Engineering Mathematics MCQ (Multiple Choice Questions)

Our 1000+ Engineering Mathematics MCQs (Multiple Choice Questions and Answers) focuses on all chapters of Engineering Mathematics covering 100+ topics. You should practice these MCQs for 1 hour daily for 2-3 months. This way of systematic learning will prepare you easily for Engineering Mathematics exams, contests, online tests, quizzes, MCQ-tests, viva-voce, interviews, and certifications.

Engineering Mathematics Multiple Choice Questions Highlights

- 1000+ Multiple Choice Questions & Answers (MCQs) in Engineering Mathematics with a detailed explanation of every question.
- These MCQs cover theoretical concepts, true-false(T/F) statements, fill-in-the-blanks and match the following style statements.
- These MCQs also cover numericals as well as diagram oriented MCQs.
- These MCQs are organized chapterwise and each Chapter is futher organized topicwise.
- Every MCQ set focuses on a specific topic of a given Chapter in Engineering Mathematics Subject.

Who should Practice Engineering Mathematics MCQs?

– Students who are preparing for college tests and exams such as mid-term tests and semester tests on Engineering Mathematics.
- Students who are preparing for Online/Offline Tests/Contests in Engineering Mathematics.
– Students who wish to sharpen their knowledge of Engineering Mathematics Subject.
- Anyone preparing for Aptitude test in Engineering Mathematics.
- Anyone preparing for interviews (campus/off-campus interviews, walk-in interview and company interviews).
- Anyone preparing for entrance examinations and other competitive examinations.
- All - Experienced, Freshers and College / School Students.

Engineering Mathematics Chapters

Here's the list of chapters on the "Engineering Mathematics" subject covering 100+ topics. You can practice the MCQs chapter by chapter starting from the 1st chapter or you can jump to any chapter of your choice.

1. Differential Calculus

The section contains multiple choice questions and answers on leibniz rule, nth derivatives, rolles and lagrange mean value theorem, taylor mclaurin series, indeterminate forms, curvature, evolutes, envelopes, polar curves, arc length derivation, area derivatives, angle between radius vector and tangent, cauchy’s and generalized mean value theorem

The nth Derivative of Some Elementary Functions – 1 The nth Derivative of Some Elementary Functions – 2 Leibniz Rule – 1 Leibniz Rule – 2 Leibniz Rule – 3 Rolle’s Theorem – 1 Rolle’s Theorem – 2 Lagrange’s Mean Value Theorem – 1 Lagrange’s Mean Value Theorem – 2 Cauchy’s Mean Value Theorem Generalized Mean Value Theorem Taylor Mclaurin Series – 1 Taylor Mclaurin Series – 2

Taylor Mclaurin Series – 3 Taylor Mclaurin Series – 4 Indeterminate Forms – 1 Indeterminate Forms – 2 Indeterminate Forms – 3 Indeterminate Forms – 4 Polar Curves Derivative of Arc Length Derivatives of Area Curvature Evolutes Envelopes Angle Between the Radius Vector and the Tangent

2. Partial Differentiation

The section contains questions and answers on limits and derivatives of variables, implicit and partial differentiation, eulers theorem, jacobians, quadrature, integral sign differentiation, total derivative, implicit partial differentiation and functional dependence.

Limits and Derivatives of Several Variables – 1 Limits and Derivatives of Several Variables – 2 Limits and Derivatives of Several Variables – 3 Limits and Derivatives of Several Variables – 4 Variable Treated as Constant Total Derivative Implicit Differentiation Partial Differentiation – 1

Partial Differentiation – 2 Implicit Partial Differentiation Euler’s Theorem – 1 Euler’s Theorem – 2 Errors and Approximations Jacobians Functional Dependence Differentiation Under Integral Sign

3. Maxima and Minima

The section contains MCQs on maxima and minima of variables, taylors theorem two variables, lagrange method to find maxima or minima.

Taylors Theorem Two Variables Maxima and Minima of Two Variables – 1 Maxima and Minima of Two Variables – 2

Maxima and Minima of Two Variables – 3 Lagrange Method of Multiplier to find Maxima or Minima

4. Curve Tracing

The section contains multiple choice questions and answers on cartesian form curves and standard curves, parametric curves, standard polar and parametric curves.

