CDS Exam (I)- 2017 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2017 - Elementary Mathematics

CDS Exam (I)- 2017 - Elementary Mathematics Defence Questions

41.
What is the LCM of \( x^{3} + 8 \), \( x^{2} + 5x + 6 \) and \( x^{3} + 4x^{2} + 4x \)?
A.
\( x(x + 2)^{2}(x + 3)(x^{2} - 2x + 4) \)
B.
\( x(x - 2)^{2}(x - 3)(x^{2} + 2x + 4) \)
C.
\( (x + 2)^{2}(x + 3)(x^{2} - 2x + 4) \)
D.
\( (x - 2)^{2}(x - 3)(x^{2} - 2x + 4) \)
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ANSWER :
A. \( x(x + 2)^{2}(x + 3)(x^{2} - 2x + 4) \)
42.
The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?
A.
\( p + q \)
B.
\( p - q \)
C.
pq
D.
\( (pq)^{-1} \)
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ANSWER :
D. \( (pq)^{-1} \)
43.
What is the value of \( \sqrt[3]{4\frac{12}{125}} \)?
A.
\( 1\frac{3}{5} \)
B.
\( 1\frac{2}{5} \)
C.
\( 1\frac{1}{5} \)
D.
\( 2\frac{2}{5} \)
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ANSWER :
A. \( 1\frac{3}{5} \)
44.
A thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and that of the policeman is 10 km/hour, then how far will the thief have to run before he is overtaken?
A.
200 m
B.
300 m
C.
400 m
D.
500 m
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ANSWER :
C. 400 m
45.
Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are
A.
\( -4, -3 \)
B.
6, 1
C.
4, 3
D.
\( -6, -1 \)
😑 View Answer Error
ANSWER :
B. 6, 1
46.
Consider the following statements :
1. Of two consecutive integers, one is even.
2. Square of an odd integer is of the form \( 8n + 1 \).
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
47.
The system of equations \( 2x + 4y = 6 \) and \( 4x + 8y = 8 \) is
A.
Consistent with a unique solution
B.
Consistent with infinitely many solutions
C.
Inconsistent
D.
None of the above
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ANSWER :
C. Inconsistent
48.
\( (N^{p-1} - 1) \) is a multiple of p, if N is prime to p and p is a
A.
Prime number
B.
Rational number
C.
Real number
D.
Composite number
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ANSWER :
A. Prime number
49.
The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the squares of these two numbers?
A.
1024
B.
1256
C.
1536
D.
1640
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ANSWER :
C. 1536
50.
25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?
A.
1 : 2
B.
2 : 3
C.
3 : 5
D.
7 : 11
😑 View Answer Error
ANSWER :
D. 7 : 11
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