Sample QuestionsDeterminants questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $\left|\begin{array}{ll}3 & 3 \\ x & 1\end{array}\right|=\left|\begin{array}{cc}-3 & x \\ 1 & 1\end{array}\right|$ then value of $x$ is :
Answer: B.
View full solution →Suppose $X =\left[x_{i j}\right]$ a matrix, where
$
X=\left[\begin{array}{ccc}
1 & -1 & 2 \\
3 & 4 & -5 \\
2 & -1 & 3
\end{array}\right]
$
Then matrix $Y =\left[m_{i j}\right]$, where $m_{i j}=$ minor of $x_{i j}$ :
- A
$\left[\begin{array}{ccc}7 & -5 & -3 \\ 19 & 1 & -11 \\ -11 & 1 & 7\end{array}\right]$
- B
$\left[\begin{array}{ccc}7 & -19 & -11 \\ 5 & -1 & -1 \\ 3 & 11 & 7\end{array}\right]$
- C
$\left[\begin{array}{ccc}7 & 19 & -11 \\ -3 & 11 & 7 \\ -5 & -1 & -1\end{array}\right]$
- ✓
$\left[\begin{array}{ccc}7 & 19 & -11 \\ -1 & -1 & 1 \\ -3 & -11 & 7\end{array}\right]$
Answer: D.
View full solution →If $x=-1$ is a root of $\left|\begin{array}{lll}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{array}\right|=0$ then find other two roots of this equation :
Answer: A.
View full solution →For any matrix $A , A =\left[\begin{array}{cc}\alpha & -2 \\ -2 & \alpha\end{array}\right],\left| A ^3\right|=125$ then value of $\alpha$ is :
Answer: A.
View full solution →If A has $3 \times 3$ order square matrix and $| A |=-5$, then $|\operatorname{adj} A |$ is :
Answer: C.
View full solution →For which value of $x,\left|\begin{array}{ll}3 & 2 \\ 5 & x\end{array}\right|$ will be zero?
View full solution →In determinant $\left|\begin{array}{lll}1 & 3 & 2 \\ 8 & 6 & 3 \\ 9 & 5 & 4\end{array}\right|$ find the minor of element 6.
View full solution →If $\left|\begin{array}{ccc}\lambda+1 & 1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1\end{array}\right|=4$ then find the value of $\lambda$.
View full solution →Find value of determinant $\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+a & 1 \\ 1 & 1 & 1+b\end{array}\right|$.
View full solution →If $\left|\begin{array}{cc}3 x & 7 \\ -2 & 4\end{array}\right|=\left|\begin{array}{ll}8 & 7 \\ 6 & 4\end{array}\right|$ then find the value of $x$.
View full solution →If $\left|\begin{array}{ll}2 & 3 \\ y & x\end{array}\right|=3,\left|\begin{array}{ll}x & y \\ 4 & 2\end{array}\right|=5$ then find value of $x$ and $y$.
View full solution →Find the value of $x$ if $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|$.
View full solution →Find the value of the determinant $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x-1\end{array}\right|$.
View full solution →If point $A (m,-1), B (2,1)$ and $C (4,5)$ are collinear, then find value of $m$.
View full solution →If $A =\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]$, then write the value of $A .(\operatorname{adj} A )$.
View full solution →If $\Delta=\left|\begin{array}{ccc} A x & x^2 & 1 \\ B y & y^2 & 1 \\ C z & z^2 & 1\end{array}\right|$ and $\Delta_1=\left|\begin{array}{ccc} A & B & C \\ x & y & z \\ z y & z x & x y\end{array}\right|$ then prove that $\Delta-\Delta_1=0$
View full solution →If $A$ and $B$ has same order invertible square matrix, then prove that :$
(AB)^{-1}=B^{-1} \cdot A^{-1}
$
View full solution →If $A=\left[\begin{array}{ccc}3 & 1 & 2 \\ 3 & 2 & -3 \\ 2 & 0 & -1\end{array}\right]$, then find $A^{-1}$, also find the solution of system of equations as follows :
$ \begin{array}{r} 3 x+3 y+2 z=1 \\ x+2 y=4 \\ 2 x-3 y-z=5 \end{array} $
View full solution →Find the inverse matrix of matrix $\left[\begin{array}{ccc}3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2\end{array}\right]$ and after that with the help of this, find the solution of system of equations :$\left[\begin{array}{lll}3 & 0 & 3 \\2 & 1 & 0 \\4 & 0 & 2\end{array}\right]\left[\begin{array}{l}x \\y \\z\end{array}\right]=\left[\begin{array}{l}8 \\1 \\4\end{array}\right]+\left[\begin{array}{c}2 y \\z \\3 y\end{array}\right]$
View full solution →