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

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CDS Exam (II)- 2019 - Elementary Mathematics

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

11.
Let \( a \) and \( b \) be two positive real numbers such that \( a\sqrt{a} + b\sqrt{b} = 32 \) and \( a\sqrt{b} + b\sqrt{a} = 31 \). What is the value of \( \frac{5(a+b)}{7} \)?
A.
5
B.
7
C.
9
D.
Cannot be determined
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ANSWER :
C. 9
12.
If \( x = \frac{\sqrt{3}-1}{2} \) and \( y = x^{3} \), then \( y \) satisfies which one of the following equations?
A.
\( 8y^{2} - 20y - 1 = 0 \)
B.
\( 8y^{2} + 20y - 1 = 0 \)
C.
\( 8y^{2} + 20y + 1 = 0 \)
D.
\( 8y^{2} - 20y + 1 = 0 \)
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ANSWER :
B. \( 8y^{2} + 20y - 1 = 0 \)
13.
HCF of two numbers is 12. Which one of the following can never be their LCM?
A.
80
B.
60
C.
36
D.
24
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ANSWER :
A. 80
14.
Consider the following statements:
1. Unit digit in \( 17^{17} \) is 7.
2. Difference of the squares of any two odd numbers is always divisible by 8.
3. Adding 1 to the product of two consecutive odd numbers makes it a perfect square.
Which of the above statements are correct?
A.
1, 2 and 3
B.
1 and 2 only
C.
2 and 3 only
D.
1 and 3 only
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ANSWER :
A. 1, 2 and 3
15.
The rate of interest on two different schemes is the same and it is 20%. But in one of the schemes, the interest is compounded half yearly and in the other the interest is compounded annually. Equal amounts are invested in the schemes. If the difference of the returns after 2 years is ₹482, then what is the principal amount in each scheme?
A.
₹10,000
B.
₹16,000
C.
₹20,000
D.
₹24,000
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ANSWER :
C. ₹20,000
16.
For what value of \( k \) can the expression \( x^{3} + kx^{2} - 7x + 6 \) be resolved into three linear factors?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
A. 0
17.
X, Y and Z start at same point and same time in the same direction to run around a circular stadium. X completes a round in 252 seconds, Y in 308 seconds and Z in 198 seconds. After what time will they meet again at the starting point?
A.
26 minutes 18 seconds
B.
42 minutes 36 seconds
C.
45 minutes
D.
46 minutes 12 seconds
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ANSWER :
D. 46 minutes 12 seconds
18.
What is the LCM of \( \frac{1}{3} \), \( \frac{5}{6} \), \( \frac{2}{9} \), \( \frac{4}{27} \)?
A.
\( \frac{1}{18} \)
B.
\( \frac{1}{27} \)
C.
\( \frac{10}{27} \)
D.
\( \frac{20}{3} \)
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ANSWER :
D. \( \frac{20}{3} \)
19.
If the equations \( x^{2} + 5x + 6 = 0 \) and \( x^{2} + kx + 1 = 0 \) have a common root, then what is the value of \( k \)?
A.
\( -\frac{5}{2} \) or \( -\frac{10}{3} \)
B.
\( \frac{5}{2} \) or \( \frac{10}{3} \)
C.
\( \frac{2}{5} \) or \( -\frac{3}{10} \)
D.
\( -\frac{2}{5} \) or \( \frac{10}{3} \)
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ANSWER :
B. \( \frac{5}{2} \) or \( \frac{10}{3} \)
20.
A lent ₹25,000 to B and at the same time lent some amount to C at same 7% simple interest. After 4 years A received ₹11,200 as interest from B and C. How much did A lend to C?
A.
₹20,000
B.
₹25,000
C.
₹15,000
D.
₹10,000
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ANSWER :
C. ₹15,000
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