NDA MATHEMATICS QUIZ - 11

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Question 1:

If $a+b+c=s$ then the value of the determinant $\left|\begin{array}{ccc}\mathrm{s}+\mathrm{c} & \mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{s}+\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{a} & \mathrm{s}+\mathrm{b}\end{array}\right|$ is.

Question 2:

If $X=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right]$ and $X^{2}-k X-I_{2}=0$

then $k$ equals.

Question 3:

If $X=\left[\begin{array}{cc}3 & -5 \\ -4 & 2\end{array}\right]$ then the value of $X^{2}-5 X-14$ is equal to.

Question 4:

The determinant $\left|\begin{array}{ccc}1 & 1 & 1 \\ \mathrm{a} & \mathrm{b} & \mathrm{c} \\ \mathrm{a}^{3} & \mathrm{~b}^{3} & \mathrm{c}^{3}\end{array}\right|$ where $a \neq b \neq c$ is divisible by .

Question 5:

If $X$ is a square matrix then $X+X^{T}$ is a .

Question 6:

If $A=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3\end{array}\right]$ then $A^{5}$ equals $ \mathrm{}$.

Question 7:

If the inverse of matrix $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & \lambda & 5\end{array}\right]$ exists then $\lambda$ must not be equal to.

Question 8:

Let X = $\left[\begin{array}{cc}1 & \frac{-1-\sqrt{3 i}}{2} \\ \frac{-1+\sqrt{3} i}{2} & 1\end{array}\right]$ then $X^{50}$ equals.

Question 9:

Value of $\left|\begin{array}{ccc}\frac{1}{x} & x^{2} & y z \\ \frac{1}{y} & y^{2} & x z \\ \frac{1}{z} & z^{2} & x y\end{array}\right|$ is.

Question 10:

$\operatorname{Let} A=\left[\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right]$and $X=\left[\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{2}\end{array}\right]$then$A^{3} X$ is equal to

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