NDA & NA Exam (II)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2014 - Mathematics

NDA & NA Exam (II)- 2014 - Mathematics Defence Questions

21.
If \( f(x) = ax + b \) and \( g(x) = cx + d \) such that \( f(g(x)) = g(f(x)) \), then which one of the following is correct?
A.
\( f(c) = g(a) \)
B.
\( f(a) = g(c) \)
C.
\( f(c) = g(d) \)
D.
\( f(d) = g(b) \)
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ANSWER :
A. \( f(c) = g(a) \)
22.
If A and B are square matrices of second order such that \( |A| = -1 \), \( |B| = 3 \), then what is \( |3AB| \) equal to?
A.
3
B.
−9
C.
−27
D.
None of the above
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ANSWER :
C. −27
23.
For the next three (03) items that follow:
Consider the function \( f(x) = \frac{x-1}{x+1} \).

What is \( \frac{f(x)+1}{f(x)-1} + x \) equal to?
A.
0
B.
1
C.
2x
D.
4x
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ANSWER :
A. 0
24.
What is \( f(2x) \) equal to?
A.
\( \frac{f(x)+1}{f(x)+3} \)
B.
\( \frac{f(x)+1}{3f(x)+1} \)
C.
\( \frac{3f(x)+1}{f(x)+3} \)
D.
\( \frac{f(x)+3}{3f(x)+1} \)
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ANSWER :
C. \( \frac{3f(x)+1}{f(x)+3} \)
25.
What is \( f(f(x)) \) equal to?
A.
x
B.
−x
C.
\( -\frac{1}{x} \)
D.
None of the above
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ANSWER :
C. \( -\frac{1}{x} \)
26.
For the next five (05) items that follow:
Consider the expansion \( \left(x^{2} + \frac{1}{x}\right)^{15} \).

What is the independent term in the given expansion?
A.
2103
B.
3003
C.
4503
D.
None of the above
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ANSWER :
B. 3003
27.
What is the ratio of coefficient of \( x^{15} \) to the term independent of x in the given expansion?
A.
1
B.
\( \frac{1}{2} \)
C.
\( \frac{2}{3} \)
D.
\( \frac{3}{4} \)
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ANSWER :
A. 1
28.
Consider the following statements:
1. There are 15 terms in the given expansion.
2. The coefficient of \( x^{12} \) is equal to that of \( x^{3} \).
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
29.
Consider the following statements:
1. The term containing \( x^{2} \) does not exist in the given expansion.
2. The sum of the coefficients of all the terms in the given expansion is \( 2^{15} \).
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 :
C. Both 1 and 2
30.
What is the sum of the coefficients of the middle terms in the given expansion?
A.
C(15, 9)
B.
C(16, 9)
C.
C(16, 8)
D.
None of the above
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ANSWER :
C. C(16, 8)
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