NDA & NA Exam (I)- 2021 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (I)- 2021 - Mathematics

NDA & NA Exam (I)- 2021 - Mathematics Defence Questions

1.
The smallest positive integer \( n \) for which \( \left(\frac{1-i}{1+i}\right)^{n} = 1 \), where \( i = \sqrt{-1} \), is
A.
2
B.
4
C.
6
D.
8
😑 View Answer Error
ANSWER :
B. 4
2.
The value of \( x \), satisfying the equation \( \log_{\cos x} \sin x = 1 \), where \( 0 < x < \frac{\pi}{2} \), is
A.
\( \frac{\pi}{12} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{6} \)
😑 View Answer Error
ANSWER :
C. \( \frac{\pi}{4} \)
3.
If \( \Delta \) is the value of the determinant
\( \begin{vmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{vmatrix} \)
then what is the value of the following determinant?
\( \begin{vmatrix} pa_{1} & b_{1} & qc_{1} \\ pa_{2} & b_{2} & qc_{2} \\ pa_{3} & b_{3} & qc_{3} \end{vmatrix} \)
(\( p \neq 0 \) or 1, \( q \neq 0 \) or 1)
A.
\( p\Delta \)
B.
\( q\Delta \)
C.
\( (p+q)\Delta \)
D.
\( pq\Delta \)
😑 View Answer Error
ANSWER :
D. \( pq\Delta \)
4.
If \( C_{0}, C_{1}, C_{2}, \ldots, C_{n} \) are the coefficients in the expansion of \( (1+x)^{n} \), then what is the value of \( C_{1} + C_{2} + C_{3} + \ldots + C_{n} \)?
A.
\( 2^{n} \)
B.
\( 2^{n} - 1 \)
C.
\( 2^{n-1} \)
D.
\( 2^{n} - 2 \)
😑 View Answer Error
ANSWER :
B. \( 2^{n} - 1 \)
5.
If \( a + b + c = 4 \) and \( ab + bc + ca = 0 \), then what is the value of the following determinant?
\( \begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix} \)
A.
32
B.
−64
C.
−128
D.
64
😑 View Answer Error
ANSWER :
B. −64
6.
The number of integer values of \( k \), for which the equation \( 2 \sin x = 2k + 1 \) has a solution, is
A.
zero
B.
one
C.
two
D.
four
😑 View Answer Error
ANSWER :
C. two
7.
If \( a_{1}, a_{2}, a_{3}, \ldots, a_{9} \) are in GP, then what is the value of the following determinant?
\( \begin{vmatrix} \ln a_{1} & \ln a_{2} & \ln a_{3} \\ \ln a_{4} & \ln a_{5} & \ln a_{6} \\ \ln a_{7} & \ln a_{8} & \ln a_{9} \end{vmatrix} \)
A.
0
B.
1
C.
2
D.
4
😑 View Answer Error
ANSWER :
A. 0
8.
If the roots of the quadratic equation \( x^{2} + 2x + k = 0 \) are real, then
A.
\( k < 0 \)
B.
\( k \leq 0 \)
C.
\( k < 1 \)
D.
\( k \leq 1 \)
😑 View Answer Error
ANSWER :
D. \( k \leq 1 \)
9.
If \( n = 100! \), then what is the value of the following?
\( \frac{1}{\log_{2} n} + \frac{1}{\log_{3} n} + \frac{1}{\log_{4} n} + \ldots + \frac{1}{\log_{100} n} \)
A.
0
B.
1
C.
2
D.
3
😑 View Answer Error
ANSWER :
B. 1
10.
If \( Z = 1 + i \), where \( i = \sqrt{-1} \), then what is the modulus of \( Z + \frac{2}{Z} \)?
A.
1
B.
2
C.
3
D.
4
😑 View Answer Error
ANSWER :
B. 2
Prev Next page