Algebra PYQ — Page 7

If $|\vec{a}| = 1$, $|\vec{b}| = 2$, $|2\vec{a}+\vec{b}| = 2\sqrt{3}$ then $|\vec{a}-\vec{b}|$ is:

The corner points of the bounded feasible region determined by the system of linear inequalities are $(0, 0)$, $(2, 4)$, $(0, 5)$ and $(4, 0)$. If the maximum value of $z = ax + by$, where $a, b > 0$ occurs at both $(2, 4)$ and $(4, 0)$, then

If the random variable X has the following probability distribution: | X | 0 | 1 | 2 | Otherwise | |---|---|---|---|---| | P(X) | K | 3K | 5K | 0 | then K is equal to

The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0), (5, 0), (6, 5), (6, 8), (4, 10), (0,8)$. Let $z = 3x - 4y$ be the objective function. Then the minimum value of the objective function z occurs at

The mean of the number of heads in a simultaneous toss of three coins is

If A and B are symmetric matrices of same order, then which of the following are correct? (A) AB-BA is a skew-symmetric matrix. (B) AB+BA is a skew-symmetric matrix. (C) $AB^T-BA^T$ is a skew-symmetric matrix. (D) AB+BA is a symmetric matrix. Choose the correct answer from the options given below:

A bag contains 6 red balls, 4 green balls and 10 blue balls. Three balls are drawn with replacement. The probability of getting at least 1 green ball is:

The solution set of the inequation $|2x - 3| ≤ 4$ is

If $\vec{a}$, $\vec{b}$ and $\sqrt{3}\vec{a} - \vec{b}$ are three unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ is:

Let N be set of natural numbers, then the function $f: \mathbb{N} \rightarrow \mathbb{N}$, defined by $f(x) = \begin{cases} \frac{n+1}{2} & \text{, if } n \text{ is odd} \\ \frac{n}{2} & \text{, if } n \text{ is even} \end{cases}$, 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, b, c are positive real numbers, then the least value of $(a+b+c)(ab+bc+ca)$ is:

Which of the following are correct? (A) For a square matrix A, if A³ = I, then A⁻¹ = A². (B) The determinant of only a square matrix can be defined. (C) If A is a square matrix of order 3, then the number of minors of the matrix A is 3. (D) If A and B are two non-singular matrices of the same order, then (AB)⁻¹ = B⁻¹A⁻¹. Choose the correct answer from the options given below:

For two matrices $A = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B^T = \begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}$, A - B equals

Which of the following statements is (are) true? (A) $B^T AB$ is a skew-symmetric matrix if A is a symmetric matrix (B) $B^T AB$ is a symmetric matrix if A is a symmetric matrix (C) $B^T AB$ is a symmetric matrix if A is a skew-symmetric matrix (D) $B^T AB$ is a skew-symmetric matrix if B is a skew-symmetric matrix (E) $B^T AB$ is a symmetric matrix if B is a symmetric matrix Choose the correct answer from the options given below:

If A and B are square matrices of order 3 such that |A| = -1 and |B| = 5, then the value of |3AB| is

If $P\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix}$, then matrix P is equal to:

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ and $|\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$, then the angle between $\vec{a}$ and $\vec{b}$ is

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: 

If $A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}$ be such that $A^{-1} = KA$, then the value of K is:

Which of the following statement is/are correct? (A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij} = a_{ji}$ for all $i, j$ (B) $A = [a_{ij}]_{m \times m}$ is a diagonal matrix if $a_{ij} = 0$ when $i = j$ (C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i, j$ (D) The multiplication of diagonal matrices of same order is commutative Choose the correct answer from the options given below:

The constraints of the given shaded feasible region below of an L.P.P., for non-negative variable constraints $x$ and $y$ are 

A random variable 'X' denotes the number of sixes obtained in three throws of a die. Then, the mean of the distribution is:-

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of same order as A, then the matrix $(2I+A)^3 - 19A - 3I$ is equal to