Algebra PYQ — Page 45

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 $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ 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?

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 _____

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 :

The value of $P(E/E_1)$ is

The probability that the study time of students is not more than one hour.

The feasible solution to the LPP is-

Choose the correct statement A. If any two rows or any two columns are identical or proportional, then value of determinant is Zero. B. Minor of an element $a_{ij}$ of the determinant of matrix A is the determinant obtained by deleting $i^{th}$ row and $j^{th}$ column C. If $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$, then A is Skew-symmetric matrix D. If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$, then $(A + A')$ is Symmetric matrix E. If $|A| = 0$, then A is non-singular matrix

Match List - I with List - II. | | List - I | | List - II | |---|---|---|---| | (A) | $A = \begin{bmatrix} 6 & 9 \\ 2 & 3 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 6 & 0 \\ 7 & 9 & 8 \end{bmatrix}$, AB will be | (I) | $\begin{bmatrix} 75 & 117 & 72 \\ 35 & 39 & 24 \end{bmatrix}$ | | (B) | $P = \begin{bmatrix} 8 & 45 & 30 \\ 17 & 19 & 5 \end{bmatrix}$, $Q = \begin{bmatrix} 67 & 72 & 42 \\ 8 & 30 & 19 \end{bmatrix}$, P+Q will be | (II) | $\begin{bmatrix} 75 & 117 & 72 \\ 25 & 39 & 24 \end{bmatrix}$ | | (C) | $\begin{bmatrix} 85 & 42 & 69 \\ 73 & 42 & 50 \end{bmatrix} - \begin{bmatrix} 10 & -75 & -3 \\ 38 & 3 & 26 \end{bmatrix}$ | (III) | $\begin{bmatrix} 75 & 117 & 72 \\ 25 & 49 & 24 \end{bmatrix}$ | | (D) | $2 \begin{bmatrix} 34 & 36 & 30 \\ 12 & 18 & 20 \end{bmatrix} + \begin{bmatrix} 7 & 55 & 12 \\ 1 & 13 & -16 \end{bmatrix}$ | (IV) | $\begin{bmatrix} 75 & 127 & 72 \\ 25 & 49 & 24 \end{bmatrix}$ | Choose the correct answer from the options given below :

If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then

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 :

When the doctor arrives late, what is the probability that he comes by cab?

The constraints are - A. $2x + y \leq 8$ B. $2x + y \geq 8$ C. $x + 2y \leq 10$ D. $x + 2y \geq 10$ E. $x, y \geq 0$ Choose the correct answer from the options given below:

If two numbers are selected at random from the first 25 natural numbers, then the probability that their sum will be odd is:

Read the following statements carefully: A. Determinant is a square matrix B. If A be any given square matrix of order n, then $A(\text{adj}A) = (\text{adj}A)A = |A|I$. C. If A and B are nonsingular matrices of the same order, then AB and BA are also nonsingular matrices of the same order. D. If A is a nonsingular matrix, then its inverse does not exist Which of the above statements are true? Choose the correct answer from the options given below:

If A and B are two independent events with $P(A) = \frac{1}{5}$ and $P(B) = \frac{1}{3}$, then $P(A'/B)$ is:

The value of $y$ is

The length of the plot is:

If $A=\begin{bmatrix}2 & 0 & 0 \\ -1 & 2 & 3 \\ 3 & 3 & 5\end{bmatrix}$, then $A(\text{adj } A)$ is equal to :

The objective function (z) to maximize the profit is:

Three friends A, B and C are playing with a pair of dice. They throw two dice alternately. Coming of a doublet on two dice leads to a success and the game stops. If A starts the game, then the probability of his winning, is :

If an unbiased coin is tossed 10 times, probability of obtaining more head than tail is :