CDS Exam (I)- 2019 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2019 - Elementary Mathematics

CDS Exam (I)- 2019 - Elementary Mathematics Defence Questions

21.
For \( x = \frac{4\sqrt{6}}{\sqrt{2}+\sqrt{3}} \), what is the value of \( \frac{x+2\sqrt{2}}{x-2\sqrt{2}} + \frac{x+2\sqrt{3}}{x-2\sqrt{3}} \)?
A.
1
B.
\( \sqrt{2} \)
C.
\( \sqrt{3} \)
D.
2
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ANSWER :
D. 2
22.
x, y and z are three numbers such that x is 30% of z and y is 40% of z. If x is p% of y, then what is the value of p?
A.
45
B.
55
C.
65
D.
75
😑 View Answer Error
ANSWER :
D. 75
23.
A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?
A.
75 seconds
B.
90 seconds
C.
105 seconds
D.
135 seconds
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ANSWER :
C. 105 seconds
24.
Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:
1. Both p and q may be prime numbers.
2. Both p and q may be composite numbers.
3. One of p and q may be prime and the other composite.
Which of the above statements are correct?
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
25.
In a class of 100 students, the average weight is 30 kg. If the average weight of the girls is 24 kg and that of the boys is 32 kg, then what is the number of girls in the class?
A.
25
B.
26
C.
27
D.
28
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ANSWER :
A. 25
26.
For any two real numbers a and b, \( (a-b)^{2} + (b-a)^{2} \) is
A.
always zero
B.
never zero
C.
positive only if \( a \neq b \)
D.
positive if and only if a > b
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ANSWER :
C. positive only if \( a \neq b \)
27.
If a : b = c : d = 1 : 6, then what is the value of \( \frac{a^{2}+c^{2}}{b^{2}+d^{2}} \)?
A.
\( \frac{1}{600} \)
B.
\( \frac{1}{60} \)
C.
\( \frac{1}{36} \)
D.
\( \frac{1}{6} \)
😑 View Answer Error
ANSWER :
C. \( \frac{1}{36} \)
28.
What is \( 0.5\bar{3} + 0.\overline{53} \) equal to?
A.
\( 1.0\overline{68} \)
B.
\( 1.06\bar{8} \)
C.
\( 1.\overline{068} \)
D.
\( 1.068 \)
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ANSWER :
A. \( 1.0\overline{68} \)
29.
The inequality \( 3^{N} > N^{3} \) holds when
A.
N is any natural number
B.
N is a natural number greater than 2
C.
N is a natural number greater than 3
D.
N is a natural number except 3
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ANSWER :
D. N is a natural number except 3
30.
Which one of the following is an irrational number?
A.
\( \sqrt{59049} \)
B.
\( \frac{231}{593} \)
C.
0.45454545......
D.
0.12112211122211112222.......
😑 View Answer Error
ANSWER :
D. 0.12112211122211112222.......
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