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

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NDA & NA Exam (I)- 2014 - Mathematics

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

21.
The sum of the series formed by the sequence \( 3, \sqrt{3}, 1, \ldots \) up to infinity is
A.
\( \frac{3\sqrt{3}(\sqrt{3}+1)}{2} \)
B.
\( \frac{3\sqrt{3}(\sqrt{3}-1)}{2} \)
C.
\( \frac{3(\sqrt{3}+1)}{2} \)
D.
\( \frac{3(\sqrt{3}-1)}{2} \)
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ANSWER :
A. \( \frac{3\sqrt{3}(\sqrt{3}+1)}{2} \)
22.
If \( |Z + \bar{Z}| = |Z - \bar{Z}| \), then the locus of Z is
A.
a pair of straight lines
B.
a line
C.
a set of four straight lines
D.
a circle
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ANSWER :
A. a pair of straight lines
23.
The number 251 in decimal system is expressed in binary system by
A.
11110111
B.
11111011
C.
11111101
D.
11111110
😑 View Answer Error
ANSWER :
B. 11111011
24.
What is the argument of the complex number \( \frac{(1+i)(2+i)}{3-i} \), where \( i = \sqrt{-1} \)?
A.
0
B.
\( \frac{\pi}{4} \)
C.
\( -\frac{\pi}{4} \)
D.
\( \frac{\pi}{2} \)
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ANSWER :
D. \( \frac{\pi}{2} \)
25.
Consider the following statements in respect of the matrix
\( A = \begin{bmatrix} 0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0 \end{bmatrix} \)
1. The matrix A is skew-symmetric.
2. The matrix A is symmetric.
3. The matrix A is invertible.
Which of the above statements is/are correct?
A.
1 only
B.
3 only
C.
1 and 3
D.
2 and 3
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ANSWER :
A. 1 only
26.
Consider two matrices \( A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 2 & -4 \\ 2 & 1 & -4 \end{bmatrix} \).
Which one of the following is correct?
A.
B is the right inverse of A
B.
B is the left inverse of A
C.
B is the both sided inverse of A
D.
None of the above
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ANSWER :
B. B is the left inverse of A
27.
One of the roots of \( \begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix} = 0 \) is
A.
abc
B.
a + b + c
C.
−(a + b + c)
D.
−abc
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ANSWER :
C. −(a + b + c)
28.
If A is any matrix, then the product AA is defined only when A is a matrix of order \( m \times n \) where
A.
\( m > n \)
B.
\( m < n \)
C.
\( m = n \)
D.
\( m \leq n \)
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ANSWER :
C. \( m = n \)
29.
The determinant of an odd order skew-symmetric matrix is always
A.
zero
B.
one
C.
negative
D.
depends on the matrix
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ANSWER :
A. zero
30.
If any two adjacent rows or columns of a determinant are interchanged in position, the value of the determinant
A.
becomes zero
B.
remains the same
C.
changes its sign
D.
is doubled
😑 View Answer Error
ANSWER :
C. changes its sign
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