CDS Exam (I)- 2015 - Elementary Mathematics Defence Question Paper

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CDS Exam (I)- 2015 - Elementary Mathematics

CDS Exam (I)- 2015 - Elementary Mathematics Defence Questions

1.
What is the remainder when \( 4^{96} \) is divided by 6?
A.
4
B.
3
C.
2
D.
1
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ANSWER :
A. 4
2.
If \( \frac{37}{13} = 2 + \frac{1}{x + \frac{1}{y + \frac{1}{z}}} \) where x, y, z are natural numbers, then what is z equal to?
A.
1
B.
2
C.
3
D.
Cannot be determined due to insufficient data
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ANSWER :
B. 2
3.
For what value of k is \( (x - 5) \) a factor of \( x^{3} - 3x^{2} + kx - 10 \)?
A.
\( -8 \)
B.
4
C.
2
D.
1
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ANSWER :
A. \( -8 \)
4.
What is \( \frac{5 + \sqrt{10}}{5\sqrt{5} - 2\sqrt{20} - \sqrt{32} + \sqrt{50}} \) equal to?
A.
5
B.
\( 5\sqrt{2} \)
C.
\( 5\sqrt{5} \)
D.
\( \sqrt{5} \)
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ANSWER :
D. \( \sqrt{5} \)
5.
The digit in the units place of the product \( 81 \times 82 \times 83 \times 84 \times \ldots \times 99 \) is
A.
0
B.
4
C.
6
D.
8
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ANSWER :
A. 0
6.
The square root of \( \frac{(0.75)^{3}}{1 - 0.75} + \left[0.75 + (0.75)^{2} + 1\right] \) is
A.
1
B.
2
C.
3
D.
4
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ANSWER :
B. 2
7.
What is the remainder obtained when \( 1421 \times 1423 \times 1425 \) is divided by 12?
A.
1
B.
2
C.
3
D.
4
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ANSWER :
C. 3
8.
Consider the following statements:
1. The equation \( 1990x - 173y = 11 \) has no solution in integers for x and y.
2. The equation \( 3x - 12y = 7 \) has no solution in integers for x and y.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
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ANSWER :
B. 2 only
9.
A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was
A.
12
B.
15
C.
25
D.
32
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ANSWER :
A. 12
10.
What is the number of possible pairs of (P, Q) if the number 357P25Q is divisible by both 3 and 5?
A.
7
B.
6
C.
5
D.
None of the above
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ANSWER :
A. 7
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