Algebra PYQ — Page 23

The feasible region of a LPP is bounded. The corresponding objective function is Z= 6x - 7y. Then objective function attains:

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + 3y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is:

Let $\vec{a} = \hat{i} + \hat{j}$, $\vec{b} = \hat{i} - \hat{j}$ and $\vec{c} = \hat{i} + \hat{j} + \hat{k}$. If $\hat{m}$ is a unit vector perpendicular to both $\vec{a}$ and $\vec{b}$, then $|\vec{c}.\hat{m}|$ is equal to

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where $k > 0$ is 30 sq. units, then the value of k is

Let A be any square matrix of order 3 and $B = \begin{bmatrix} 0 & -4 & 2 \\ 4 & 0 & 3 \\ -2 & -3 & 0 \end{bmatrix}$. Then the matrix $ABA^T$ is a

The solution set of the linear inequation $|4x - 3| \leq \frac{3}{4}$ is:

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

Which of the following is NOT correct?

If $A = \begin{bmatrix} 2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{bmatrix}$, then the value of det (adj (2A)) is:

The maximum value of $z = 5x + 7y$ subjected to constraints $x + y \leq 5$, $x \geq 0$, $y \geq 0$ is:

Let $A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}$, where $0 \leq \theta \leq 2\pi$. Then which of the following are true? (A) $|A| = 2 + 2 \sin^{2} \theta$ (B) $|A| = 2 + \sin^{2} \theta$ (C) minimum value of $|A|$ is $1$ (D) maximum value of $|A|$ is $4$ Choose the correct answer from the options given below:

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

If A is square matrix of order 3 × 3 and |adj A| = 64, then the value of |5A| is

The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then

Let $A = [a_{ij}]_{2 \times 4}$ and $B = [b_{ij}]_{4 \times 2}$, then $|3AB|$ is equal to

Match List-I with List-II Let A and B be any two events | List-I | List-II | | --- | --- | | (A) $P(A')$ | (I) $\frac{P(A \cap B)}{P(A)}; P(A) \neq 0$ | | (B) $P(\phi)$ | (II) $\frac{P(A \cap B)}{P(B)}; P(B) \neq 0$ | | (C) $P(A\vert B)$ | (III) $1 - P(A)$ | | (D) $P(B\vert A)$ | (IV) 0 | Choose the correct answer from the options given below:

If $\left|\begin{matrix} x & 8 \\ 4 & x \end{matrix}\right| = \left|\begin{matrix} 6 & 2 \\ 18 & 6 \end{matrix}\right|$, then $x$ is/are equal to

Let $\begin{vmatrix} 3 & y \\ x & 1 \end{vmatrix} = \begin{vmatrix} 3 & 2 \\ 4 & 1 \end{vmatrix}$ and $x, y$ are natural numbers, then the number of solutions for the system is:

The probability distribution function of a normal variate with mean $\mu$ and variance $\sigma^2$ is given by: $f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, $-\infty < x < \infty$, $-\infty < \mu < \infty$, $\sigma > 0$ If $y = f(x)$ be the normal probability curve, then which of the following is correct? (A) The normal curve is symmetrical about the line $x = \mu$. (B) Mean, median and mode of the distribution coincide. (C) Y- axis is an asymptote to the normal curve. (D) If x increases numerically, $f(x)$ decreases rapidly. Choose the correct answer from the options given below:

For the linear programming problem (LPP): Maximize $Z = x + 1.5y$, subject to constraints, $x + 2y \leq 40$, $2x + y \leq 40$, $x + y \leq 25$, $x \geq 0$, $y \geq 0$. Which of the following is NOT correct?

The number of all possible matrices of order 3 with each entry either 0 or 1 is:

If $A$ and $B$ are square matrices of the same order, then which of the following statements are correct? (A) $|A^{-1}| = |A|^{-1}$ (B) $adj(A) = |A|A^{-1}$ (C) $(A + B)^{-1} = B^{-1} + A^{-1}$ (D) $(AB)^{-1} = B^{-1}A^{-1}$ Choose the correct answer from the options given below:

Match List-I with List-II | List-I (Matrix A) | List-II (Determinant of Adjoint of A) | |---|---| | (A) $\begin{bmatrix} 3 & 1 \\ 4 & 2 \end{bmatrix}$ | (I) 9 | | (B) $\begin{bmatrix} 5 & -1 \\ 4 & 2 \end{bmatrix}$ | (II) 8 | | (C) $\begin{bmatrix} 6 & -1 \\ 2 & 1 \end{bmatrix}$ | (III) 14 | | (D) $\begin{bmatrix} 4 & 1 \\ 3 & 3 \end{bmatrix}$ | (IV) 2 | Choose the correct answer from the options given below:

If the events A and B are independent, then which of the following statements are true? (A) P(A'B) = [1-P(A)] P(B) (B) A and B are mutually exclusive (C) P(A) = P(B) (D) P(A'B') = [1-P(A)] [1-P(B)] Choose the correct answer from the options given below: