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

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2017 - Elementary Mathematics

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

21.
a, b, c, d are non-zero integers such that (ab) divides (cd). If a and c are coprime, then which one of the following is correct?
A.
a is a factor of c
B.
a is a factor of b
C.
a is a factor of d
D.
d is a factor of a
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ANSWER :
C. a is a factor of d
22.
If the roots of the equation \( a(b - c)x^{2} + b(c - a)x + c(a - b) = 0 \) are equal, then which one of the following is correct?
A.
2b = a + c
B.
\( b^{2} = ac \)
C.
\( \frac{2}{b} = \frac{1}{a} + \frac{1}{c} \)
D.
\( \frac{1}{b} = \frac{1}{a} + \frac{1}{c} \)
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ANSWER :
C. \( \frac{2}{b} = \frac{1}{a} + \frac{1}{c} \)
23.
The non-zero solution of the equation \( \frac{a - x^{2}}{bx} - \frac{b - x}{c} = \frac{c - x}{b} - \frac{b - x^{2}}{cx} \), where \( b \neq 0, c \neq 0 \), is
A.
\( \frac{b^{2} + ac}{b^{2} + c^{2}} \)
B.
\( \frac{b^{2} - ac}{a^{2} + c^{2}} \)
C.
\( \frac{b^{2} - ac}{b^{2} + c^{2}} \)
D.
\( \frac{b^{2} + ac}{a^{2} + c^{2}} \)
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ANSWER :
A. \( \frac{b^{2} + ac}{b^{2} + c^{2}} \)
24.
If k is an integer, then \( x^{2} + 7x - 14(k^{2} + 1) = 0 \) has
A.
Both integral roots
B.
At least one integral root
C.
No integral root
D.
Both positive integral roots
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ANSWER :
C. No integral root
25.
How many numbers between 500 and 1000 are divisible by 13?
A.
36
B.
37
C.
38
D.
39
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ANSWER :
C. 38
26.
To maintain 8 cows for 60 days, a milkman has to spend ₹ 6,400. To maintain 5 cows for n days, he has to spend ₹ 4,800. What is the value of n?
A.
46 days
B.
50 days
C.
58 days
D.
72 days
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ANSWER :
D. 72 days
27.
A student has to secure 40% of marks to pass an examination. He gets only 45 marks and fails by 5 marks. The maximum marks are
A.
120
B.
125
C.
130
D.
150
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ANSWER :
B. 125
28.
What is the non-zero value of u in the system of equations 3(2u + v) = 7uv, 3(u + 3v) = 11uv?
A.
0
B.
\( \frac{1}{2} \)
C.
2
D.
1
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ANSWER :
D. 1
29.
Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram?
A.
30 years
B.
32 years
C.
36 years
D.
40 years
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ANSWER :
B. 32 years
30.
Ram buys 4 chairs and 9 stools for ₹ 1,340. If he sells chairs at 10% profit and stools at 20% profit, he earns a total profit of ₹ 188. How much money did he have to pay for the chairs?
A.
₹ 200
B.
₹ 400
C.
₹ 800
D.
₹ 1,600
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ANSWER :
C. ₹ 800
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