CDS Exam (I)- 2019 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (I)- 2019 - Elementary Mathematics

CDS Exam (I)- 2019 - Elementary Mathematics Defence Questions

1.
What is the remainder when \( \left(17^{43} + 19^{43}\right) \) is divided by 18?
A.
6
B.
2
C.
1
D.
0
😑 View Answer Error
ANSWER :
D. 0
2.
What is the largest value of n such that \( 10^{n} \) divides the product
\( 2^{5} \times 3^{3} \times 4^{8} \times 5^{3} \times 6^{7} \times 7^{8} \times 8^{12} \times 9^{9} \times 10^{8} \times 15^{12} \times 20^{14} \times 22^{11} \times 25^{14} \)?
A.
65
B.
55
C.
650
D.
45
😑 View Answer Error
ANSWER :
A. 65
3.
How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd?
A.
5
B.
6
C.
9
D.
11
😑 View Answer Error
ANSWER :
A. 5
4.
Consider the multiplication 999 × abc = def132 in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f respectively?
A.
6, 6, 8, 6, 8, 7
B.
8, 6, 8, 6, 7, 8
C.
6, 8, 8, 7, 8, 6
D.
8, 6, 8, 8, 6, 7
😑 View Answer Error
ANSWER :
D. 8, 6, 8, 8, 6, 7
5.
Three cars A, B and C started from a point at 5 p.m., 6 p.m. and 7 p.m. respectively and travelled at uniform speeds of 60 km/hr, 80 km/hr and x km/hr respectively in the same direction. If all the three met at another point at the same instant during their journey, then what is the value of x?
A.
120
B.
110
C.
105
D.
100
😑 View Answer Error
ANSWER :
A. 120
6.
Priya's age was cube of an integral number (different from 1) four years ago and square of an integral number after four years. How long should she wait so that her age becomes square of a number in the previous year and cube of a number in the next year?
A.
7 years
B.
12 years
C.
14 years
D.
21 years
😑 View Answer Error
ANSWER :
C. 14 years
7.
Which of the following statements is not true?
A.
The difference of two prime numbers, both greater than 2, is divisible by 2.
B.
For two different integers m, n and a prime number p, if p divides the product m × n, then p divides either m or n.
C.
If a number is of the form 6n − 1 (n being a natural number), then it is a prime number.
D.
There is only one set of three prime numbers such that there is a gap of 2 between two adjacent prime numbers.
😑 View Answer Error
ANSWER :
C. If a number is of the form 6n − 1 (n being a natural number), then it is a prime number.
8.
For x > 0, what is the minimum value of \( x + \frac{x+2}{2x} \)?
A.
1
B.
2
C.
\( 2\frac{1}{2} \)
D.
Cannot be determined
😑 View Answer Error
ANSWER :
C. \( 2\frac{1}{2} \)
9.
If \( \left(\frac{1+px}{1-px}\right)\sqrt{\frac{1-qx}{1+qx}} = 1 \), then what are the non-zero solutions of x?
A.
\( \pm \frac{1}{p}\sqrt{\frac{2p-q}{q}}, 2p \neq q \)
B.
\( \pm \frac{1}{q}\sqrt{\frac{p-q}{p}}, p \neq q \)
C.
\( \pm \frac{1}{q}\sqrt{\frac{p}{p-q}}, p \neq q \)
D.
\( \pm \frac{1}{p}\sqrt{\frac{q}{2p-q}}, 2p \neq q \)
😑 View Answer Error
ANSWER :
A. \( \pm \frac{1}{p}\sqrt{\frac{2p-q}{q}}, 2p \neq q \)
10.
In a hostel the rent per room is increased by 20%. If number of rooms in the hostel is also increased by 20% and the hostel is always full, then what is the percentage change in the total collection at the cash counter?
A.
30%
B.
40%
C.
44%
D.
48%
😑 View Answer Error
ANSWER :
C. 44%
Prev Next page