\[ \textbf{Difficult MCQs on Measure Theory and Integration with Answers} \] \[ \textbf{Q1: Which of the following is a property of a measure on a measurable space?} \] \[ \text{(A) } \text{It is a set function that is countably additive.} \] \[ \text{(B) } \text{It is a function that maps sets to real numbers.} \] … 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
\[ \textbf{Difficult MCQs on Fluid Dynamics with Answers} \] \[ \textbf{Q1: The Navier-Stokes equations are derived from which fundamental principle?} \] \[ \text{(A) } Conservation of Mass \quad \text{(B) } Conservation of Momentum \quad \text{(C) } Conservation of Energy \quad \text{(D) } Bernoulli’s Principle \] \[ \textbf{Answer: (B) Conservation of Momentum} \] \[ \textbf{Q2: In … Read more
\[ \textbf{Partial Differential Equations MCQs with Answers} \] \[ \textbf{Q1: Which of the following is the canonical form of a second-order linear PDE in two variables?} \] \[ \text{(A) } a \frac{\partial^2 u}{\partial x^2} + b \frac{\partial^2 u}{\partial x \partial y} + c \frac{\partial^2 u}{\partial y^2} + d \frac{\partial u}{\partial x} + e \frac{\partial u}{\partial … Read more
\[ \textbf{MCQs on Probability Theory with Answers} \] \[ \textbf{Q1: The probability of an impossible event is:} \] \[ \text{(A) } 0 \quad \text{(B) } 1 \quad \text{(C) } Between 0 and 1 \quad \text{(D) } None of these \] \[ \textbf{Answer: (A) } 0 \] \[ \textbf{Q2: The sum of probabilities of all possible … Read more
\[ \textbf{MCQs on Vector and Tensor Analysis with Answers} \] \[ \textbf{Q1: The divergence of the vector field } \vec{F} = \nabla \cdot \vec{F} \text{ is:} \] \[ \text{(A) } \text{A scalar quantity} \quad \text{(B) } \text{A vector quantity} \quad \text{(C) } \text{A tensor quantity} \quad \text{(D) } \text{None of these} \] \[ \textbf{Answer: (A) … Read more
\[ \textbf{MCQs on Topology with Answers} \] \[ \textbf{Q1: Which of the following is a topological space?} \] \[ \text{(A) } \mathbb{R}^2 \quad \text{(B) } \mathbb{N} \quad \text{(C) } \mathbb{Z} \quad \text{(D) } \mathbb{Q} \] \[ \textbf{Answer: (A) } \mathbb{R}^2 \] \[ \textbf{Q2: A subset } A \text{ of a topological space } X \text{ … Read more
\[ \textbf{MCQs on Complex Analysis with Answers} \] \[ \textbf{Q1: Which of the following is a complex number?} \] \[ \text{(A) } 5 \quad \text{(B) } 2 + 3i \quad \text{(C) } \sqrt{2} \quad \text{(D) } 0 \] \[ \textbf{Answer: (B) } 2 + 3i \] \[ \textbf{Q2: The complex conjugate of } z = … Read more