Question 1 :
If $\begin{vmatrix} a & a & x\\ m & m & m\\ b & x & b\end{vmatrix}=0$ then $x=?$
Question 2 :
If $\Delta=\begin{vmatrix} a & b & c\\x & y & z \\ p & q & r\end{vmatrix}$ then $\begin{vmatrix} ka & kb & kc\\kx & ky & kz \\ kp & kq & kr\end{vmatrix}$ is equal to<br>
Question 3 :
$\displaystyle \bigtriangleup =\left | \begin{matrix}1/a &1 &bc \\ 1/b &1 &ca \\ 1/c &1 &ab \end{matrix} \right |=$
Question 4 :
The value of $\begin{vmatrix} x & x-1 \\ x+1 & x \end{vmatrix}$ is
Question 5 :
If $f\left( x \right) = a + bx + c{x^2}$ and $\alpha ,\beta ,\gamma $ are the roots of the equation ${x^3} = 1$, then $\left| {\begin{array}{*{20}{c}}a & b & c\\b & c & a\\c & a & b\end{array}} \right|$ is equal to
Question 6 :
If $k$ is a scalar and $A$ is an $n\times n$ square matrix, then $|kA|=$
Question 7 :
If $A$ and $B$ are square matrices of order $3$ such that $|A| = -1, \space |B| = 3$, then $|3AB|$ equals
Question 8 :
The value of the determinant $<br>\Delta =\begin{vmatrix}<br>log\, x & log\, \, y & log\, \, z\\ <br>log2x & log2y &log2z \\ <br>log3x &log3y & log3z<br>\end{vmatrix}$ is
Question 9 :
If $\Delta=\begin{vmatrix} a & 0 & 0\\ b & c & a\\ c & a & b\end{vmatrix}$ then $\begin{vmatrix} p^2a & 0 & 0\\ pb & c & a\\ pc & a & b\end{vmatrix}$ is equal to<br>
Question 10 :
The number of solutions of equations<br><span>$\begin{vmatrix} \sin { 3\theta } & -1 & 1 \\ \cos { 2\theta } & 4 & 3 \\ 2 & 7 & 7 \end{vmatrix}=0$ in $[0, 2{\pi}]$ is </span>
Question 11 :
If $\displaystyle x\neq y\neq z$ and $\displaystyle \begin{vmatrix} x &y &z \\x^{2} &y^{2} &z^{2} \\1+x^{3} <br> &1+y^{3} &1+z^{3} \end{vmatrix}= 0 $ then xyz equals<br>
Question 12 :
The value of $\displaystyle \left | \begin{matrix}<br>x &4 &y+z \\ <br>y &4 &z+x \\ <br> z&4 &x+y <br>\end{matrix} \right |,$is<br>
Question 13 :
If $x,y,z$ are all different and if<br>$\begin{vmatrix} x & { x }^{ 2 } & 1+{ x }^{ 3 } \\ y & { y }^{ 2 } & 1+{ y }^{ 3 } \\ z & { z }^{ 2 } & 1+{ z }^{ 3 } \end{vmatrix}=0$ then $1+xyz=$<br>
Question 14 :
If ${a}, {b},{c} >0$ and ${x},{y},{z} \in R$, then the determinant $\begin{vmatrix} { ({ a }^{ x }+{ a }^{ -x }) }^{ 2 } & { ({ a }^{ x }-{ a }^{ -x }) }^{ 2 } & 1 \\ { ({ b }^{ y }+{ b }^{ -y }) }^{ 2 } & { ({ b }^{ y }-{ b }^{ -y }) }^{ 2 } & 1 \\ { ({ c }^{ z }+{ c }^{ -z }) }^{ 2 } & { ({ c }^{ z }-{ c }^{ -z }) }^{ 2 } & 1 \end{vmatrix}$ is equal to :<br>
Question 15 :
If x, y, z $\in$ R, then the value of determinant $\<span>\begin{vmatrix}</span> (5^x+5^{-x})^2 & (5^x-5^{-x})^2 & 1\\ (6^x+6^{-x})^2 & (6^x-6^{-x})^2 & 1\\ (7^x+7^{-x})^2 & (7^x-7^{-x})^2 & 1\end{matrix}$ is?
Question 16 :
If $a=\sin \theta $, $b=\sin \left ( \theta +2\pi /3 \right )$, $c=\sin \left ( \theta +4\pi /3 \right )$, $x=\cos \theta $, $y=\cos \left ( \theta +2\pi /3 \right )$, $z=\cos \left ( \theta +4\pi /3 \right )$, then value of<br>$\Delta =\begin{vmatrix}<br>a & b & c\\ <br>x & y & z\\ <br>bc & ca & ab<br>\end{vmatrix}$<br>is<br>
Question 17 :
If $S=\left\{x\epsilon [0, 2\pi ]:\begin{vmatrix} 0 & \cos x & -\sin x\\ \sin x & 0 & \cos x\\ \cos x & \sin x & 0\end{vmatrix}=0\right\}$, then $\displaystyle \sum_{x\epsilon S}\tan\left(\displaystyle\frac{\pi}{3}+x\right)$ is equal to
Question 18 :
If $p$ and $q$ are distinct primes, and<br/>$\Delta =\begin{vmatrix}<br/>\sqrt{pq} & pi & q+\sqrt{pq}\\ <br/>p\sqrt{q} & \sqrt{p}+p\sqrt{p}i & q\sqrt{p}+\sqrt{p}qi\\ <br/>q\sqrt{p} & \sqrt{p}+p\sqrt{q}i & q\sqrt{q}+pi<br/>\end{vmatrix}$<br/>then $\Delta $ is<br/>
Question 19 :
The Value of the determinant<b> </b>$\begin{vmatrix} { b }^{ 2 }-ab & \quad b-c & \quad bc-ac \\ ab-{ a }^{ 2 } & \quad a-b & { \quad b }^{ 2 }-ab \\ bc-ac & \quad c-a & \quad ab-{ a }^{ 2 } \end{vmatrix}$ =<i></i>
Question 20 :
If $\left| \begin{matrix} x+a & a^{ 2 } & a^{ 3 } \\ x+b & b^{ 2 } & b^{ 3 } \\ x+c & c^{2} & c^{3} \end{matrix} \right| =0$ and $a \neq b\neq c$, then $x$ is equal to
