CUET Mathematics Applied Mathematics > Algebra PYQs

If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$, then $x =$

The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^2 = 8A + kI$, the value of k is :

Let X & Y be 2 invertible square matrix, then which of the following is true (A) $(AB)^{-1} = A^{-1} B^{-1}$ (B) $(AB)^{-1} = B^{-1} A^{-1}$ (C) $(AB)' = A' B'$ (D) $(AB)' = B' A'$ Choose the answer from the options given below

If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$, If $5Q - 3P + 2R = 0$, then the matrix R is

Solution for the inequality $|3x - 7| \leq 2$ is :

<img src="https://balti.afterboards.in/p9DwD9JrEuGMwjM" width="300px"/>Which of the following are true for the given graph. (A) Break even point is at x = 10 (B) Break even point is at x = 8 (C) Break even point is at x = 6 (D) Fixed cost is 20 (E) Fixed cost is 0 Choose the correct answer from the options :

If $\begin{bmatrix} 2x & -7 \\ 5y & 8 \end{bmatrix} = \begin{bmatrix} 6 & -7 \\ -5 & 3x + y \end{bmatrix}$, then value of $5x - 3y$ is :

The least positive integer X satisfying $28 \equiv x (\mod 6)$ is :

If $A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix}$ and $B = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix}$, then AB is equals to :

If a matrix A is both symmetric and skew symmetric then :

the least non-negative remainder when $3^{17}$ is divided by 7 is :

If $\begin{bmatrix} 5x + 8 & 7 \\ y + 3 & 10x + 12 \end{bmatrix} = \begin{bmatrix} 2 & 3y + 1 \\ 5 & 0 \end{bmatrix}$, then the value of $5x + 3y$ is equal to :

If A and B are events such that $P(A/B) = P(B/A)$, then :

A die is thrown. If A is the event 'the number appearing is a multiple of 3 and B is the event 'the number appearing is even', then A and B are

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

If $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$, then x is equal to :

A matrix has 24 elements , which of the following cannot be the possible order of the matrix

A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?

Evaluate $3^{15} \mod(7)$

If $A = \begin{bmatrix} -2 & 1 \\ 3 & 2 \end{bmatrix}$ and $B' = \begin{bmatrix} -1 & 1 \\ 0 & 2 \end{bmatrix}$, then $(A+2B)' =$

Matrix $A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is skew - symmetric, then the values of a, b c are :

Let $P = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, $R = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, then the matrix S such that QS - RP = 0 will be :

If a square matrix B satisfies $B^2 = I - B$ and $B^n = 5I - 8B$, then the value of n is :

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**. | | List - I (Matrix) | | List - II (Type) | |---|---|---|---| | (A) | $\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$ | (I) | Lower Triangular Matrix | | (B) | $\begin{bmatrix} 1 & 5 & 0 & -1 \end{bmatrix}$ | (II) | Row Matrix | | (C) | $\begin{bmatrix} 3 & 0 & 0 \\ 1 & -1 & 0 \\ 2 & 5 & 4 \end{bmatrix}$ | (III) | Diagonal Matrix | | (D) | $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ | (IV) | Scalar Matrix | 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 | LIST I | LIST II | |---|---| | A. The solution of $3x + 7 > 12$ is | I. $[-1, \infty)$ | | B. The solution of $\frac{3x+5}{2} \geq 1$ is | II. $\left[\frac{17}{8}, \infty\right)$ | | C. The solution of $2x + 5 < 7x + 9$ is | III. $\left(\frac{5}{3}, \infty\right)$ | | D. The solution of $6x - 5 \geq -2x + 12$ is | IV. $\left(-\frac{4}{5}, \infty\right)$ | 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 | LIST I | LIST II | |---|---| | A. A matrix that has unequal number of rows and columns is called | I. Non-singular matrix | | B. A matrix whose determinant is non-zero is called | II. Null matrix | | C. A diagonal matrix whose diagonal elements are equal is called | III. Rectangular matrix | | D. A matrix that is both symmetric and skew-symmetric is | IV. Scalar matrix | Choose the correct answer from the options given below:

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