NDA & NA Exam (II)- 2018 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2018 - Mathematics

NDA & NA Exam (II)- 2018 - Mathematics Defence Questions

11.
What is the coefficient of the middle term in the binomial expansion of \( (2 + 3x)^{4} \)?
A.
6
B.
12
C.
108
D.
216
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ANSWER :
D. 216
12.
For a square matrix A, which of the following properties hold?
1. \( (A^{-1})^{-1} = A \)
2. \( \det(A^{-1}) = \frac{1}{\det A} \)
3. \( (\lambda A)^{-1} = \lambda A^{-1} \), where \( \lambda \) is a scalar
Select the correct answer using the code given below.
A.
1 and 2 only
B.
2 and 3 only
C.
1 and 3 only
D.
1, 2 and 3
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ANSWER :
A. 1 and 2 only
13.
Which one of the following factors does the expansion of the determinant \( \begin{vmatrix} x & y & 3 \\ x^{2} & 5y^{3} & 9 \\ x^{3} & 10y^{5} & 27 \end{vmatrix} \) contain?
A.
x − 3
B.
x − y
C.
y − 3
D.
x − 3y
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ANSWER :
A. x − 3
14.
What is the adjoint of the matrix \( \begin{bmatrix} \cos(-\theta) & -\sin(-\theta) \\ -\sin(-\theta) & \cos(-\theta) \end{bmatrix} \)?
A.
\( \begin{bmatrix} \cos\theta & -\sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \)
B.
\( \begin{bmatrix} \cos\theta & \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \)
C.
\( \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \)
D.
\( \begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \)
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ANSWER :
A. \( \begin{bmatrix} \cos\theta & -\sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \)
15.
What is the value of \( \left(\frac{-1 + i\sqrt{3}}{2}\right)^{3n} + \left(\frac{-1 - i\sqrt{3}}{2}\right)^{3n} \), where \( i = \sqrt{-1} \)?
A.
3
B.
2
C.
1
D.
0
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ANSWER :
B. 2
16.
There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?
A.
C(17, 11)
B.
C(12, 8)
C.
C(17, 5) × C(5, 3)
D.
C(5, 3) × C(12, 8)
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ANSWER :
D. C(5, 3) × C(12, 8)
17.
What is the value of \( \log_{9} 27 + \log_{8} 32 \)?
A.
\( \frac{7}{2} \)
B.
\( \frac{19}{6} \)
C.
4
D.
7
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ANSWER :
B. \( \frac{19}{6} \)
18.
If A and B are two invertible square matrices of same order, then what is \( (AB)^{-1} \) equal to?
A.
\( B^{-1}A^{-1} \)
B.
\( A^{-1}B^{-1} \)
C.
\( B^{-1}A \)
D.
\( A^{-1}B \)
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ANSWER :
A. \( B^{-1}A^{-1} \)
19.
If a + b + c = 0, then one of the solutions of \( \begin{vmatrix} a-x & c & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix} = 0 \) is
A.
x = a
B.
\( x = \sqrt{\frac{3(a^{2} + b^{2} + c^{2})}{2}} \)
C.
\( x = \sqrt{\frac{2(a^{2} + b^{2} + c^{2})}{3}} \)
D.
x = 1
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ANSWER :
B. \( x = \sqrt{\frac{3(a^{2} + b^{2} + c^{2})}{2}} \)
20.
What should be the value of x so that the matrix \( \begin{bmatrix} 2 & 4 \\ -8 & x \end{bmatrix} \) does not have an inverse?
A.
16
B.
−16
C.
8
D.
−8
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ANSWER :
B. −16
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