NDA & NA Exam (II)- 2019 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2019 - Mathematics

NDA & NA Exam (II)- 2019 - Mathematics Defence Questions

21.
If \( x = 1 + i \), then what is the value of \( x^{6} + x^{4} + x^{2} + 1 \)?
A.
\( 6i - 3 \)
B.
\( -6i + 3 \)
C.
\( -6i - 3 \)
D.
\( 6i + 3 \)
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ANSWER :
C. \( -6i - 3 \)
22.
What is the value of \( \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + \ldots \infty}}} \)?
A.
\( \sqrt{2} - 1 \)
B.
\( \sqrt{2} + 1 \)
C.
3
D.
4
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ANSWER :
A. \( \sqrt{2} - 1 \)
23.
If \( P(n, r) = 2520 \) and \( C(n, r) = 21 \), then what is the value of \( C(n + 1, r + 1) \)?
A.
7
B.
14
C.
28
D.
56
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ANSWER :
C. 28
24.
How many terms are there in the expansion of \( (1 + 2x + x^{2})^{5} + (1 + 4y + 4y^{2})^{5} \)?
A.
12
B.
20
C.
21
D.
22
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ANSWER :
C. 21
25.
If the middle term in the expansion of \( \left(x^{2} + \frac{1}{x}\right)^{2n} \) is \( 184756x^{10} \), then what is the value of n?
A.
10
B.
8
C.
5
D.
4
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ANSWER :
A. 10
26.
If \( A = \begin{bmatrix} 1 & 2 \\ 2 & 3 \\ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix} \), then which one of the following is correct?
A.
Both AB and BA exist
B.
Neither AB nor BA exists
C.
AB exists but BA does not exist
D.
AB does not exist but BA exists
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ANSWER :
C. AB exists but BA does not exist
27.
If n! has 17 zeros, then what is the value of n?
A.
95
B.
85
C.
80
D.
No such value of n exists
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ANSWER :
D. No such value of n exists
28.
Let \( A \cup B = \{x \mid (x - a)(x - b) > 0\} \), where \( a < b \). What are A and B equal to?
A.
\( A = \{x \mid x > a\} \) and \( B = \{x \mid x > b\} \)
B.
\( A = \{x \mid x < a\} \) and \( B = \{x \mid x > b\} \)
C.
\( A = \{x \mid x < a\} \) and \( B = \{x \mid x < b\} \)
D.
\( A = \{x \mid x > a\} \) and \( B = \{x \mid x < b\} \)
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ANSWER :
B. \( A = \{x \mid x < a\} \) and \( B = \{x \mid x > b\} \)
29.
If the constant term in the expansion of \( \left(\sqrt{x} - \frac{k}{x^{2}}\right)^{10} \) is 405, then what can be the value of k?
A.
\( \pm 2 \)
B.
\( \pm 3 \)
C.
\( \pm 5 \)
D.
\( \pm 9 \)
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ANSWER :
B. \( \pm 3 \)
30.
What is \( C(47, 4) + C(51, 3) + C(50, 3) + C(49, 3) + C(48, 3) + C(47, 3) \) equal to?
A.
\( C(47, 4) \)
B.
\( C(52, 5) \)
C.
\( C(52, 4) \)
D.
\( C(47, 5) \)
😑 View Answer Error
ANSWER :
C. \( C(52, 4) \)
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