8
B.
9
C.
10
D.
12
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ANSWER :
C. 10
5.
What is the HCF of \( (x^{8} - y^{8}) \) and \( (x^{7} - y^{7} + x^{5}y^{2} - x^{2}y^{5}) \)?
A.
\( (x^{2} + y^{2}) \)
B.
\( (x^{2} - y^{2}) \)
C.
\( (x^{3} - y^{3} - x^{2}y + xy^{2}) \)
D.
\( (x^{3} - y^{3} + x^{2}y - xy^{2}) \)
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ANSWER :
C. \( (x^{3} - y^{3} - x^{2}y + xy^{2}) \)
6.
If the sum of the squares of the roots of the equation \( x^{2} - 14x + k = 0 \) is 100, then what is the value of k?
A.
42
B.
48
C.
52
D.
56
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ANSWER :
B. 48
7.
If (x + k) is the HCF of \( x^{2} + px + q \) and \( x^{2} + qx + p \), where \( p \neq q \), then what is the value of k?
A.
-1
B.
0
C.
\( \frac{1}{2} \)
D.
1
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ANSWER :
A. -1
8.
If three times the greater of two numbers is divided by the smaller number, the quotient will be 6 and the remainder will be 6. If five times the smaller number is divided by the greater number, the quotient will be 2 and the remainder will be 3. What is the difference between the numbers?
A.
8
B.
9
C.
10
D.
12
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ANSWER :
B. 9
9.
Consider the following statements:
1. (ab + bc + ca) is a factor of \( a^{2}(b - c)^{3} + b^{2}(c - a)^{3} + c^{2}(a - b)^{3} \).
2. (a + b + c) is a factor of \( a^{2}(b - c)^{3} + b^{2}(c - a)^{3} + c^{2}(a - b)^{3} \).
Which of the statements given above is/are correct?
A.
Only 1
B.
Only 2
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
A. Only 1
10.
What is \( \frac{1}{x(x - y)(x - z)} + \frac{1}{y(y - z)(y - x)} + \frac{1}{z(z - x)(z - y)} \) equal to?
A.
0
B.
1
C.
\( \frac{1}{xyz} \)
D.
\( -\frac{1}{xyz} \)
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ANSWER :
C. \( \frac{1}{xyz} \)
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