CUET UG Mathematics — Algebra previous year questions with solutions.
The value of $\begin{vmatrix} 1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b \end{vmatrix}$ is
If in a binomial distribution $n = 4$, $P(X=0) = \frac{16}{81}$, then $P(X=4)$ equals :
The order of a null matrix is :
The programming problem Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :
If the probability distribution of a random variable X is as given below : | X | -1 | 0 | 1 | 2 | 3 | |---|---|---|---|---|---| | P(X) | K | $\frac{1}{5}$ | 2K | $\frac{3}{10}$ | K | Then the value of K is :
Probabilities to solve a specific problem by A, B and C are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Probability that at least one will solve the problem is:
All points lying inside the triangle formed by the points (5, 0), (-1, 2) and (1, 3) satisfy : (A) $3x + 2y - 18 > 0$ (B) $3x + 2y > 0$ (C) $2x + y + 13 < 0$ (D) $2x - 3y - 12 < 0$ (E) $2x - 3y + 12 > 0$ Choose the **correct** answer from the options given below :
Let A be a square matrix of order 3 then |3A| is equal to
Given relation $R = \{(x, y) : y = x + 5, x < 4, x, y \in N\}$. Where N is a set of natural numbers then :
In a Linear Programming problem, the objective function is always :
The black and red die are rolled. The conditional probability of obtaining a sum greater than 9 given that the black die resulted in a 5 is :
If $f(x) = \sqrt{x}$, $g(x) = 2x - 3$, then domain of $fog(x)$ is :
If A is a square matrix of order 3, B = kA and |B| = $x$|A| then,
The position vector of a point R which divides the line joining two points P and Q whose position vectors are $\hat{i} + 2\hat{j} - \hat{k}$ and $-\hat{i} + \hat{j} + \hat{k}$ respectively in the ratio 2 : 1 externally is :
The feasible region of an LPP Max $Z = 3x + 2y$ subject to $x \geq 0, y \geq 0, x - 2y \leq 3$ is:
A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$ The above Linear Programming Problem [LPP] is given by
The feasible region for an LPP is shown below. Let $Z = 3x - 4y$ be the objective function. Maximum of Z occurs at : 
The mean of the number of heads in a simultaneous toss of three coins is :
Choose the wrong statement from the following :
Let X be the random variable with probability distribution given by the following table. | X | 0 | 1 | 2 | 3 | |---|---|---|---|---| | P(X = x) | $\frac{1}{8}$ | k | $\frac{3}{8}$ | $\frac{1}{8}$ | The value of $P(X \leq 1)$ is:
A man is known to speak truth 4 out of 5 times. He throws a die and reports that five appears. Then the probability that actual five appears on the dice is
If $A^2 - A + I = O$, where O is the zero matrix and I is the identity matrix, then $A^{-1}$ is
A. A relation $R$ on a set $A$ is called an equivalence relation, if it is reflexive, symmetric and transitive. B. The function $f : R \to R$ defined by $f(x) = e^x$ is not one-one. C. The one-one function is also known as injective function. D. The onto function is also known as subjective function. E. A function $f : X \to Y$ is said to be many-one, if two or more than two elements in set $X$ have the different image in set $Y$. Choose the correct answer from the option given below:
The corner points of the feasible region for an L.P.P. are $(0, 10)$, $(5, 5)$, $(15, 15)$ and $(0, 20)$. If the objective function is $z = px + qy$; $p, q > 0$, then the condition on $p$ and $q$ so that the maximum of $z$ occurs at $(15, 15)$ and $(0, 20)$ is