1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let A = $\left(\begin{array}{ccc}0 & \sin^2 \theta & \cos^2 \theta \\ \cos^2 \theta & 0 & \sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta & 0\end{array}\right)$ and A = P + Q where P is symmetric matrix and Q is skew-symmetric matrix.

What is P equal to ?

A
$\left(\begin{array}{ccc}0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0\end{array}\right)$
B
$\left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right)$
C
cos 2θ$\left(\begin{array}{ccc}0 & −1 & 1 \\ 1 & 0 & −1 \\ −1 & 1 & 0\end{array}\right)$
D
cos 2θ$\left(\begin{array}{ccc}0 & −1/2 & 1/2 \\ 1/2 & 0 & −1/2 \\ −1/2 & 1/2 & 0\end{array}\right)$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let A = $\left(\begin{array}{ccc}0 & \sin^2 \theta & \cos^2 \theta \\ \cos^2 \theta & 0 & \sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta & 0\end{array}\right)$ and A = P + Q where P is symmetric matrix and Q is skew-symmetric matrix.

What is Q equal to ?

A
$\left(\begin{array}{ccc}0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0\end{array}\right)$
B
$\left(\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right)$
C
cos 2θ$\left(\begin{array}{ccc}0 & −1 & 1 \\ 1 & 0 & −1 \\ −1 & 1 & 0\end{array}\right)$
D
cos 2θ$\left(\begin{array}{ccc}0 & −1/2 & 1/2 \\ 1/2 & 0 & −1/2 \\ −1/2 & 1/2 & 0\end{array}\right)$
3
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following in respect of the matrices:

A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \\ -m\end{bmatrix} $

 

1. CA = CB

2. AC = BC

3. C(A + B) = CA + CB

Which of the above statements is/are correct?

A
1 only
B
2 only
C
2 and 3
D
1 and 2
4
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \\ -2\cos \theta & \sin \theta & 0 \\ -1 & 1 & 1 \end{bmatrix},$ then what is A(adj A) equal to?

(where) I is the identity matrix.

A
Null matrix
B
-I
C
I
D
2I
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