A. Engineering Mathematics | Algebra | 1. Definition of complex number, conjugate, modulus, and amplitude 2. Algebra of complex numbers 3. Cube root of unity and its properties 4. De Moivre's theorem and applications 5. Permutation and combination 6. Binomial theorem for any rational index 7. Relationship between binomial coefficients |
| Determinant and Matrices | 1. Properties of determinants 2. Crammer’s Rule 3. Types of matrices 4. Transpose, adjoint, and inverse of matrices (up to third order) 5. Solution of simultaneous equations using matrix method |
| Trigonometry | 1. Trigonometric ratios 2. Multiple and submultiple angles 3. Solution of trigonometric equations 4. Properties of triangles 5. Inverse circular functions and properties |
| Analytical Geometry | 1. Distance formula 2. Division formula 3. Area of trapezium 4. Area of triangle 5. Equation of straight lines (various forms) 6. Distance of a point from a line 7. Equation of a circle (various forms) |
| Vector Algebra | 1. Definition and algebra of vectors 2. Position vector 3. Resolution into components 4. Normal vector, unit vector 5. Scalar and vector product of two vectors 6. Scalar triple product |
| Calculus | 1. Limit and continuity of functions 2. Derivative of standard, composite, implicit, and parametric functions 3. Logarithmic differentiation 4. Successive differentiation 5. Maxima, minima, points of inflection 6. Partial derivatives 7. Euler’s theorem for homogeneous functions |
| Integration | 1. Methods: by parts, substitution, partial fractions 2. Definite integrals and properties 3. Area bounded by curves |
| Ordinary Differential Equations | 1. Order and degree 2. Formation and solution of first order and first degree (linear and homogeneous) |
| Coordinate Geometry (3D) | 1. Distance and division formulae 2. Direction cosine and direction ratios 3. Conditions for perpendicularity and parallelism 4. Equation of a plane 5. Angle between two planes 6. Equation of a sphere |
| Probability and Statistics | 1. Measures of central tendency: mean, median, mode 2. Measures of dispersion: mean deviation, standard deviation, variance 3. Probability: Definition, equally likely, mutually exclusive and independent events 4. Addition theorem of probability |
B. Engineering Mechanics | Force and Moments | 1. Force and its effects 2. Classification of forces 3. Principles of transmissibility and superposition 4. Action and reaction 5. Tension and compression 6. Free body diagram 7. Coplanar forces: Resultant, equilibrium, parallelogram law, components, Lami’s theorem |
| Center of Gravity & Moment of Inertia | 1. Centroid, center of gravity (C.G.) of geometric shapes (line, triangle, rectangle, circle, etc.) 2. Moment of inertia (M.I.) of plane figures (rectangles, triangles, circles, etc.) 3. Perpendicular and parallel axis theorems |
| Friction | 1. Frictional force, angle of friction, limiting friction, coefficient of friction 2. Laws of static friction 3. Problems on ladder and inclined planes |
| Gear Drive | 1. Types of gears 2. Gear terminology 3. Velocity ratio for simple gears 4. Types of gear trains (simple and compound) |
| Simple Lifting Machines | 1. Definition of machine 2. Mechanical advantage, velocity ratio, efficiency 3. Laws of machines 4. Simple, differential pulleys, screw jack |
| Simple Stress and Strain | 1. Types of stress (tensile, compressive, shear) 2. Hooke’s Law 3. Poisson’s ratio 4. Elastic constants (E, G, K) 5. Stress-strain curve for ductile materials |
| Dynamics | 1. Kinematics and kinetics 2. Newton’s laws of motion 3. D’Alembert’s principle 4. Work, power, energy, momentum, impulse 5. Conservation of energy, linear momentum |
C. Basic Electricla & Electronics Engineering | C 1. Basic Electrical Engineering | |
| Fundamentals and AC Theory | 1. Concept of source and load, Ohm’s Law, series and parallel DC circuits 2. Kirchhoff’s laws 3. Faraday’s laws 4. Fleming’s left and right-hand rules 5. AC and DC: differences, concepts, values, phasor diagrams, AC circuits, impedance and power triangles |
| Conversion of Electrical Energy | 1. DC machine components 2. DC generators (operation and emf equation) 3. DC motors (operation, classification, torque, back emf) 4. Transformers (single and three-phase) 5. Induction motors |
| Power Billing | 1. Power calculation for electrical appliances 2. Energy consumption 3. Earthing installation (pipe and plate earthing) |
| Measuring Instruments and Storage Devices | 1. Measuring instruments: PMMC, MI type 2. Connection diagrams for AC/DC ammeter, voltmeter, wattmeter 3. Storage devices and types (lead-acid batteries, maintenance) |
| C 2. Basic Electronics Engineering | |
| Electronic Devices | 1. Electrical conductivity of materials (conductor, semiconductor, insulator) 2. PN junction diode, Zener diode, LED 3. Integrated circuits |
| Electronic Circuits | 1. Rectifiers (types, merits, demerits) 2. Transistor configurations (CE, CB, CC) 3. Biasing (CE configuration) 4. Amplifiers (CE) |
| Communication System | 1. Basic communication system 2. Modulation and demodulation (AM, FM, PM) |
| Transducers & Measuring Instruments | 1. Transducers and sensors 2. Working of photo emissive, photoconductive, photovoltaic transducers 3. Multimeter and applications |
