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

11.
If \( A \) and \( B \) are two matrices such that \( AB \) is of order \( n \times n \), then which one of the following is correct?
A.
A and B should be square matrices of same order.
B.
Either A or B should be a square matrix.
C.
Both A and B should be of same order.
D.
Orders of A and B need not be the same.
😑 View Answer Error
ANSWER :
D. Orders of A and B need not be the same.
12.
How many matrices of different orders are possible with elements comprising all prime numbers less than 30?
A.
2
B.
3
C.
4
D.
6
😑 View Answer Error
ANSWER :
C. 4
13.
Let
\( \Delta = \begin{vmatrix} p & q \\ r & s \end{vmatrix} \)
where \( p, q, r \) and \( s \) are any four different prime numbers less than 20. What is the maximum value of the determinant?
A.
215
B.
311
C.
317
D.
323
😑 View Answer Error
ANSWER :
C. 317
14.
If \( A \) and \( B \) are square matrices of order 2 such that \( \det(AB) = \det(BA) \), then which one of the following is correct?
A.
A must be a unit matrix.
B.
B must be a unit matrix.
C.
Both A and B must be unit matrices.
D.
A and B need not be unit matrices.
😑 View Answer Error
ANSWER :
D. A and B need not be unit matrices.
15.
What is \( \cot 2x \cot 4x - \cot 4x \cot 6x - \cot 6x \cot 2x \) equal to?
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
16.
If \( \tan x = -\frac{3}{4} \) and \( x \) is in the second quadrant, then what is the value of \( \sin x \cdot \cos x \)?
A.
\( \frac{6}{25} \)
B.
\( \frac{12}{25} \)
C.
\( -\frac{6}{25} \)
D.
\( -\frac{12}{25} \)
😑 View Answer Error
ANSWER :
D. \( -\frac{12}{25} \)
17.
What is the value of the following?
\( cosec\left(\frac{\pi}{6}\right) \sec\left(\frac{2\pi}{3}\right) \)
A.
\( \frac{4}{3} \)
B.
4
C.
−4
D.
\( -\frac{4}{3} \)
😑 View Answer Error
ANSWER :
C. −4
18.
If the determinant
\( \begin{vmatrix} x & 1 & 3 \\ 0 & 0 & 1 \\ 1 & x & 4 \end{vmatrix} = 0 \)
then what is \( x \) equal to?
A.
−2 or 2
B.
−3 or 3
C.
−1 or 1
D.
3 or 4
😑 View Answer Error
ANSWER :
C. −1 or 1
19.
What is the value of the following?
\( \tan 31^{\circ} \tan 33^{\circ} \tan 35^{\circ} \ldots \tan 57^{\circ} \tan 59^{\circ} \)
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
20.
If
\( f(x) = \begin{vmatrix} 1 & x & x+1 \\ 2x & x(x-1) & x(x+1) \\ 3x(x-1) & x(x-1)(x-2) & x(x+1)(x-1) \end{vmatrix} \)
then what is \( f(-1) + f(0) + f(1) \) equal to?
A.
0
B.
1
C.
100
D.
−100
😑 View Answer Error
ANSWER :
A. 0
Prev Next page