CDS Exam (II)- 2021 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2021 - Elementary Mathematics

CDS Exam (II)- 2021 - Elementary Mathematics Defence Questions

11.
For which values of \( k \), does the equation \( x^{2} - kx + 2 = 0 \) have real and distinct solutions?
A.
\( -2\sqrt{2} < k < 2\sqrt{2} \)
B.
\( k < -2\sqrt{2} \) only
C.
\( k > 2\sqrt{2} \) only
D.
\( k < -2\sqrt{2} \) or \( k > 2\sqrt{2} \)
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ANSWER :
D. \( k < -2\sqrt{2} \) or \( k > 2\sqrt{2} \)
12.
If \( \alpha + \beta + \gamma = \alpha\beta + \beta\gamma + \gamma\alpha \), then what is \( (1 - \alpha)(1 - \beta)(1 - \gamma) \) equal to?
A.
\( 1 - \alpha\beta\gamma \)
B.
\( 1 + \alpha\beta\gamma \)
C.
\( \alpha^{2} + \beta^{2} + \gamma^{2} \)
D.
\( (\alpha - \beta)(\beta - \gamma)(\gamma - \alpha) \)
😑 View Answer Error
ANSWER :
A. \( 1 - \alpha\beta\gamma \)
13.
If \( \log_{10} x + \log_{10} x^{2} = 2\log_{10} x + 1 \), then what is the value of \( x \)?
A.
1
B.
2
C.
5
D.
10
😑 View Answer Error
ANSWER :
D. 10
14.
The LCM of two prime numbers \( p \) and \( q \) is 2231, where \( p > q \). What is the value of \( p - q \)?
A.
67
B.
70
C.
74
D.
81
😑 View Answer Error
ANSWER :
C. 74
15.
Three runners are running in a circular track, and they complete one round in 20, 30 and 35 minutes respectively. When will they next meet at the starting point?
A.
After 3 hour 30 minutes
B.
After 4 hour 30 minutes
C.
After 3 hours
D.
After 7 hours
😑 View Answer Error
ANSWER :
D. After 7 hours
16.
5 pencils, 6 notebooks and 7 erasers cost ₹250; whereas 6 pencils, 4 notebooks and 2 erasers cost ₹180. What is the cost of 2 notebooks and 4 erasers?
A.
₹90
B.
₹75
C.
₹60
D.
₹40
😑 View Answer Error
ANSWER :
B. ₹75
17.
How many zeros are there in the product \( 1^{50} \times 2^{49} \times 3^{48} \times \ldots \times 50^{1} \)?
A.
262
B.
261
C.
246
D.
235
😑 View Answer Error
ANSWER :
A. 262
18.
If \( p \) and \( q \) \( (p > q) \) are the roots of the equation \( x^{2} - 60x + 899 = 0 \), then which one of the following is correct?
A.
\( p - q - 1 = 0 \)
B.
\( p - 2q + 27 = 0 \)
C.
\( 2p - q - 30 = 0 \)
D.
\( 3p - 2q - 43 = 0 \)
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ANSWER :
B. \( p - 2q + 27 = 0 \)
19.
If the roots of the equation
\( x^{2} - 4x - \log_{10} N = 0 \)
are real, then what is the minimum value of \( N \)?
A.
0.1
B.
0.01
C.
0.001
D.
0.0001
😑 View Answer Error
ANSWER :
D. 0.0001
20.
If \( 5^{x-1} = (2.5)^{\log_{10} 5} \), then what is the value of \( x \)?
A.
1
B.
\( \log_{10} 2 \)
C.
\( \log_{10} 5 \)
D.
\( 2\log_{10} 5 \)
😑 View Answer Error
ANSWER :
D. \( 2\log_{10} 5 \)
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