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

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CDS Exam (II)- 2023 - Elementary Mathematics

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

1.
If \( a^{2} - bc = \alpha \), \( b^{2} - ac = \beta \), \( c^{2} - ab = \gamma \), then what is \( \frac{a\alpha + b\beta + c\gamma}{(a + b + c)(\alpha + \beta + \gamma)} \) equal to?
A.
\( a + b - c \)
B.
\( a - b + c \)
C.
\( -a + b + c \)
D.
1
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ANSWER :
D. 1
2.
If \( (x - 1)^{3} \) is a factor of \( x^{4} + \alpha x^{3} + \beta x^{2} + \gamma x - 1 \), then the other factor will be:
A.
\( x + 1 \)
B.
\( x - 3 \)
C.
\( x + 2 \)
D.
x
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ANSWER :
A. \( x + 1 \)
3.
A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits?
A.
5
B.
2
C.
1
D.
0
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ANSWER :
D. 0
4.
If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work?
A.
8 days
B.
5 days
C.
4 days
D.
3 days
😑 View Answer Error
ANSWER :
C. 4 days
5.
A person borrowed ₹ 10,000 at 12% rate of interest per annum compounded quarterly for a period of 9 months. What is the interest paid by him to settle his account after 9 months?
A.
₹ 927.27
B.
₹ 947.47
C.
₹ 967.67
D.
₹ 987.87
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ANSWER :
A. ₹ 927.27
6.
For what relation between a and b is the equation \( \sin \theta = \frac{a + b}{2\sqrt{ab}} \) possible?
A.
\( a = b \)
B.
\( a \leq b \)
C.
\( a \geq b \)
D.
\( a > b \)
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ANSWER :
A. \( a = b \)
7.
Three persons A, B and C together can do a piece of work in 36 days. A and B together can do five times as much work as C alone; B and C together can do as much work as A alone. If A and C together can do n times as much work as B alone, then what is the value of n?
A.
1.5
B.
2
C.
2.5
D.
3
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ANSWER :
B. 2
8.
If \( \frac{2a}{3} = \frac{4b}{5} = \frac{3c}{4} \), then what is the value of \( \frac{18}{a}\sqrt{a^{2} + c^{2} - b^{2}} \)?
A.
\( 3\sqrt{5} \)
B.
\( \sqrt{355} \)
C.
\( \sqrt{375} \)
D.
\( 3\sqrt{15} \)
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ANSWER :
B. \( \sqrt{355} \)
9.
The sum of deviations of n numbers from 10 and 20 are a, b respectively. If \( \frac{b}{a} = -4 \), then what is the mean of these n numbers?
A.
12
B.
14
C.
16
D.
18
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ANSWER :
A. 12
10.
If the median of observations
12, 1, 8, 54, 61, 28, 45, 35, 21, 17
is M, then what is the value of \( 2M + 5 \)?
A.
12
B.
28
C.
52
D.
54
😑 View Answer Error
ANSWER :
D. 54
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