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If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 2 & 3 \end{bmatrix}$

then $(3A + 2B)'$ is :

The number of all possible matrices of order 3 $\times$ 3 with each entry 2 or 3 is.

For a 3 $\times$ 3 matrix A = [a$_{ij}$], whose element a$_{ij}$ is given by $a_{ij} = \sqrt{i^2 + 3j}$ then what is element a$_{31}$?

The set of values of $x$ satisfying $26 \equiv 5 \pmod{x}$ is _______.

The solution set of the inequation $\frac{7+5x}{4} \geq \frac{x}{3} - 10$, $x \in \mathbb{R}$ is :

The digit in the unit's place of $13^{37}$ is :

If A is square matrix of order 3 with $|A| = 3$, then $|4 \text{ adj} A|$ is equal to :

If the matrix $\begin{bmatrix} 0 & 2 & 5x \\ -2 & 0 & 6 \\ 10 & -6 & y \end{bmatrix}$ is skew-symmetric matrix, then the value of $(y - 4x)$ is :

Match List - I with List - II.

Choose the correct answer from the options given below :

If $K \equiv 5 \pmod{11}$, then all the possible non-negative values of K are :

A point $P(3a, -2b)$ lies in region $4x + 7y \leq (-3)$ which of the following options is true ?

$5^{100} (\mod 9) =$

The minimum value of $ax + by$, where $xy = c^2$ and a, b, c are positive, is :

Let A be a square matrix. Then,

(A) $A + A^T$ is a symmetric matrix

(B) $A - A^T$ is a skew-symmetric matrix

(C) $AA^T$ is a skew-symmetric matrix

(D) $A^T A$ is a symmetric matrix

Choose the correct answer from the options given below :

The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :

If $-\frac{1}{3x - 5} \leq 0$, then :

If the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^T A = I_3$, then $x^2 + y^2 + z^2$ is :

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

Match List I with List II

Choose the correct answer from the options given below:

If $\begin{bmatrix} 2x + 3 & y + 1 \\ 2x - z & 3y \end{bmatrix} = \begin{bmatrix} 7 & -2 \\ -4 & -9 \end{bmatrix}$, then matrix $\begin{bmatrix} 3z + 1 & 4 \\ -2 & 4 \end{bmatrix}$ is equal to:

The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

Match List I with List II

Choose the correct answer from the options given below:

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is: