CDS Exam (I)- 2016 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2016 - Elementary Mathematics

CDS Exam (I)- 2016 - Elementary Mathematics Defence Questions

31.
Under what condition on p and q, one of the roots of the equation \( x^{2} + px + q = 0 \) is the square of the other?
A.
\( 1 + q + q^{2} = 3pq \)
B.
\( 1 + p + p^{2} = 3pq \)
C.
\( p^{3} + q + q^{2} = 3pq \)
D.
\( q^{3} + p + p^{2} = 3pq \)
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ANSWER :
C. \( p^{3} + q + q^{2} = 3pq \)
32.
What is the maximum value of m, if the number \( N = 90 \times 42 \times 324 \times 55 \) is divisible by \( 3^{m} \)?
A.
8
B.
7
C.
6
D.
9
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ANSWER :
B. 7
33.
A bike consumes 20 mL of petrol per kilometre, if it is driven at a speed in the range of 25-50 km/hour and consumes 40 mL of petrol per kilometre at any other speed. How much petrol is consumed by the bike in travelling a distance of 50 km, if the bike is driven at a speed of 40 km/hour for the first 10 km, at a speed of 60 km/hour for the next 30 km and at a speed of 30 km/hour for the last 10 km?
A.
1 L
B.
1.2 L
C.
1.4 L
D.
1.6 L
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ANSWER :
D. 1.6 L
34.
Consider the following statements:
1. Every natural number is a real number.
2. Every real number is a rational number.
3. Every integer is a real number.
4. Every rational number is a real number.
Which of the above statements are correct?
A.
1, 2 and 3
B.
1, 3 and 4
C.
2 and 3 only
D.
3 and 4 only
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ANSWER :
B. 1, 3 and 4
35.
For what value of k is \( (x + 1) \) a factor of \( x^{3} + kx^{2} - x + 2 \)?
A.
4
B.
3
C.
1
D.
-2
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ANSWER :
D. -2
36.
Consider the following statements:
1. There exists a positive real number m such that \( \cos x = 2^{m + 1} \).
2. \( mn \geq m + n \) for all m, n belonging to set of natural numbers.
Which of the above statements 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
37.
The solution of the inequation \( 1 + \frac{1}{x} - \frac{1}{x^{2}} \geq 0 \) is (given that \( x \neq 0 \))
A.
\( x > 0 \)
B.
\( x < 0 \)
C.
\( \frac{-1 - \sqrt{5}}{2} < x < \frac{-1 + \sqrt{5}}{2} \)
D.
\( x \leq \frac{-1 - \sqrt{5}}{2} \) or \( x \geq \frac{-1 + \sqrt{5}}{2} \)
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ANSWER :
D. \( x \leq \frac{-1 - \sqrt{5}}{2} \) or \( x \geq \frac{-1 + \sqrt{5}}{2} \)
38.
Which of the points P(5, -1), Q(3, -2) and R(1, 1) lie in the solution of the system of inequations \( x + y \leq 4 \) and \( x - y \geq 2 \)?
A.
Q and R only
B.
P and R only
C.
P and Q only
D.
P, Q and R
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ANSWER :
C. P and Q only
39.
A passenger train takes 1 hour less for a journey of 120 km, if its speed is increased by 10 km/hour from its usual speed. What is its usual speed?
A.
50 km/hour
B.
40 km/hour
C.
35 km/hour
D.
30 km/hour
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ANSWER :
D. 30 km/hour
40.
The value of k, for which the system of equations \( 3x - ky - 20 = 0 \) and \( 6x - 10y + 40 = 0 \) has no solution, is
A.
10
B.
6
C.
5
D.
3
😑 View Answer Error
ANSWER :
C. 5
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