JEE Main Algebra — practice questions
32 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Algebra in the app →For the system $a_1x+b_1y=c_1$, $a_2x+b_2y=c_2$, Cramer's rule givesWhich property of determinants is correct?If $M_{ij}$ is the minor of an element $a_{ij}$, then its cofactor $C_{ij}$ isFor the matrix equation $AX=B$, if $|A|\neq 0$, the unique solution isWhich of the following statements about rank is given in the chapter?In a non-zero matrix $A$, the rank $r$ means thatA square matrix $A$ is orthogonal whenIf $A$ is skew-symmetric, which of the following must be true?A square matrix $A$ is symmetric ifIf $A=\begin{bmatrix}2&-3&-1\\4&2&3\end{bmatrix}$, then $A'$ isIf $A$ is of order $2\times 3$ and $B$ is of order $3\times 4$, then the product $AB$ is defined and has orderFor matrix addition $A+B$ to be defined, which condition must hold?Which of the following is a diagonal matrix?Which of the following best defines a matrix of order $m\times n$?If $A$ is a matrix of order $3 \times 4$ and $B$ is of order $4 \times 5$, then the order of the product $AB$ The identity matrix $I_n$ is a square matrix in which:For any square matrix $A$, the matrix $A + A'$ is:The diagonal entries of any skew-symmetric matrix are:If $A$ and $B$ are matrices for which $AB$ is defined, then $(AB)'$ equals:A square matrix $A$ is **invertible** if and only if:If $A$ and $B$ are invertible $n \times n$ matrices, then $(AB)^{-1}$ equals:For a non-singular $n \times n$ matrix $A$, the relation between $\det(\operatorname{adj} A)$ and $\det A$ is:A square matrix $A$ is called **idempotent** if:For the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$, the inverse $A^{-1}$ iThe trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is:A square matrix $A$ satisfies $A^T A = I$. Such a matrix is called:If $A$ is a square matrix with $|A| = 3$ and order $n = 3$, then $|\operatorname{adj}(A)|$ equals:For $n$ even, the maximum value among the binomial coefficients ${}^nC_r$ occurs atThree numbers are in harmonic progression if and only if their reciprocals are inIf $S_n=an^2+bn+c$, then the $n$th term $t_n$ of the sequence isThe principal argument of a complex number is defined to lie in which interval?
