CDS Exam (II)- 2014 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2014 - Elementary Mathematics

CDS Exam (II)- 2014 - Elementary Mathematics Defence Questions

31.
The LCM of two distinct positive integers is 1237. What is their HCF?
A.
37
B.
19
C.
1
D.
Cannot be determined
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ANSWER :
C. 1
32.
What is \( \frac{1}{a - b} - \frac{1}{a + b} - \frac{2b}{a^{2} + b^{2}} - \frac{4b^{3}}{a^{4} + b^{4}} - \frac{8b^{7}}{a^{8} - b^{8}} \) equal to?
A.
\( a + b \)
B.
\( a - b \)
C.
1
D.
0
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ANSWER :
D. 0
33.
A man rides one-third of the distance from A to B at the rate of x km/hr and the remainder at the rate of 2y km/hr. If he had travelled at a uniform rate of 6z km/hr, he could have ridden from A to B and back again in the same time. Which one of the following is correct?
A.
\( z = x + y \)
B.
\( 3z = x + y \)
C.
\( \frac{1}{z} = \frac{1}{x} + \frac{1}{y} \)
D.
\( \frac{2}{z} = \frac{1}{x} + \frac{1}{y} \)
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ANSWER :
C. \( \frac{1}{z} = \frac{1}{x} + \frac{1}{y} \)
34.
If \( ax + by - 2 = 0 \) and \( axby = 1 \), where \( a \neq 0, b \neq 0 \), then what is \( (a^{2}x + b^{2}y) \) equal to?
A.
\( a + b \)
B.
\( 2ab \)
C.
\( a^{2} + b^{2} \)
D.
\( a^{4} + b^{4} \)
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ANSWER :
A. \( a + b \)
35.
Consider the following statements:
1. \( (a - b - c) \) is one of the factors of \( 3abc + b^{3} + c^{3} - a^{3} \).
2. \( (b + c - 1) \) is one of the factors of \( 3bc + b^{3} + c^{3} - 1 \).
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
36.
\( 7^{10} - 5^{10} \) is divisible by
A.
10
B.
7
C.
5
D.
11
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ANSWER :
D. 11
37.
Consider the following statements in respect of four spheres A, B, C and D having respective radii 6, 8, 10 and 12 cm:
1. The surface area of sphere C is equal to the sum of surface areas of spheres A and B.
2. The volume of sphere D is equal to the sum of volumes of spheres A, B and C.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
C. Both 1 and 2
38.
What is the number of divisors of 360?
A.
12
B.
18
C.
24
D.
None of the above
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ANSWER :
C. 24
39.
The multiplication of a three-digit number XY5 with digit Z yields X215. What is X + Y + Z equal to?
A.
13
B.
15
C.
17
D.
18
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ANSWER :
A. 13
40.
If the equation \( x^{2} + 2(1 + k)x + k^{2} = 0 \) has equal roots, then what is the value of k?
A.
\( \frac{1}{2} \)
B.
\( -\frac{1}{2} \)
C.
1
D.
−1
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ANSWER :
B. \( -\frac{1}{2} \)
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