CBCS PATTERN SYLLABUS
Mat/ Sem VI/ C 13- Mechanics II
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Instruction: -
Ten questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions candidates will be required to answer 6 questions selecting at least one from each group. Each question will be of 10 marks.
GROUP - A
Condition of equilibrium of forces in three dimension. 1 Question Central axis, Wrench, Pitch, Null lines. 1 Question
Principle of virtual work and its application in two dimensional cases. 1 Question
Common Catenary 1 Question Stable equilibrium, energy test of stability (problems involving one variable only). Motion of a particle under a central force, differential equations of central orbit in both polar and pedal co-ordinates. 1 Question
GROUP - B
Newton’s law of gravitation, planetary orbits, Keplar’s laws of motion. 1 Question
Motion of a projectile under gravity in a non-resisting medium. 1 Question
Motion of mass centre and motion relative to mass centre, D’ Alembert’s principle. 1 Question
Two dimensional motion of a rigid body, compound pendulum. 1 Question
Books Recommended :
1. Statics – S L Loney.
2. Statics – Goyal & Gupta
3. Dynamics – S L Loney.
4. Dynamics – R K Gupta & D C Agarwal.
CBCS PATTERN SYLLABUS
Mat/ Sem VI/ C 14 – Numerical Analysis
Instruction: -
Ten questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions candidates will be required to answer 6 questions selecting at least one from each group. Each question will be of 10 marks.
GROUP - A
Solution of algebraic and transcendental equations:
Bisection method, Regula-Falsi method, Newton-Raphson method. 1 Question
Solution of simultaneous equations:
Gauss’s elimination method, Matrix inversion by triangularization method. 1 Question
Calculus of finite difference:
The operators ∆ ∇, ,E , factorial notation, their properties and inter-relation between them, Fundamental theorem of difference calculus, divided differences. 2 Questions
GROUP - A
Interpolation:
Newton’s forward and backward difference interpolation formula, Lagrange’s interpolation formula, central difference interpolation, Gauss’s forward, backward and central difference interpolation formula. 2 Questions
Numerical differentiation:
Derivative using forward, backward and central difference interpolation formulae. 1 Question
Numerical integration:
General quadrature formula, Simpson’s one-third and three - eighth rule, Weddle’s rule, Newton-Cote’s method. 1 Question
Solution of ordinary differential equations: Picard’s method of successive approximations, 1 Question
NB : USE OF SCIENTIFIC CALCULATOR ALLOWED.
Books Recommended:
1. Numerical Analysis – J B Scarborough.
2. Numerical Analysis – G S Mallik
3. Numerical Analysis – G Shankar Rao, New Age Int. Publishers.
4. Numerical Methods – B S Grewal.
CBCS PATTERN SYLLABUS
Mat / Sem VI /DSE 3 - LINEAR PROGRAMMING
Instruction for Generic Elective: -
Eleven Questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions will be required to answer 6 questions selecting at least one from each group. Each question will be of 10 marks.
GROUP - A
Convex sets and their properties, Introduction to linear programming problem, solution by graphical method, simplex method, optimality and unboundednes, artificial variables, two‐phase method, Big‐M method. 4 Questions
Duality, formulation of the dual problem, primal‐dual relationships, economic interpretation of the dual. 1 Question
GROUP - B
Transportation problem and its mathematical formulation, northwest‐corner method, least cost method and Vogel approximation method for determination of starting basic solution, algorithm for solving transportation problem. 2 Questions
Assignment problem and its mathematical formulation, Hungarian method for solving assignment problem. 2 Questions
Books Recommended:
1. Mokhtar S. Bazaraa, John J. Jarvis and Hanif D. Sherali, Linear Programming and Network Flows, 2nd Ed., John Wiley and Sons, India, 2004.
2. F.S. Hillier and G.J. Lieberman, Introduction to Operations Research, 9th Ed., Tata McGraw Hill, Singapore, 2009.
3. Hamdy A. Taha, Operations Research, An Introduction, 8th Ed., Prentice‐Hall India, 2006.
4. G. Hadley, Linear Programming, Narosa Publishing House, New Delhi, 2002.
5. Operations Research – S D Sharma.
6. Linear Programming Problems – R K Gupta.
CBCS PATTERN SYLLABUS
Mat/ Sem VI/ DSE 4 – Fluid Mechanics
Instruction for Generic Elective: -
Eleven Questions will be set. Candidates will be required to answer Seven Questions.
Question no. 1 will be Compulsory consisting of 10 short answer type covering entire syllabus uniformly. Each question will be of 2 marks. Out of remaining 9 questions will be required to answer 6 questions selecting at least one from each group. Each question will be of 10 marks.
GROUP - A
Nature and properties of fluid pressure, pressure of heavy liquids. Equilibrium of fluids under given system of forces. Centre of pressure. Thrust on plane and curved surfaces. 5 Questions
GROUP - B
Fluid Motion:
Lagrangian and Eulerian methods. Equation of continuity in different forms. Euler,s equation of motion for perfect fluid. Bernoulli’s theorem. 4 Questions
Book Recommended:
1. Hydrostatics – M Rahman
2. Hydrostatics – J P Sinha
3. Hydrodynamics – Shanti Swaroop
4. Hydrodynamics – M D Raisinghania