CUET UG Mathematics — Algebra previous year questions with solutions.
If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ then $A^2 - 5A$ is equal to (where I is identity matrix of order 2)
If $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals
Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is
If $A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then the matrix AB is equal to
If $\vec{a}$ is a non-zero vector, then always
If matrix $A_p = \begin{bmatrix} p(p+1) \\ p(p-1) \end{bmatrix}_{p \in N} \ $(where N is the set of natural numbers), then the value of $|A_1| + |A_2| + |A_3| + ... + |A_{2025}|$ is:
If $\begin{bmatrix} 1 & 2 & 1\end{bmatrix}$ $\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x\end{bmatrix} = 0, $then value of x is
If A and B are invertible matrices of same order, then which one of the following is NOT true?
If $\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$, then $2x + y + 3t + w$ is equal to
If $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors such that $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$, then the value of $2\vec{a}.\vec{b} - 6\vec{b}.\vec{c} - 3\vec{c}.\vec{a}$ is
Let A be a square matrix of order 2 such that $\begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, then A is:
If $\begin{vmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{vmatrix} = 86$, then product of all values of $a$ is:
If $\begin{bmatrix} -1 & 1 & 0 \\ a & b & 1 \\ 1 & 2 & 1 \end{bmatrix}$ is a singular matrix, then the relation between $a$ and $b$ is:
If $A = \begin{bmatrix} 2 & -3 \\ -4 & 7 \end{bmatrix}$ and $2A^{-1} = KI - A$, where K is a real number and I is the identity matrix of order 2, then the value of K is:
If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = 7$, $|\vec{b}| = 3$ and $|\vec{c}| = 5$, then angle between $\vec{b}$ and $\vec{c}$ is
If $x = -4$ is a root of $\begin{vmatrix}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{vmatrix} = 0$, then the sum of the other 2 roots is
The matrix $X$ in the equation $AX = B$, such that $A = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix}$ is given by
If $C_{ij}$ represents the cofactor of element $a_{ij}$ of the matrix $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5 \end{bmatrix}$ then the value of $C_{23} + C_{31} - C_{22}$ is
The value of $\begin{vmatrix} 2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x \end{vmatrix}$, where $x \neq 0$ is:
Match List-I with List-II | List-I | List-II | |---|---| | (A) Corner point of a feasible region | (I) The line segment joining any two arbitrary points of the region always lies entirely within the region | | (B) Bounded feasible region | (II) can not be enclosed within a circle | | (C) Unbounded feasible region | (III) can be enclosed within a circle | | (D) Convex region | (IV) Is a point of intersection of two boundary lines in the feasible region | Choose the correct answer from the options given below:
If A and B are two non-singular matrices of order n, then which of the following statement/statements is/are not correct? (A) AB is non-singular. (B) AB is singular. (C) $(AB)^{-1} = A^{-1}B^{-1}$ (D) $(AB)^{-1}$ does not exist. Choose the correct answer from the options given below:
If $A = \begin{bmatrix} 5 & 6 \\ 3 & 2 \end{bmatrix}$ then which of the following is correct? (A) $|A|$ is positive (B) $|adj\ A| = -8$ (C) Cofactor of 3 is 6 (D) $|2A| = -32$ Choose the **correct** answer from the options given below:
The system of linear equations $kx + 5y = 5$, $2x + 3y = 5$ will be consistent if
If the matrix $\begin{bmatrix} 0 & 1 & 4x\ \\ -1 & 0 & -5 \\ 2 & 5 & y \end{bmatrix}$ is skew-symmetric, then