CMTR Examination, 2019
1. The paper will contain 50 questions including five questions ( MCQ ) from each of the following branches.
2. All questions are compulsory. Each question carries 4 marks for the correct answer and 1 mark will be deducted for each wrong answer.
3. The examination duration will be of 2 hours.
- Differential Calculus : Limit, Continuty, Differentiability, Roll’s theorem, Lagrange’s and Cauchy mean value theorems, Taylor’s theorem. Asymptotes, Curvature, Concavity & Convexity, singular points, Maxima & Minima of functions of One and Two variables, Partial Differentiation, Envelope and Evolutes
- Integral Calculus : Quadrature, Rectification, Double and Triple Integrals and their applications. Surface and volume of Solids of Revolution, Beta and Gamma Functions.
- Vector Calculus : Vector differentiation, Differential Operators ( Gradient, Divergence, Curl ) Application of Gauss, Green & Stoke’s theorems.
- Three dimensional Coordinate Geometry : Sphere , Cone , Cylinder and Ellipsoid.
- Ordinary Differential Equations : Differential equations of First Order and First Degree, Linear Differential Equations , Exact DE, Homogeneous DE, Orthogonal Trajectory, Second order DE , method of variation of parameters.
- Partial Differential Equations : Linear PDE of First Order, The Cauchy Problem, Standard forms of Non Linear PDE, Charpit’s Method, Linear PDE with constant coefficients, Second order PDE with constant coefficients.
- Algebra : Groups and Subgroups, Cyclic groups, Cosets, Permutation Groups, Cayley’s Theorem, Lagrange’s theorem,Group morphism, Isomorphism, Normal subgroups & Quotient groups.
- Complex Analysis : Complex numbers as ordered pairs, Complex plane, Complex valued functions, Limits, Continuity and Differentiablity, Analytical functions, Cauchy Riemann equations, Harmonic Functions, Conformal Mapping, Complex integration, Applications of Cauchy Integral Theorem.
- Numerical Analysis : Basic operators, their inter relationships, Interpolation, Newton’s backward and forward differences for equal intervals, Numerical Differentiation and Integration, Simpson’s rule.
- Optimization Techniques : LPP, Formulation and its graphical solution feasible solution, Basic FS, OS, Convex sets, Hyperplanes.