JEE Advanced Determinants — practice questions
17 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Determinants in the app →If $A$ is a $3\times3$ matrix with $|A| = 4$, then $|2A|$ equals:The area of the triangle with vertices $(3,8)$, $(-4,2)$ and $(5,1)$ is:Three points are collinear if and only if the determinant formed from their coordinates is:If $A$ is a $3\times3$ matrix with $|A| = 5$, then $|\,\text{adj}\,A\,|$ equals:For a square matrix $A$ of order $n$, the product $A\,(\text{adj}\,A)$ equals:A square matrix $A$ is invertible if and only if:If $A$ and $B$ are $3\times3$ matrices with $|A| = 2$ and $|B| = 3$, then $|AB|$ equals:The value of the determinant $\begin{vmatrix} 2 & 4 \\ 3 & 5 \end{vmatrix}$ is:The matrix $\begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix}$ is singular when $k$ equals:A system of linear equations $AX = B$ (with $A$ square) has a unique solution if and only if:If $|A| = 4$ for an invertible matrix $A$, then $|A^{-1}|$ equals:The value of $\begin{vmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{vmatrix}$ is:If $A$ is a $3\times3$ matrix with $|A| = 2$, then $|3A|$ equals:The determinant of $\begin{pmatrix}3 & 2 \\ 1 & 4\end{pmatrix}$ is:Swapping two rows of a determinant changes its value by a factor of:If $A$ is a $3\times 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is:Three points $(1, 2), (3, 4), (5, 6)$ on the school graph paper are: