CDS Exam (II)- 2017 - Elementary Mathematics Defence Question Paper

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CDS Exam (II)- 2017 - Elementary Mathematics

CDS Exam (II)- 2017 - Elementary Mathematics Defence Questions

1.
What is the value of \( a (a \neq 0) \) for which \( x^{2} - 5x + a \) and \( x^{2} - 7x + 2a \) have a common factor?
A.
6
B.
4
C.
8
D.
2
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ANSWER :
A. 6
2.
How many numbers from 1 to 1000 are divisible by 2, 3, 4 and 5?
A.
16
B.
17
C.
32
D.
None of the above
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ANSWER :
A. 16
3.
What are the factors of \( x^{3} + 4x^{2} - 11x - 30 \)?
A.
(x − 2), (x + 3) and (x + 5)
B.
(x + 2), (x + 3) and (x − 5)
C.
(x + 2), (x − 3) and (x + 5)
D.
(x + 2), (x − 3) and (x − 5)
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ANSWER :
C. (x + 2), (x − 3) and (x + 5)
4.
If x = 111...1 (20 digits), y = 333...3 (10 digits) and z = 222...2 (10 digits), then what is \( \frac{x - y^{2}}{z} \) equal to?
A.
5
B.
1
C.
2
D.
3
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ANSWER :
B. 1
5.
What is the positive value of m for which the roots of the equation \( 12x^{2} + mx + 5 = 0 \) are in the ratio 3 : 2?
A.
\( 5\sqrt{10} \)
B.
\( \frac{5\sqrt{10}}{12} \)
C.
\( \frac{5}{12} \)
D.
\( \frac{12}{5} \)
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ANSWER :
A. \( 5\sqrt{10} \)
6.
Let f(x) and g(x) be two polynomials (with real coefficients) having degrees 3 and 4 respectively. What is the degree of f(x)g(x)?
A.
12
B.
7
C.
4
D.
3
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ANSWER :
B. 7
7.
If \( 5x^{3} + 5x^{2} - 6x + 9 \) is divided by (x + 3), then the remainder is
A.
135
B.
−135
C.
63
D.
−63
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ANSWER :
D. −63
8.
The product of two non-zero expressions is \( (x + y + z)p^{3} \). If their HCF is \( p^{2} \), then their LCM is
A.
\( (x + y + z) \)
B.
\( (x + y + z)p^{2} \)
C.
\( (x + y + z)p^{3} \)
D.
\( (x + y + z)p \)
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ANSWER :
D. \( (x + y + z)p \)
9.
If the points P and Q represent the real numbers \( 0.8\bar{3} \) and \( 0.6\bar{2} \) on the number line, then the distance between P and Q is
A.
\( \frac{21}{90} \)
B.
\( \frac{19}{90} \)
C.
\( \frac{21}{100} \)
D.
\( \frac{56}{90} \)
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ANSWER :
B. \( \frac{19}{90} \)
10.
Sudhir purchased a chair with three consecutive discounts of 20%, 12.5% and 5%. The actual deduction will be
A.
33.5%
B.
30%
C.
32%
D.
35%
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ANSWER :
A. 33.5%
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