Curves in Cartesian Form Standard Curves in Cartesian Form Standard Polar Curves

Parametric Curves Standard Parametric Curves

5. Integral Calculus

The section contains questions and answers on integral reduction formula, improper integrals, quadrature, rectification, surface area and volume of solid, polar and parametric forms rectification.

Integral Reduction Formula Quadrature Rectification Rectification in Polar and Parametric Forms

Volume of Solid of Revolution Improper Integrals – 1 Improper Integrals – 2 Surface Area of Solid of Revolution

6. Multiple Integrals

The section contains MCQs on double integrals and its applications, variables changing in double and triple integrals, dirichlet’s integral, triple integral and its applications.

Double Integrals Application of Double Integrals Change of Order of Integration:Double Integral Change of Variables In a Double Integral

Triple Integral Change of Variables In a Triple Integral Applications of Triple Integral Dirichlet’s Integral

7. Ordinary Differential Equations – First Order & First Degree

The section contains multiple choice questions and answers on first order first degree differential equations, homogeneous form, seperable and homogeneous equations, bernoulli equations, clairauts and lagrange equations, orthogonal trajectories, natural growth and decay laws, newtons law of cooling and escape velocity, simple electrical networks solution, mathematical modeling basics, geometrical applications, first order linear and nonlinear differential equations.

Basic Definitions First Order First Degree Differential Equations Seperable and Homogeneous Equations Reducible to Homogeneous Form First Order Linear Differential Equations Bernoulli Equations First Order Nonlinear Differential Equations Clairauts and Lagrange Equations

Formation of Ordinary Differential Equations by Elimination of Arbitrary Constants Geometrical Applications Orthogonal Trajectories Law of Natural Growth and Decay Newtons Law of Cooling and Escape Velocity Simple Electrical Networks Solution Introduction to Mathematical Modeling Exact Differential Equations and Reducible to Exact

8. Linear Differential Equations – Second and Higher Order

The section contains questions and answers on undetermined coefficients method, harmonic motion and mass, linear independence and dependence, second order with variable and constant coefficients, non-homogeneous equations, parameters variation methods, order reduction method, differential equations with variable coefficients, rlc circuit and simple pendulum problems.

Linear Independence and Dependence Method of Undetermined Coefficients Harmonic Motion and Mass – Spring System System of Simultaneous Linear D.E with Constant Coefficients Second Order with Variable Coefficients Second Order with Constant Coefficients Higher Order Linear Homogeneous Differential Equations

Differential Equations with Variable Coefficients: Reducible to Equations with Constant Coefficients Method of Variations of Parameters Non-homogeneous Equations Method of Reduction of Order Higher Order Linear Equations with Variable Coefficients RLC Circuit and Simple Pendulum Problems

9. Series Solutions

The section contains MCQs on singularities classification, power series solution to differential equations, liouville problems, functions orthogonality and gram-schmidt orthogonalization process.

Classification of Singularities Power Series Solution to Differential Equations Frobenius and Strum – Liouville Problems

Orthogonality of Functions Gram-Schmidt Orthogonalization Process

10. Special Functions – Gamma, Beta, Bessel and Legendre

The section contains multiple choice questions and answers on special functions like gamma, beta, bessel, chebyshev and legendre, bessel’s differential equations, fourier legendre and bessel series.

Special Functions – 1 (Gamma) Special Functions – 2 (Beta) Special Functions – 4 (Legendre) Special Functions – 3 (Bessel)

Special Functions – 5 (Chebyshev) Differential Equations Reducible to Bessel’s Equation Fourier Legendre and Bessel Series

11. Laplace Transform

The section contains questions and answers on laplace transform functions and properties, laplace transform of elementary functions, newtons law and laplace convolution, functions orthogonality, inverse laplace transform, laplace transform applications and tables.

