CDS Exam (II)- 2015 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2015 - Elementary Mathematics

CDS Exam (II)- 2015 - Elementary Mathematics Defence Questions

11.
A tin of oil was \( \frac{4}{5} \) full. When 6 bottles of oil were taken out from this tin and 4 bottles of oil were poured into it, it was \( \frac{3}{4} \) full. Oil of how many bottles can the tin contain? (All bottles are of equal volume)
A.
35
B.
40
C.
45
D.
50
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ANSWER :
B. 40
12.
A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a remainder 6. If the same number when divided by 11 leaves a remainder m and the resulting quotient when divided by 7 leaves a remainder n, what are the values of m and n respectively?
A.
1 and 4
B.
4 and 1
C.
3 and 6
D.
6 and 3
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ANSWER :
A. 1 and 4
13.
Consider the following in respect of the equation \( y = \frac{|x - 1|}{x - 1} \):
1. y = 1 if x > 1
2. y = −1 if x < 1
3. y exists for all values of x
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
1 and 2 only
D.
1, 2 and 3
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ANSWER :
C. 1 and 2 only
14.
If (x + 1) is the HCF of \( Ax^{2} + Bx + C \) and \( Bx^{2} + Ax + C \) where \( A \neq B \), then the value of C is
A.
A
B.
B
C.
A − B
D.
0
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ANSWER :
D. 0
15.
The seven digit number 876p37q is divisible by 225. The values of p and q can be respectively
A.
9, 0
B.
0, 0
C.
5, 0
D.
9, 5
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ANSWER :
D. 9, 5
16.
If a, b and c satisfy the equation \( x^{3} - 3x^{2} + 2x + 1 = 0 \) then what is the value of \( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \)?
A.
\( -\frac{1}{2} \)
B.
2
C.
−2
D.
\( \frac{1}{2} \)
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ANSWER :
C. −2
17.
A and B are two taps which can fill a tank individually in 10 minutes and 20 minutes respectively. However, there is a leakage at the bottom, which can empty a filled tank in 40 minutes. If the tank is empty initially, how much time will both the taps take to fill the tank with leakage?
A.
2 minutes
B.
4 minutes
C.
5 minutes
D.
8 minutes
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ANSWER :
D. 8 minutes
18.
Which one of the following is correct?
A.
\( \sqrt{2} < \sqrt[4]{6} < \sqrt[3]{4} \)
B.
\( \sqrt{2} > \sqrt[4]{6} > \sqrt[3]{4} \)
C.
\( \sqrt[4]{6} < \sqrt{2} < \sqrt[3]{4} \)
D.
\( \sqrt[4]{6} > \sqrt{2} > \sqrt[3]{4} \)
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ANSWER :
A. \( \sqrt{2} < \sqrt[4]{6} < \sqrt[3]{4} \)
19.
The value of a single discount on some amount which is equivalent to a series of discounts of 10%, 20% and 40% on the same amount, is equal to
A.
43.2%
B.
50%
C.
56.8%
D.
70%
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ANSWER :
C. 56.8%
20.
If k = x − y + 2z where \( -2 \leq x \leq 1 \), \( -1 \leq y \leq 2 \) and \( 3 \leq z \leq 6 \), then which one of the following is correct?
A.
\( 0 \leq k \leq 9 \)
B.
\( 5 \leq k \leq 11 \)
C.
\( 2 \leq k \leq 14 \)
D.
\( 2 \leq k \leq 11 \)
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ANSWER :
C. \( 2 \leq k \leq 14 \)
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