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

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CDS Exam (I)- 2019 - Elementary Mathematics

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

31.

A race has three parts. The speed and time required to complete the individual parts for a runner is displayed on the following chart:

  Part I Part II Part III
Speed (kmph) 9 8 7.5
Time (minutes) 50 80 100

What is the average speed of this runner?

A.

8.17 kmph

B.

8.00 kmph

C.

7.80 kmph

D.

7.77 kmph

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ANSWER :

B. 8.00 kmph

32.
If \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \), then which one of the following statements is correct?
A.
Each fraction is equal to 1 or −1.
B.
Each fraction is equal to \( \frac{1}{2} \) or 1.
C.
Each fraction is equal to \( \frac{1}{2} \) or −1.
D.
Each fraction is equal to \( \frac{1}{2} \) only.
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ANSWER :
C. Each fraction is equal to \( \frac{1}{2} \) or −1.
33.
The number \( 3^{521} \) is divided by 8. What is the remainder?
A.
1
B.
3
C.
7
D.
9
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ANSWER :
B. 3
34.
A prime number contains the digit X at unit's place. How many such digits of X are possible?
A.
3
B.
4
C.
5
D.
6
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ANSWER :
D. 6
35.
If an article is sold at a gain of 6% instead of a loss of 6%, the seller gets ₹6 more. What is the cost price of the article?
A.
₹18
B.
₹36
C.
₹42
D.
₹50
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ANSWER :
D. ₹50
36.
A field can be reaped by 12 men or 18 women in 14 days. In how many days can 8 men and 16 women reap it?
A.
26 days
B.
24 days
C.
9 days
D.
8 days
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ANSWER :
C. 9 days
37.
If \( 3^{x} = 4^{y} = 12^{z} \), then z is equal to
A.
xy
B.
x + y
C.
\( \frac{xy}{x+y} \)
D.
4x + 3y
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ANSWER :
C. \( \frac{xy}{x+y} \)
38.
If (4a + 7b)(4c − 7d) = (4a − 7b)(4c + 7d), then which one of the following is correct?
A.
\( \frac{a}{b} = \frac{c}{d} \)
B.
\( \frac{a}{d} = \frac{c}{b} \)
C.
\( \frac{a}{b} = \frac{d}{c} \)
D.
\( \frac{4a}{7b} = -\frac{c}{d} \)
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ANSWER :
A. \( \frac{a}{b} = \frac{c}{d} \)
39.
Given that the polynomial \( \left(x^{2} + ax + b\right) \) leaves the same remainder when divided by (x − 1) or (x + 1). What are the values of a and b respectively?
A.
4 and 0
B.
1 and 3
C.
3 and 0
D.
0 and any integer
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ANSWER :
D. 0 and any integer
40.
Tushar takes 6 hours to complete a piece of work, while Amar completes the same work in 10 hours. If both of them work together, then what is the time required to complete the work?
A.
3 hours
B.
3 hours 15 minutes
C.
3 hours 30 minutes
D.
3 hours 45 minutes
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ANSWER :
D. 3 hours 45 minutes
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