Existence & Laplace Transform of Elementary Functions-1 Existence & Laplace Transform of Elementary Functions-2 Laplace Transform by Properties – 1 Laplace Transform by Properties – 2 Laplace Transform by Properties – 3 Laplace Transform of Periodic Function General Properties of Inverse Laplace Transform Convolution

Solution of DE With Constant Coefficients Using the Laplace Transform Table of General Properties of Laplace Transform Orthogonality of Functions Inverse Laplace Transform Use of Partial Functions of Find Inverse L.T. Application of Laplace Transform to System of Simultaneous Differential Equations Table of some Laplace Transforms

12. Matrices

The section contains MCQs on matrices types and properties, finding inverse and rank of a matrix, matrix rank in row echelon, paq and normal form, system equations and their consistencies, equations using gauss elimination method, curve fitting, solving equations by crout’s method, system of homogeneous and linear non-homogeneous equations, lu-decompositions, tridiagonal systems solution, derogatory and non-derogatory matrices.

Types and Properties of Matrices Finding Inverse and Rank of a Matrix Rank of Matrix in Row Echelon Form Rank of Matrix in PAQ and Normal Form System of Equations and their Consistencies System of Equation using Gauss Elimination Method Curve Fitting

Solving Equations by Crout’s Method Derogatory and Non-Derogatory Matrices System of Linear Non-homogeneous Equations System of Homogeneous Equations LU-decompositions LU-decomposition from Gaussian Elimination Solution to Tridiagonal Systems

13. Eigen Values and Eigen Vectors

The section contains multiple choice questions and answers on eigen values and vectors of a matrix, cayley hamilton theorem, elementary functions linear transformation, eigenvalues and eigenvectors properties, real matrices like symmetric, skew-symmetric and orthogonal quadratic form, canonical form, sylvester’s law of inertia, complex matrices like hermitian, skew-hermitian and unitary matrices.

Eigenvalues and Vectors of a Matrix Cayley Hamilton Theorem Diagonalization Powers of a Matrix Real Matrices: Symmetric, Skew-symmetric, Orthogonal Quadratic Form Canonical Form: Or Sum of Squares Form Transformation (Reduction) of Quadratic Form to Canonical Form

Linear Transformation of Elementary Functions Using Properties of Eigenvalues and Eigenvectors Sylvester’s Law of Inertia and Canonical Forms of Matrices Complex Matrices: Hermitian, Skew-Hermitian, Unitary Matrices Sylvester’s Law of Inertia

14. Vector Differential Calculus

The section contains questions and answers on directional derivative, divergence and curl of vector field, function and conservative field, divergence and curl properties, coordinates conversions, vector differentiation and second-order differential operator.

Directional Derivative Gradient of a Function and Conservative Field Divergence and Curl of a Vector Field Using Properties of Divergence and Curl

Conversion From Cartesian, Cylindrical and Spherical Coordinates Vector Differentiation Second-order Differential Operator

15. Vector Integral Calculus

The section contains MCQs on line, surface and volume integrals, vector function integration, plane green’s theorem, stokes and gauss divergence theorem.

Surface Integrals Volume Integrals Stokes and Gauss Divergence Theorem

Integration of a Vector Function of a Scalar Argument Line Integrals Green’s Theorem in a Plane

16. Fourier Series

The section contains multiple choice questions and answers on fourier series expansions, fourier half range series, buler’s formulae, fourier series for even and odd functions and practical harmonic analysis.

Fourier Series Expansions Fourier Half Range Series Buler’s (Fourier-Euler’s) Formulae

Fourier Series for Even and Odd Functions Fourier Series for Functions Having Period 2L Practical Harmonic Analysis

17. Partial Differential Equations

The section contains questions and answers on first order pde, partial differential equations basics, first order linear and non-linear pde, charpit’s method, homogeneous and non-homogeneous linear pde with constant coefficient, cauchy type differential equation and second order pde solution.

