CUET UG Mathematics — Algebra previous year questions with solutions.
The minimum value of $z = 3x + 2y$ subjected to the constraints $2x + y \geq 7, x + 2y \geq 8, x, y \geq 0$ is
Consider the LPP: Maximize $z = 5x + 3y$ subject to $3x + 5y \leq 15$, $5x + 2y \leq 10$, $x,y \geq 0$. The optimal feasible solution occurs at
Let $AX = B$ be a system of three linear equations in three variables. Then the system has (A) a unique solutions if $|A| = 0$ (B) a unique solutions if $|A| \neq 0$ (C) no solutions if $|A| = 0$ and (adj A) $B \neq 0$ (D) infinitely many solutions if $|A| = 0$ and (adj A)$B = 0$ Choose the correct answer from the options given below:
If $\vec{a} = \hat{i} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$ such that $\vec{r} \times \vec{b} = \vec{c} \times \vec{b}$ and $\vec{r} \cdot \vec{a} = 0$, then $\vec{r}$ is:
Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is:
If $A = \begin{bmatrix}0 & x^2-6 & -3\\-x & 0 & -8\\x^2-2x & 8 & 0\end{bmatrix}$ is a skew symmetric matrix, then the value(s) of x is/ are - (A) 3 (B) -3 (C) -2 (D) -1 Choose the correct answer from the options given below:
A die is tossed once. If the random variable X is defined as $X = \begin{cases} 1, & \text{if the die result in an odd number} \\ -1, & \text{if the die result in an even number} \end{cases}$, then the variance of X is
If $A = \begin{bmatrix} 5 & 3 \\ 2 & 4 \end{bmatrix}$, then the matrix $A^2 - 6A + 14$ I is (where I is an identity matrix of order 2)
If $M = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$ and $N = [7 \quad 1 \quad -4]$, then $(MN)^T$ will be equal to:
From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function $z = 1.50x + 1.00y$; the maximum value of $z$ will be: 
A random variable X has the following probability distribution | X | 0 | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---|---| | P(X) | 0.1 | k | 0.2 | 2k | 0.3 | k | Then P (X < 3) is
The value of $\begin{vmatrix} 1 & x & y \\ 1 & x+y & y \\ 1 & x & x+y \end{vmatrix}$ is
A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$, then $f$ is:
If $3\begin{bmatrix} x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 & x + y \\ z + w & 3 \end{bmatrix}$, then the values of $x, y, z$ and $w$ are
In the given figure, feasible region represented by the constraints $4x + y \geq 80$, $x + 5y \geq 115$, $3x + 2y \leq 150$, $x,y \geq 0$ is 
If $A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ and $I$ is an identity matrix of order 2, then $A - 3I$ equals
For a Binomial distribution, B(n,p), where p+q=1, the sum and product of mean and variance are 8 and 12 respectively, when the value of n is:
The value of $\begin{vmatrix} x^2 - x + 1 & x - 1 \\ x + 1 & x + 1 \end{vmatrix}$ is equal to:
Consider the LPP: Minimize $Z = x + 2y$ subject to $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$. The optimal feasible solution occurs at
If $f(x) = \begin{vmatrix} 0 & x-1 & x-2 \\ x+1 & 0 & x-3 \\ x+2 & x+3 & 0 \end{vmatrix}$, then the value of $f(0)$ is equal to:
A bag contains 4 red and 6 green balls. A ball is drawn at random. Its colour is noted and is returned to the bag. One additional ball of the colour drawn is put in the bag. Again a ball is then drawn from the bag. The probability of this ball to be of green colour is
If $|\vec{a}| = 10$, $|\vec{b}| = 2$ and $\vec{a} \cdot \vec{b} = 12$, then value of $|\vec{a} \times \vec{b}|$ is :
If A and B are symmetric matrices of the same order, then
Match List-I with List-II | List-I | List-II | |---|---| | (A) Angle between î and -ĵ is | (I) $\frac{\pi}{6}$ | | (B) Angle between 2î + k̂ and 10î + 5k̂ is | (II) $\frac{\pi}{4}$ | | (C) Angle between î and î + ĵ is | (III) 2π | | (D) Angle between √3ĵ - k̂ and ĵ is | (IV) $\frac{\pi}{2}$ | Choose the correct answer from the options given below: