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

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CDS Exam (II)- 2020 - Elementary Mathematics

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

1.
\( x^{3} + x^{2} + 16 \) is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is
A.
3
B.
4
C.
5
D.
6
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ANSWER :
C. 5
2.
The number of (a, b, c), where a, b, c are positive integers such that abc = 30, is
A.
30
B.
27
C.
9
D.
8
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ANSWER :
B. 27
3.
If the roots of the quadratic equation \( x^{2} - 4x - \log_{10} N = 0 \) are real, then what is the minimum value of N?
A.
1
B.
\( \frac{1}{10} \)
C.
\( \frac{1}{100} \)
D.
\( \frac{1}{10000} \)
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ANSWER :
D. \( \frac{1}{10000} \)
4.
The number of different solutions of the equation x + y + z = 12, where each of x, y and z is a positive integer, is
A.
53
B.
54
C.
55
D.
56
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ANSWER :
C. 55
5.
If \( I = a^{2} + b^{2} + c^{2} \), where a and b are consecutive integers and c = ab, then I is
A.
an even number and it is not a square of an integer
B.
an odd number and it is not a square of an integer
C.
square of an even integer
D.
square of an odd integer
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ANSWER :
D. square of an odd integer
6.
If the number 23P62971335 is divisible by the smallest odd composite number, then what is the value of P?
A.
4
B.
5
C.
6
D.
7
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ANSWER :
A. 4
7.
What is the remainder when the sum \( 1^{5} + 2^{5} + 3^{5} + 4^{5} + 5^{5} \) is divided by 4?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
B. 1
8.
What is the digit in the unit place of \( 3^{99} \)?
A.
1
B.
3
C.
7
D.
9
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ANSWER :
C. 7
9.
LCM of two numbers is 28 times their HCF. The sum of the HCF and the LCM is 1740. If one of these numbers is 240, then what is the other number?
A.
420
B.
640
C.
820
D.
1040
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ANSWER :
A. 420
10.
\( (x^{n} - a^{n}) \) is divisible by (x - a), where \( x \neq a \), for every
A.
natural number n
B.
even natural number n only
C.
odd natural number n only
D.
prime number n only
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ANSWER :
A. natural number n
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