First Order PDE First Order Linear PDE First Order Non-Linear PDE Homogeneous Linear PDE with Constant Coefficient Non-Homogeneous Linear PDE with Constant Coefficient

Solution of Second Order P.D.E. Charpit’s Method Partial Differential Equations Introduction Cauchy Type Differential Equation Non-Linear PDE of Second Order: Monge’s Method

18. Applications of Partial Differential Equations

The section contains MCQs on solution of 1d heat equation and pde solution by variable separation method, variables seperation method, derivation of one-dimensional heat and wave equation, derivation of two-dimensional heat and wave equation, circular membrane vibration and transmission line equation.

Method of Separation of Variables Solution of 1D Heat Equation Derivation of One-dimensional Wave Equation Solution of PDE by Variable Separation Method Derivation and Solution of Two-dimensional Heat Equation Derivation and Solution of Two-dimensional Wave Equation Classification of Partial Differential Equations of Second Order

Derivation of One-dimensional Heat Equation Solution of One-dimensional Wave Equation by Separation of Variables Laplace’s Equation or Potential Equation or Two-dimensional Steady-state Heat Flow Laplace Equation in Polar Coordinates Vibration of Circular Membrane Transmission Line Equation

19. Fourier Integral, Fourier Transforms and Integral Transforms

The section contains multiple choice questions and answers on fourier transform and convolution, linear difference equations, z-transforms, fourier integral theorem, parseval’s identity, finite fourier sine and cosine transforms.

Fourier Transform and Convolution Linear Difference Equations and Z – Transforms Fourier Integral Theorem

Finite Fourier Sine and Cosine Transforms Parseval’s Identity

20. Complex Numbers

The section contains questions and answers on deMoivre’s theorem, trigonometric functions expansion, complex conjugates, complex plane regions, complex numbers logarithm, powers and roots.

DeMoivre’s Theorem Expansion of Trigonometric Functions Logarithm of Complex Numbers Complex Conjugates

Roots of Complex Numbers Regions in the Complex Plane Powers and Roots

21. Complex Function Theory

The section contains MCQs on complex function, complex function continuity, complex variable functions, differentiability and analyticity, cauchy-riemann equations, harmonic and conjugate harmonic functions.

Functions of a Complex Variable Continuity Differentiability Analyticity

Cauchy-Riemann (C-R) Equations: In Cartesian Coordinates Harmonic and Conjugate Harmonic Functions Complex Function Cauchy-Riemann Equations: In Polar Coordinates

22. Complex Integration

The section contains multiple choice questions and answers on cauchy’s integral theorem and formula, analytic functions derivation, complex plane line integral, complex sequence, series, and power series, zeros and poles, taylor’s and laurent series.

Cauchy’s Integral Theorem Cauchy’s Integral Formula Taylor’s Series Laurent Series

Zeros and Poles Line Integral in Complex Plane Derivation of Analytic Functions Complex Sequence, Series, and Power Series

23. Theory of Residues

The section contains questions and answers on residue, residue theorem, real integrals evaluation, argument principle, algebra fundamental theorem, rouche’s and liouville theorems.

Residue Residue Theorem Evaluation of Real Integrals Argument Principle

Rouche’s Theorem Fundamental Theorem of Algebra Liouville Theorem

24. Conformal Mapping

The section contains MCQs on conformal mapping, elementary functions conformal mapping, transformations, joukvowski’s transformation, bilinear and schwarz-christoffel transformation.

Mapping w = z2 Transformation w = ez Transformation w = sin z Bilinear Transformation Mapping (or Transformation or Operator)

Conformal Mapping Conformal Mapping by Elementary Functions Transformation w = zn Joukvowski’s (Zhukovsky’s) Transformation Schwarz-Christoffel Transformation

25. Probability and Statistics (Mathematics III / M3)

The section contains multiple choice questions and answers on probability and statistics.

Probability and Statistics Questions and Answers

26. Numerical Methods / Numerical Analysis (Mathematics IV / M4)

The section contains questions and answers on numerical analysis and methods.

Numerical Methods Questions and Answers

If you would like to learn "Engineering Mathematics" thoroughly, you should attempt to work on the complete set of 1000+ MCQs - multiple choice questions and answers mentioned above. It will immensely help anyone trying to crack an exam or an interview.

Wish you the best in your endeavor to learn and master Engineering Mathematics!