Prof. Dr. Fazal Rehman

\[ \textbf{Question 1:} \] \[ \text{What is the slope of the line } 2x – 3y = 6? \] \[ \text{(a) } \frac{2}{3}, \quad \text{(b) } -\frac{2}{3}, \quad \text{(c) } \frac{3}{2}, \quad \text{(d) } -\frac{3}{2} \] Answer: B Step by Step Solution \[ \textbf{Solution:} \] \[ \text{Rearrange the equation into slope-intercept form } y = … Read more

Question 1: \[ \text{What is the solution to the equation } 2x + 5 = 15 \text{?} \] \[ \text{(a) } x = 10, \quad \text{(b) } x = 5, \quad \text{(c) } x = -5, \quad \text{(d) } x = 2 \] Answer: B Question 2: \[ \text{Solve for } x: \quad 3x – … Read more

Question 1: \[ \text{Which of the following is an integral domain but not a field?} \] \[ \text{(a) } \mathbb{Z}, \quad \text{(b) } \mathbb{Q}, \quad \text{(c) } \mathbb{R}, \quad \text{(d) } \mathbb{C} \] Answer: A Question 2: \[ \text{Let } R \text{ be a commutative ring with unity. If } R \text{ has no zero … Read more

Question 1: \[ \text{If } a^2 + b^2 = 29 \text{ and } ab = 10, \text{ then find } (a+b)^2. \] \[ \text{(a) } 39, \quad \text{(b) } 49, \quad \text{(c) } 59, \quad \text{(d) } 69 \] Answer: B Step by Step Solution Solution: Using the identity: \[ (a+b)^2 = a^2 + b^2 … Read more

Question 1: \[ \text{If } a^2 – b^2 = 15 \text{ and } a – b = 3, \text{ then } a + b = ? \] \[ \text{(a) } 5, \quad \text{(b) } 8, \quad \text{(c) } 6, \quad \text{(d) } 9 \] Answer: C Step by Step Solution Solution: Using the identity: \[ … Read more

MCQs of  Algebra Let’s begin with some most important MCs of  Algebra. Question 1: \[ \text{After simplifying this equation } \frac{a^{-\frac{1}{3}} \times a^{\frac{1}{3}}}{a^{-\frac{1}{2}}} \text{, the result will be equal to?} \] \[ \text{(a) } a^{\frac{1}{2}}, \quad \text{(b) } a^{-\frac{1}{2}}, \quad \text{(c) } a^{-\frac{7}{18}}, \quad \text{(d) } \text{All of these} \] Answer: (b) Question 2: \[ \text{What … Read more

Question #1 [latex] \[ \text{Given the matrix } A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}, \text{ compute the determinant using cofactor expansion.} \] Question #2 \[ \text{Given the matrix } B = \begin{pmatrix} 2 & 3 & 1 \\ 4 & … Read more

[latex] Question #1: \[ \textbf{Calculate the determinant of the following upper triangular matrix:} \] \[ A = \begin{pmatrix} 4 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 0 & 6 \end{pmatrix} \] Question #2: \[ \textbf{ Calculate the determinant of the following lower triangular matrix:} \] \[ B = \begin{pmatrix} … Read more