CDS Exam (I)- 2020 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2020 - Elementary Mathematics

CDS Exam (I)- 2020 - Elementary Mathematics Defence Questions

21.
If \( \log x = 1.2500 \) and \( y = x^{\log x} \), then what is \( \log y \) equal to?
A.
4.2500
B.
2.5625
C.
1.5625
D.
1.2500
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ANSWER :
C. 1.5625
22.
If \( f(x) \) is divided by \( (x - \alpha)(x - \beta) \) where \( \alpha \neq \beta \), then what is the remainder?
A.
\( \frac{(x - \alpha)f(\alpha) - (x - \beta)f(\beta)}{\alpha - \beta} \)
B.
\( \frac{(x - \alpha)f(\beta) - (x - \beta)f(\alpha)}{\alpha - \beta} \)
C.
\( \frac{(x - \beta)f(\alpha) - (x - \alpha)f(\beta)}{\alpha - \beta} \)
D.
\( \frac{(x - \beta)f(\beta) - (x - \alpha)f(\alpha)}{\alpha - \beta} \)
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ANSWER :
C. \( \frac{(x - \beta)f(\alpha) - (x - \alpha)f(\beta)}{\alpha - \beta} \)
23.
If the area of a square is \( 2401x^{4} + 196x^{2} + 4 \), then what is its side length?
A.
\( 49x^{2} + 3x + 2 \)
B.
\( 49x^{2} - 3x + 2 \)
C.
\( 49x^{2} + 2 \)
D.
\( 59x^{2} + 2 \)
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ANSWER :
C. \( 49x^{2} + 2 \)
24.
If \( x \) varies as \( yz \), then \( y \) varies inversely as
A.
\( xz \)
B.
\( \frac{x}{z} \)
C.
\( \frac{z}{x} \)
D.
\( \frac{1}{(xz)} \)
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ANSWER :
C. \( \frac{z}{x} \)
25.
If the points \( P \) and \( Q \) represent real numbers \( 0.7\bar{3} \) and \( 0.5\bar{6} \) on the number line, then what is the distance between \( P \) and \( Q \)?
A.
\( \frac{1}{6} \)
B.
\( \frac{1}{5} \)
C.
\( \frac{16}{45} \)
D.
\( \frac{11}{90} \)
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ANSWER :
A. \( \frac{1}{6} \)
26.
What is the point on the \( xy \)-plane satisfying \( 5x + 2y = 7xy \) and \( 10x + 3y = 8xy \)?
A.
\( \left(-1, \frac{1}{6}\right) \)
B.
\( \left(\frac{1}{6}, -1\right) \)
C.
\( \left(1, \frac{1}{6}\right) \)
D.
\( \left(-\frac{1}{6}, -1\right) \)
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ANSWER :
B. \( \left(\frac{1}{6}, -1\right) \)
27.
The price of an article \( X \) increases by 20% every year and price of article \( Y \) increases by 10% every year. In the year 2010, the price of article \( X \) was ₹5000 and price of article \( Y \) was ₹2000. In which year the difference in their prices exceeded ₹5000 for the first time?
A.
2012
B.
2013
C.
2014
D.
2015
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ANSWER :
B. 2013
28.
The ratio of speeds of \( X \) and \( Y \) is 5 : 6. If \( Y \) allows \( X \) a start of 70 m in a 1.2 km race, then who will win the race and by what distance?
A.
\( X \) wins the race by 30 m
B.
\( Y \) wins the race by 90 m
C.
\( Y \) wins the race by 130 m
D.
The race finishes in a dead heat
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ANSWER :
C. \( Y \) wins the race by 130 m
29.
A train takes two hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. What is its usual speed?
A.
50 km/hr
B.
40 km/hr
C.
35 km/hr
D.
25 km/hr
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ANSWER :
D. 25 km/hr
30.
If 6 men and 8 women can do a piece of work in 10 days; and 13 men and 24 women can do the same work in 4 days, then what is the ratio of daily work done by a man to that of a woman?
A.
2 : 1
B.
1 : 2
C.
4 : 3
D.
3 : 4
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ANSWER :
A. 2 : 1
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