CDS Exam (I)- 2021 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2021 - Elementary Mathematics

CDS Exam (I)- 2021 - Elementary Mathematics Defence Questions

1.
If the number 413283P759387 is divisible by 13, then what is the value of P?
A.
3
B.
6
C.
7
D.
8
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ANSWER :
D. 8
2.
What is the remainder when \( 2^{1000000} \) is divided by 7?
A.
1
B.
2
C.
4
D.
6
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ANSWER :
B. 2
3.
How many pairs of \( (x, y) \) can be chosen from the set {2, 3, 6, 8, 9} such that \( \frac{x}{y} + \frac{y}{x} = 2 \), where \( x \neq y \)?
A.
Zero
B.
One
C.
Two
D.
Three
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ANSWER :
A. Zero
4.
Consider the pairs of prime numbers \( (m, n) \) between 50 and 100 such that \( m - n = 6 \). How many such pairs are there?
A.
2
B.
3
C.
4
D.
5
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ANSWER :
D. 5
5.
How many terms are there in the following product?
\( (a_{1} + a_{2} + a_{3})(b_{1} + b_{2} + b_{3} + b_{4})(c_{1} + c_{2} + c_{3} + c_{4} + c_{5}) \)
A.
15
B.
30
C.
45
D.
60
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ANSWER :
D. 60
6.
What is the remainder when \( 27^{27} - 15^{27} \) is divided by 6?
A.
0
B.
1
C.
3
D.
4
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ANSWER :
A. 0
7.
If \( a + b + c = 0 \), then which of the following are correct?
1. \( a^{3} + b^{3} + c^{3} = 3abc \)
2. \( a^{2} + b^{2} + c^{2} = -2(ab + bc + ca) \)
3. \( a^{3} + b^{3} + c^{3} = -3ab(a + b) \)
Select the correct answer using the code given below.
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
D. 1, 2 and 3
8.
If
\( p = \frac{\sqrt{3q + 2} + \sqrt{3q - 2}}{\sqrt{3q + 2} - \sqrt{3q - 2}} \)
then what is the value of \( p^{2} - 3pq + 2 \)?
A.
0
B.
1
C.
2
D.
3
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ANSWER :
B. 1
9.
What is the unit digit in the expansion of \( 67^{32} \)?
A.
1
B.
3
C.
7
D.
9
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ANSWER :
A. 1
10.
What is the value of \( x \), if
\( \frac{b + \sqrt{b^{2} - 2bx}}{b - \sqrt{b^{2} - 2bx}} = a \)?
A.
\( \frac{ab}{(a + b)} \)
B.
\( \frac{2ab}{(a + 1)} \)
C.
\( \frac{2ab}{(a + 1)^{2}} \)
D.
\( \frac{ab}{(a + b)^{2}} \)
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ANSWER :
C. \( \frac{2ab}{(a + 1)^{2}} \)
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