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

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2021 - Elementary Mathematics

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

31.
If one of the roots of the equation \( ax^{2} - 4ax + 15 = 0 \) is \( \frac{3}{2} \), then what is the sum of the squares of the roots?
A.
\( \frac{15}{2} \)
B.
\( \frac{17}{2} \)
C.
\( \frac{19}{2} \)
D.
\( \frac{21}{2} \)
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ANSWER :
B. \( \frac{17}{2} \)
32.
A two-digit number is such that the product of the digits is 8. If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number?
A.
6
B.
7
C.
8
D.
9
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ANSWER :
D. 9
33.
A motor boat has speed 30 km/hr in still water. It goes 60 km down stream and comes back in \( \frac{9}{2} \) hours. What is the speed of the stream?
A.
5 km/hr
B.
8 km/hr
C.
10 km/hr
D.
12 km/hr
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ANSWER :
C. 10 km/hr
34.
The present age of a father is equal to sum of the ages of his 4 children. After ten years the sum of the ages of the children will be 1.6 times the age of their father. What is the present age of father?
A.
36 years
B.
40 years
C.
42 years
D.
45 years
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ANSWER :
B. 40 years
35.
The sum of numerator and denominator of a fraction is 10. If the numerator is increased by 3 and denominator is decreased by 1, the fraction becomes 1. What is the difference between numerator and denominator of the fraction?
A.
2
B.
3
C.
4
D.
5
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ANSWER :
C. 4
36.
If the system of equations \( 7x + ky = 27 \) and \( kx + 7y = 19 \) have unique solution, then which one of the following is correct?
A.
\( k \neq 7 \)
B.
\( k \neq 13 \)
C.
\( k = 7 \)
D.
\( k = 13 \)
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ANSWER :
A. \( k \neq 7 \)
37.
A sum of money compounded annually doubles itself in 5 years. In how many years will it become four times of itself?
A.
10 years
B.
12 years
C.
15 years
D.
20 years
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ANSWER :
A. 10 years
38.
Between 3 and 4 O'clock, both hour hand and minute hand will coincide past 3 O'clock between
A.
15-16 minutes
B.
16-17 minutes
C.
17-18 minutes
D.
18-19 minutes
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ANSWER :
B. 16-17 minutes
39.
Sheela can stitch a suit in 2 days, while Meena can stitch a suit in \( 1\frac{1}{2} \) days. How many days will both take in stitching 30 suits?
A.
\( 25\frac{5}{7} \) days
B.
33 days
C.
35 days
D.
40 days
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ANSWER :
A. \( 25\frac{5}{7} \) days
40.
If \( 2x - 3y - 7 = 0 \),
then what is the value of
\( 8x^{3} - 36x^{2}y + 54xy^{2} - 27y^{3} - 340 \)?
A.
-1
B.
0
C.
1
D.
3
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ANSWER :
D. 3
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