CUET UG Mathematics — Algebra previous year questions with solutions.
Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :  Choose the correct answer from the options given below :
When the doctor arrives late, what is the probability that he comes by other means of transport?
Which of the following statements are true? (A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto. (B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto. (C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto. (D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto. (Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers) Choose the correct answer from the options given below:
$[\vec{a} + \vec{b},\ \vec{b} + \vec{c}, \vec{a} + \vec{b} + \vec{c}]$ is equal to
If $A = \begin{bmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{bmatrix}$ and square matrix $B$ satisfy $AB = 8I$, then the value of $|B|$ is:
If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to
If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then
If $0 < x < \pi$ and the matrix $\begin{bmatrix} 4\sin x & -1 \\ -3 & \sin x \end{bmatrix}$ is singular, then the values of $x$ are :
The set of all values of $\alpha$ for which the system of linear equations $x + y + z = 1$ $x + 2y + 4z = \alpha$ $x + 4y + 10z = \alpha^2$ is consistent, is
The value $x$ is:
If $A = \begin{bmatrix} 6 & -8 \\ -2 & 5 \end{bmatrix}$ and $A^2 - 10A = C$ then C is equal to
If $\begin{vmatrix} -1 & a & a^2 \\ -1 & b & b^2 \\ -1 & c & c^2 \end{vmatrix}^2 = \lambda$ and $a - b = 1$, $b - c = 2$ and $c - a = 3$, then the value of $\lambda$ is
If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$, then which of the following is the value of $(\text{adj } A)^{-1}$
If $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is
The probability that the study time of students is at least 1 hour
Let $A = (a_{ij})$ and $B = (b_{ij})$ are square matrices of same order. (A) The number of possible matrices of order $2 \times 2$ with entries $-1, 0, 1$ is 81. (B) $A + A'$ is skew symmetric matrix (C) $A \cdot A^{-1} = 0$, $|A| \neq 0$ (D) A is skew symmetric matrix if $a_{ij} = -a_{ji}$ for all $i, j$ (E) $(AB)' = A'B'$ Choose the correct answer from the options given below :
If $A = \begin{bmatrix} 6 & 4 \\ 5 & 3 \end{bmatrix}$ and $B = adj(A)$, then $|B|$ is equal to:
If the area of a triangle with vertices A(1,3), B(0,0) and C(k,0) is 3 sq. units, then k is:
If $A = \begin{bmatrix} 2x & 0 \\ x & x \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1 & 0 \\ -1 & 2 \end{bmatrix}$, then the value of $x$ is
The probability distribution of a discrete random variable X is given as : | x | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X=x) | 0.1 | k | 2k | 2k | k | The value of K is:
If $\begin{vmatrix} (a-x)^2 & (a-y)^2 & (a-z)^2 \\ (b-x)^2 & (b-y)^2 & (b-z)^2 \\ (c-x)^2 & (c-y)^2 & (c-z)^2 \end{vmatrix} = \lambda(a-b)(b-c)(c-a) \cdot (x-y)(y-z)(z-x)$ then the value of $\lambda$ is:
The values of $x$ and $y$ in the equation $2\begin{bmatrix} x & 1 \\ 4 & -3 \end{bmatrix} + 3\begin{bmatrix} -2 & 1 \\ 2 & y-2 \end{bmatrix} = \begin{bmatrix} 2 & 5 \\ 14 & 3 \end{bmatrix}$ are respectively:
The optimal value of linear programming problem maximum $Z = 3x + 4y$, subject to, $x + 3y \leq 12$ $x + y \geq 8$ $x, y \geq 0$ is
The breadth of plot is: