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

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2016 - Elementary Mathematics

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

21.
Let a two-digit number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is
A.
\( 9 - k \)
B.
\( 10 - k \)
C.
\( 11 - k \)
D.
\( k - 1 \)
ANSWER :
C. \( 11 - k \)
22.
A man walking at 5 km/hour noticed that a 225 m long train coming in the opposite direction crossed him in 9 seconds. The speed of the train is
A.
75 km/hour
B.
80 km/hour
C.
85 km/hour
D.
90 km/hour
ANSWER :
C. 85 km/hour
23.
\( \left(\frac{\sin 35^{\circ}}{\cos 55^{\circ}}\right)^{2} - \left(\frac{\cos 55^{\circ}}{\sin 35^{\circ}}\right)^{2} + 2\sin 30^{\circ} \) is equal to
A.
-1
B.
0
C.
1
D.
2
ANSWER :
C. 1
24.
A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is
A.
5 km/hour
B.
6 km/hour
C.
7 km/hour
D.
None of the above
ANSWER :
C. 7 km/hour
25.
If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is
A.
2%
B.
3%
C.
\( 3\frac{1}{3} \)%
D.
\( 4\frac{1}{3} \)%
ANSWER :
C. \( 3\frac{1}{3} \)%
26.
Let ABC and A'B'C' be two triangles in which \( AB > A'B' \), \( BC > B'C' \) and \( CA > C'A' \). Let D, E and F be the midpoints of the sides BC, CA and AB respectively. Let D', E' and F' be the midpoints of the sides B'C', C'A' and A'B' respectively. Consider the following statements:
Statement-I: \( AD > A'D' \), \( BE > B'E' \) and \( CF > C'F' \) are always true.
Statement-II: \( \frac{AB^{2} + BC^{2} + CA^{2}}{AD^{2} + BE^{2} + CF^{2}} = \frac{(A'B')^{2} + (B'C')^{2} + (C'A')^{2}}{(A'D')^{2} + (B'E')^{2} + (C'F')^{2}} \)
Which one of the following is correct in respect of the above statements?
A.
Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
B.
Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I
C.
Statement I is true but Statement II is false
D.
Statement I is false but Statement II is true
ANSWER :
D. Statement I is false but Statement II is true
27.
The annual incomes of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves ₹ 2,000 per year, what is the difference in their annual incomes?
A.
₹ 4,000
B.
₹ 4,500
C.
₹ 5,000
D.
₹ 5,500
ANSWER :
A. ₹ 4,000
28.
Let S be a set of first fourteen natural numbers. The possible number of pairs (a, b), where \( a, b \in S \) and \( a \neq b \) such that ab leaves remainder 1 when divided by 15, is
A.
3
B.
5
C.
6
D.
None of the above
ANSWER :
D. None of the above
29.
A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on. If it takes 8 seconds to strike at 5 o'clock, the time taken by it to strike at 10 o'clock is
A.
14 seconds
B.
16 seconds
C.
18 seconds
D.
None of the above
ANSWER :
C. 18 seconds
30.
In a circle of radius 2 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If \( AP > BP \), then AP is equal to
A.
\( (2 + \sqrt{5}) \) units
B.
\( (2 + \sqrt{3}) \) units
C.
\( (2 + \sqrt{2}) \) units
D.
3 units
ANSWER :
B. \( (2 + \sqrt{3}) \) units