NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I) & (II)- 2020 - Mathematics

NDA & NA Exam (I) & (II)- 2020 - Mathematics Defence Questions

1.
If matrix \( A = \begin{bmatrix} 1 - i & i \\ -i & 1 - i \end{bmatrix} \), where \( i = \sqrt{-1} \), then which one of the following is correct?
A.
A is hermitian
B.
A is skew-hermitian
C.
\( (\bar{A})^{T} + A \) is hermitian
D.
\( (\bar{A})^{T} + A \) is skew-hermitian
😑 View Answer Error
ANSWER :
C. \( (\bar{A})^{T} + A \) is hermitian
2.
The term independent of x in the binomial expansion of \( \left(\frac{2}{x^{2}} - \sqrt{x}\right)^{10} \) is equal to
A.
180
B.
120
C.
90
D.
72
😑 View Answer Error
ANSWER :
A. 180
3.
If \( (1 + 2x - x^{2})^{6} = a_{0} + a_{1}x + a_{2}x^{2} + \ldots + a_{12}x^{12} \), then what is \( a_{0} - a_{1} + a_{2} - a_{3} + a_{4} - \ldots + a_{12} \) equal to?
A.
32
B.
64
C.
2048
D.
4096
😑 View Answer Error
ANSWER :
B. 64
4.
If \( C(20, n + 2) = C(20, n - 2) \), then what is n equal to?
A.
18
B.
25
C.
10
D.
12
😑 View Answer Error
ANSWER :
C. 10
5.
For how many values of k, is the matrix \( \begin{bmatrix} 0 & k & 4 \\ -k & 0 & -5 \\ -k & k & -1 \end{bmatrix} \) singular?
A.
Only one
B.
Only two
C.
Only four
D.
Infinite
😑 View Answer Error
ANSWER :
D. Infinite
6.
The number \( (1101101 + 1011011)_{2} \) can be written in decimal system as
A.
\( (198)_{10} \)
B.
\( (199)_{10} \)
C.
\( (200)_{10} \)
D.
\( (201)_{10} \)
😑 View Answer Error
ANSWER :
C. \( (200)_{10} \)
7.
What is the value of \( \frac{1}{10} \log_{2} 1024 - \log_{2} 10 + \frac{1}{5} \log_{2} 3125 \)?
A.
0
B.
1
C.
2
D.
3
😑 View Answer Error
ANSWER :
A. 0
8.
If \( x = \log_{c}(ab) \), \( y = \log_{a}(bc) \), \( z = \log_{b}(ca) \), then which of the following is correct?
A.
\( xyz = 1 \)
B.
\( x + y + z = 1 \)
C.
\( (1 + x)^{-1} + (1 + y)^{-1} + (1 + z)^{-1} = 1 \)
D.
\( (1 + x)^{-2} + (1 + y)^{-2} + (1 + z)^{-2} = 1 \)
😑 View Answer Error
ANSWER :
C. \( (1 + x)^{-1} + (1 + y)^{-1} + (1 + z)^{-1} = 1 \)
9.
Let \( A = \begin{bmatrix} x + y & y \\ 2x & x - y \end{bmatrix} \), \( B = \begin{bmatrix} 2 \\ -1 \end{bmatrix} \) and \( C = \begin{bmatrix} 3 \\ 2 \end{bmatrix} \). If \( AB = C \), then what is the value of the determinant of the matrix A?
A.
−10
B.
−14
C.
−24
D.
−34
😑 View Answer Error
ANSWER :
B. −14
10.
If \( 1.5 \leq x \leq 4.5 \), then which one of the following is correct?
A.
\( (2x - 3)(2x - 9) > 0 \)
B.
\( (2x - 3)(2x - 9) < 0 \)
C.
\( (2x - 3)(2x - 9) \geq 0 \)
D.
\( (2x - 3)(2x - 9) \leq 0 \)
😑 View Answer Error
ANSWER :
D. \( (2x - 3)(2x - 9) \leq 0 \)
Prev Next page