CUET UG Mathematics — Algebra previous year questions with solutions.
If the mean and variance of a binomially distributed random variable X are 4 and 2 respectively, then $P(X = 2)$ is equal to
The feasible region and optimal solution of a LPP with objective function, max.$(z) = 600x + 400y$, subject to : $x + 2y \leq 12$, $2x + y \leq 12$, $x + 1.25y \geq 5$, $x \geq 0$ and $y \geq 0$, is: The feasible region and optimal solution is _____
The system of equations $3x + 4y = 5$, $6x + 7y = -8$ is written in matrix form as
If $\vec{p} = \hat{i} + \hat{j} - 2\hat{k}$ and $\vec{q} = 2\hat{i} + \hat{j} - \hat{k}$, then the area of parallelogram having diagonals $(\vec{p} + \vec{q})$ and $(\vec{p} - \vec{q})$ is
A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs. 50 and that on type B circuit is Rs. 60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer. A. $x + 2y \geq 15$ B. $2x + y \leq 20$ C. $x + 2y \leq 12$ D. $x, y \leq 0$ Choose the correct answer from the options given below
Let A and B be square matrices of order 3 and k is a constant. If $|A| \neq 0$ and $|B| \neq 0$, where $|A|$ represents the determinant of A, then which of the following statements are true ? (where A' denotes the transpose of matrix A) (A) $(AB)^{-1} = B^{-1} A^{-1}$ (B) $(A+B)' = A' \times B'$ (C) $(AB)' = A'B'$ (D) $|kA| = k^3 |A|$ (E) $|A'| = |A|$ Choose the correct answer from the options given below :
It is given that student marked the answer correctly, the probability that he guesses is
The solution of LPP max.(z) = $5x + 3y$ subject to $2x + y \leq 6$ $x + y \leq 4$ $x \geq 0, y \geq 0$, is
The unit vector in the direction of the sum of vectors $\vec{a} = 2\hat{i} + 2\hat{j} - 5\hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}$ is :
The probability that B alone complete the task on time is:
The corner points of the feasible region determined by inequalities of LPP are $(4, 10)$, $(6, 8)$ and $(6, 5)$. Let $z = 3x + 4y$ be the objective function. Then the sum of maximum value of z and minimum value of z is :
The objective function for a L.P.P. is $Z = 5x + 7y$ and the corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4) and (0, 2), then the maximum value of Z occurs at
If $|\vec{a}| = 3|\vec{b}|$, $|\vec{b}| = 2$ and angle between $\vec{a}$ and $\vec{b}$ is $60^\circ$, then $|\vec{a} - \vec{b}|$ is equal to:
A vector perpendicular to a plane containing a triangle ABC having vertices as $A(1,1,0)$, $B(2,1,1)$ and $C(0,3,2)$, is:
Let A be a non singular square matrix of $2 \times 2$. Then, $|adj\ A|$ is equal to
If $A$ and $B$ are independent events such that $0 < P(A) < 1$ and $0 < P(B) < 1$, then identify the correct statements. (A) $A$ and $B'$ are independent (B) $A'$ and $B$ are independent (C) $A$ and $B$ are mutually exclusive (D) $A'$ and $B'$ are independent Choose the correct answer from the options given below :
The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is:
The optimal solution of the Linear Programming problem Maximize $Z = 3x_1 + 5x_2$, s.t. $3x_1 + 2x_2 \leq 18$ $x_1 \leq 4$ $x_2 \leq 6$ $x_1 \geq 0, x_2 \geq 0$ is
Let $\vec{a} = 2\hat{i} + 3\hat{j} - 4\hat{k}$ and $\vec{b} = 3\hat{i} - 5\hat{j} + 6\hat{k}$. Let $\vec{c}$ be a vector such that $\vec{c} \times \vec{a} = \vec{b} \times \vec{c}$ and $\vec{c}\cdot(2\vec{a}-3\vec{b}) = 238\sqrt{2}$ then $|\vec{c}|^2$ is equal to :
When the doctor arrives late, what is the probability that he comes by bike?
Match List - I with List - II. | List - I | List - II | |---|---| | (A) The value of $\hat{i}\cdot(\hat{j}\times\hat{k}) + \hat{j}\cdot(\hat{i}\times\hat{k}) + \hat{k}\cdot(\hat{i}\times\hat{j})$ | (I) 16 | | (B) If $\lvert\vec{a}\rvert=10$, $\lvert\vec{b}\rvert=2$ and $\vec{a}\cdot\vec{b}=12$, then the value of $\lvert\vec{a}\times\vec{b}\rvert$ is | (II) $\frac{\pi}{4}$ | | (C) If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$, then the value of $\theta$, for which $\vec{a}\cdot\vec{b} = \lvert\vec{a}\times\vec{b}\rvert$ is | (III) 14 | | (D) If $\vec{a}$ and $\vec{b}$ are perpendicular and $\vec{a} = 2\hat{i}+4\hat{j}+\lambda\hat{k}$ and $\vec{b} = 3\hat{i}-5\hat{j}+\hat{k}$, then the value of $\lambda$ is | (IV) 1 | Choose the correct answer from the options given below :
If $A = \begin{bmatrix} 0 & 2 & -3 \\ y & 0 & -1 \\ z & x & 0 \end{bmatrix}$ is skew symmetric matrix, then $x^3 + y^3 + z^3 - 3xyz$ is equal to :
The value of $P(E/E_1)$ is
Bag I contains 4 red and 5 black balls, while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be black. Then the probability that it was drawn from Bag II, is