Exercise: [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Diagonal Matrix?} \\ \hline \begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix} & ? … Read more
Exercise [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Square Matrix?} \\ \hline \begin{pmatrix} 2 & 4 & 6 \\ 1 & 3 & 5 \\ 7 & 8 & 9 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 & 2 & 3 \\ 4 … Read more
<h2>Exercise</h2> Suggest type of matrix for each of the followings; [latex] \[ \begin{array}{|c|c|} \hline \textbf{Matrix} & \textbf{Type (Row/Column)} \\ \hline \begin{pmatrix} 2 & 4 & 6 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 1 \\ 3 \\ 5 \end{pmatrix} & ? \\ \hline \begin{pmatrix} -1 & 0 & 2 \end{pmatrix} & ? \\ \hline \begin{pmatrix} 7 … Read more
\[ \textbf{Difficult MCQs on Group Theory and Applications with Answers} \] \[ \textbf{Q1: Which of the following is a group under matrix multiplication?} \] \[ \text{(A) The set of all \(2 \times 2\) invertible matrices} \] \[ \text{(B) The set of all \(2 \times 2\) matrices} \] \[ \text{(C) The set of all \(2 \times … Read more
\[ \textbf{Difficult MCQs on Mathematical Ecology with Answers} \] \[ \textbf{Q1: In the Lotka-Volterra predator-prey model, which of the following equations represents the prey population growth?} \] \[ \text{(A) } \frac{dN}{dt} = rN – \alpha NP \] \[ \text{(B) } \frac{dP}{dt} = \beta NP – \gamma P \] \[ \text{(C) } \frac{dN}{dt} = rN \] … Read more
\[ \textbf{Difficult MCQs on Python for Scientific Computing with Answers} \] \[ \textbf{Q1: Which of the following is the correct method to generate a random number between 0 and 1 using NumPy?} \] \[ \text{(A) } \text{random() } \text{from random module} \] \[ \text{(B) } \text{np.random.random()} \] \[ \text{(C) } \text{np.random.uniform(0, 1)} \] \[ \text{(D) … Read more
\[ \textbf{Difficult MCQs on Measure Theory and Integration with Answers} \] \[ \textbf{Q1: Which of the following is a property of a measure on a measurable space?} \] \[ \text{(A) } \text{It is a set function that is countably additive.} \] \[ \text{(B) } \text{It is a function that maps sets to real numbers.} \] … Read more
\[ \textbf{Difficult MCQs on Functional Analysis with Answers} \] \[ \textbf{Q1: What is the definition of a Banach space?} \] \[ \text{(A) } \text{A vector space equipped with a norm where every Cauchy sequence converges.} \] \[ \text{(B) } \text{A vector space equipped with a norm where every sequence is bounded.} \] \[ \text{(C) } … Read more
\[ \textbf{Difficult MCQs on Actuarial Mathematics with Answers} \] \[ \textbf{Q1: What is the actuarial present value (APV) of a life insurance policy?} \] \[ \text{(A) } \text{The present value of future premiums} \] \[ \text{(B) } \text{The present value of future benefits} \] \[ \text{(C) } \text{The present value of the future cash flows, … Read more
\[ \textbf{Difficult MCQs on Engineering Mathematics with Answers} \] \[ \textbf{Q1: The solution to the differential equation } y” + 4y’ + 4y = 0 \text{ is:} \] \[ \text{(A) } y = (C_1 + C_2 e^{-4x}) \] \[ \text{(B) } y = C_1 e^{-2x} + C_2 e^{-4x} \] \[ \text{(C) } y = C_1 … Read more
\[ \textbf{Mathematical Physics – MCQs with Answers} \] \[ \textbf{Q1: The Fourier transform of the Dirac delta function, \(\delta(x)\), is:} \] \[ \text{(A) } 1 \quad \text{(B) } e^{ikx} \quad \text{(C) } \delta(k) \quad \text{(D) } \frac{1}{2\pi} \] \[ \textbf{Answer: (A) } 1 \] \[ \textbf{Q2: The Wronskian of two solutions \(y_1(x)\) and \(y_2(x)\) of … Read more
\[ \textbf{Difficult MCQs on Dynamical Systems with Answers (Mathematics)} \] \[ \textbf{Q1: The eigenvalues of the Jacobian matrix at a fixed point determine:} \] \[ \text{(A) } \text{The stability and nature of the fixed point} \] \[ \text{(B) } \text{The system’s energy dissipation} \] \[ \text{(C) } \text{The system’s time period} \] \[ \text{(D) } … Read more