CDS Exam (II)- 2022 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2022 - Elementary Mathematics

CDS Exam (II)- 2022 - Elementary Mathematics Defence Questions

31.
If a = 3b, 4b = 5c, 6c = 7d, then what is \( \frac{d + a}{d - a} \) equal to?
A.
\( \frac{27}{43} \)
B.
\( \frac{43}{27} \)
C.
\( -\frac{27}{43} \)
D.
\( -\frac{43}{27} \)
😑 View Answer Error
ANSWER :
D. \( -\frac{43}{27} \)
32.
What are the values of k for which the polynomial \( (k - 3)x^{2} - kx - 1 \) has no real linear factors?
A.
\( k < -6 \)
B.
\( -6 < k < 2 \)
C.
\( 2 < k < 6 \)
D.
\( k > 6 \)
😑 View Answer Error
ANSWER :
B. \( -6 < k < 2 \)
33.
If bc + cd = 2bd and a + c = 2b, then which one of the following is correct?
A.
ab - cd = 0
B.
ac - bd = 0
C.
ad - bc = 0
D.
ad + bc = 0
😑 View Answer Error
ANSWER :
C. ad - bc = 0
34.
In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hr and time of flight increased by 30 minutes. What was the original average speed of the aircraft?
A.
700 km/hr
B.
750 km/hr
C.
800 km/hr
D.
900 km/hr
😑 View Answer Error
ANSWER :
C. 800 km/hr
35.
If x = b + c, y = c + a, z = a + b, then what is \( (x + y + z)^{3} - 24xyz \) equal to?
A.
\( a^{3} + b^{3} + c^{3} \)
B.
\( 2(a^{3} + b^{3} + c^{3}) \)
C.
\( 8(a^{3} + b^{3} + c^{3}) \)
D.
None of the above
😑 View Answer Error
ANSWER :
C. \( 8(a^{3} + b^{3} + c^{3}) \)
36.
A person X starts from a place A and another person Y starts simultaneously from another place B which is d km away from A. They walk in the same direction. X walks at an average speed of u km/hr and Y walks at an average speed of v km/hr. How far will X have walked before he overtakes Y?
A.
\( \frac{ud}{(u - v)} \)
B.
\( \frac{vd}{(u - v)} \)
C.
\( \frac{(ud - vd)}{(u - v)} \)
D.
\( \frac{(ud + vd)}{(u + v)} \)
😑 View Answer Error
ANSWER :
A. \( \frac{ud}{(u - v)} \)
37.
If p is the difference between a number and its reciprocal and q is the difference between the square of the same number and the square of its reciprocal, then what is \( p^{4} + 4p^{2} \) equal to?
A.
4q
B.
8q
C.
\( 4q^{2} \)
D.
\( q^{2} \)
😑 View Answer Error
ANSWER :
D. \( q^{2} \)
38.
If \( x = 2 + 2^{\frac{1}{2}} \), then what is the value of \( x^{4} + 16x^{-4} \)?
A.
152
B.
144
C.
136
D.
132
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ANSWER :
C. 136
39.
X takes 3 hours longer than Y to walk 30 km. If X doubles his speed, he takes 2 hours less than Y. What is the speed of Y?
A.
3 km/hr
B.
4 km/hr
C.
\( 4\frac{2}{7} \) km/hr
D.
\( 4\frac{3}{7} \) km/hr
😑 View Answer Error
ANSWER :
C. \( 4\frac{2}{7} \) km/hr
40.
If C is the compound interest on ₹ 10,000 for one year at 4% per annum when compounded quarterly, then which one of the following is correct?
A.
\( C < \) ₹ 100
B.
₹ 100 \( < C < \) ₹ 200
C.
₹ 200 \( < C < \) ₹ 400
D.
\( C > \) ₹ 400
😑 View Answer Error
ANSWER :
D. \( C > \) ₹ 400
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