CDS Exam (I)- 2023 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2023 - Elementary Mathematics

CDS Exam (I)- 2023 - Elementary Mathematics Defence Questions

31.
Let a, b, c and d be four positive integers such that a + b + c + d = 200. If \( S = (-1)^{a} + (-1)^{b} + (-1)^{c} + (-1)^{d} \), then what is the number of possible values of S?
A.
One
B.
Two
C.
Three
D.
Four
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ANSWER :
C. Three
32.
The number \( 97^{30} - 14^{30} \) is divisible by:
A.
37 but not 83
B.
83 but not 37
C.
Both 37 and 83
D.
Neither 37 nor 83
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ANSWER :
C. Both 37 and 83
33.
Consider the following statements:
1. \( \log_{10} 50 \) is a rational number.
2. \( \log_{100} 10 \) is an irrational number.
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
D. Neither 1 nor 2
34.
If 17 women and 24 men can do a piece of work in 5 days and 12 women and 23 men can do it in 6 days, then which one of the following is correct?
A.
Efficiency of 13 women = Efficiency of 18 men
B.
Efficiency of 11 women = Efficiency of 16 men
C.
Efficiency of 13 women = Efficiency of 17 men
D.
Efficiency of 11 women = Efficiency of 15 men
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ANSWER :
A. Efficiency of 13 women = Efficiency of 18 men
35.
Three taps A, B and C together can fill a tank in 6 hours. Tap C alone can fill the tank in 12 hours. To fill the tank, when it is empty, all the three taps are started together. After working t hours, tap C is closed and the tank is filled in 8 more hours. What is t equal to?
A.
1
B.
2
C.
4
D.
6
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ANSWER :
B. 2
36.
A, B and C can complete a work in x, 1.5x and 2x days respectively. If they complete the work together, in what ratio should they be paid?
A.
2 : 3 : 4
B.
6 : 4 : 3
C.
3 : 2 : 1
D.
4 : 3 : 2
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ANSWER :
B. 6 : 4 : 3
37.
Consider the following statements:
1. \( n^{3} - n \) is divisible by 6.
2. \( n^{5} - n \) is divisible by 5.
3. \( n^{5} - 5n^{3} + 4n \) is divisible by 120.
Which of the statements given above 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
38.
What is the last digit of the sum \( S = 9^{27} + 27^{9} \)?
A.
3
B.
6
C.
7
D.
9
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ANSWER :
B. 6
39.
If \( x = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} \) and \( y = \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \), then what is the value \( x^{3} - y^{3} \)?
A.
60
B.
\( 45\sqrt{3} \)
C.
\( 30\sqrt{3} \)
D.
90
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ANSWER :
C. \( 30\sqrt{3} \)
40.
The speed of a boat in still water is 15 km/hr. If it can travel 42 km downstream and 28 km upstream in the same time, then what is the speed of the stream?
A.
2.5 km/hr
B.
3 km/hr
C.
4.5 km/hr
D.
6 km/hr
😑 View Answer Error
ANSWER :
B. 3 km/hr
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