Engineering Mathematics MCQ (Multiple Choice Questions)

Engineering Mathematics MCQ - Multiple Choice Questions and Answers

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
  2. Partial Differentiation
  3. Maxima and Minima
  4. Curve Tracing
  5. Integral Calculus
  6. Multiple Integrals
  7. Ordinary Differential Equations – First Order & First Degree
  8. Linear Differential Equations – Second and Higher Order
  9. Series Solutions
  10. Special Functions – Gamma, Beta, Bessel and Legendre
  11. Laplace Transform
  12. Matrices
  13. Eigen Values and Eigen Vectors
  14. Vector Differential Calculus
  15. Vector Integral Calculus
  16. Fourier Series
  17. Partial Differential Equations
  18. Applications of Partial Differential Equations
  19. Fourier Integral, Fourier Transforms and Integral Transforms
  20. Complex Numbers
  21. Complex Function Theory
  22. Complex Integration
  23. Theory of Residues
  24. Conformal Mapping
  25. Probability and Statistics (Mathematics III / M3)
  26. Numerical Methods / Numerical Analysis (Mathematics IV / M4)

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

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  • 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.

  • Method of Undetermined Coefficients
  • Harmonic Motion and Mass – Spring System
  • Linear Independence and Dependence
  • Second Order with Variable Coefficients
  • Second Order with Constant Coefficients
  • Higher Order Linear Homogeneous Differential Equations
  • Non-homogeneous Equations
  • Differential Equations with Variable Coefficients: Reducible to Equations with Constant Coefficients
  • Method of Variations of Parameters
  • System of Simultaneous Linear D.E with Constant Coefficients
  • 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
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    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
  • Integration of a Vector Function of a Scalar Argument
  • Line Integrals
  • Green’s Theorem in a Plane
  • Stokes and Gauss Divergence Theorem
  • 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
  • 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
  • Derivation of One-dimensional Wave 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
  • Complex Function
  • Analyticity
  • Cauchy-Riemann (C-R) Equations: In Cartesian Coordinates
  • Harmonic and Conjugate Harmonic Functions
  • 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.

  • Line Integral in Complex Plane
  • Cauchy’s Integral Theorem
  • Cauchy’s Integral Formula
  • Derivation of Analytic Functions
  • Complex Sequence, Series, and Power Series
  • Taylor’s Series
  • Laurent Series
  • Zeros and Poles
  • 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 (or Transformation or Operator)
  • Conformal Mapping
  • Conformal Mapping by Elementary Functions
  • Transformation w = zn
  • Mapping w = z2
  • Transformation w = ez
  • Transformation w = sin z
  • Joukvowski’s (Zhukovsky’s) Transformation
  • Bilinear 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!

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