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

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NDA & NA Exam (I)- 2019 - Mathematics

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

21.
What is the number of terms in the expansion of \( \left[ (2x - 3y)^{2} (2x + 3y)^{2} \right]^{2} \)?
A.
4
B.
5
C.
8
D.
16
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ANSWER :
B. 5
22.
In the expansion of \( (1 + ax)^{n} \), the first three terms are respectively 1, 12x and \( 64x^{2} \). What is n equal to?
A.
6
B.
9
C.
10
D.
12
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ANSWER :
B. 9
23.
The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of
A.
only one AP
B.
more than one but finite numbers of APs
C.
infinite number of APs
D.
finite number of GPs
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ANSWER :
C. infinite number of APs
24.
The sum of \( (p + q)^{th} \) and \( (p - q)^{th} \) terms of an AP is equal to
A.
\( (2p)^{th} \) term
B.
\( (2q)^{th} \) term
C.
Twice the \( p^{th} \) term
D.
Twice the \( q^{th} \) term
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ANSWER :
C. Twice the \( p^{th} \) term
25.
If A is a square matrix of order \( n > 1 \), then which one of the following is correct?
A.
\( \det(-A) = \det A \)
B.
\( \det(-A) = (-1)^{n} \det A \)
C.
\( \det(-A) = -\det A \)
D.
\( \det(-A) = n \det A \)
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ANSWER :
B. \( \det(-A) = (-1)^{n} \det A \)
26.
What is the least value of \( 25 \csc^{2} x + 36 \sec^{2} x \)?
A.
1
B.
11
C.
120
D.
121
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ANSWER :
D. 121
27.
Consider the following for the next 02 (two) items:
Let A and B be \( (3 \times 3) \) matrices with \( \det A = 4 \) and \( \det B = 3 \).

What is \( \det(2AB) \) equal to?
A.
96
B.
72
C.
48
D.
36
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ANSWER :
A. 96
28.
What is \( \det(3AB^{-1}) \) equal to?
A.
12
B.
18
C.
36
D.
48
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ANSWER :
C. 36
29.
Consider the following for the next 02 (two) items:
A complex number is given by \( z = \frac{1 + 2i}{1 - (1 - i)^{2}} \).

What is the modulus of z?
A.
4
B.
2
C.
1
D.
\( \frac{1}{2} \)
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ANSWER :
C. 1
30.
What is the principal argument of z?
A.
0
B.
\( \frac{\pi}{6} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{2} \)
😑 View Answer Error
ANSWER :
A. 0
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