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• For 03 Hours 30 Minutes Paper (Both B.Arch & B.Planning)

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• Sets & representation, 
• Union, 
• intersection & complement, 
• Power set, 
• Types of relations, 
• Equivalence relations, 
• Functions (one-one, into, onto), 
• Composition of functions.

• Complex numbers as ordered pairs of reals, 
• a+iba+iba+ib form, 
• Argand diagram, 
• Modulus & argument, 
• Quadratic equations in real & complex systems, 
• Relation between roots and coefficients, 
• Formation of equations.

• Matrices algebra, 
• Types of matrices, 
• Determinants of order 2 & 3, 
• Area of triangles, 
• Adjoint & inverse of a square matrix, 
• Consistency & solution of linear equations.

• Fundamental principle of counting, 
• Permutations and combinations, 
• Meaning of P(n,r)P(n,r)P(n,r) and C(n,r)C(n,r)C(n,r), 
• Simple applications.

• Binomial theorem for positive integral index, 
• General term, 
• Middle term, 
• Simple applications.

• Arithmetic and Geometric progressions (A.P., G.P.), 
• Insertion of A.M. and G.M., 
• Relation between A.M. and G.M.

• Real-valued functions, 
• Limits, continuity & differentiability, 
• Derivative rules (sum, product, quotient), 
• Chain rule, 
• Derivatives of order up to two, 
• Applications of derivatives (Rate of change, Monotonic functions, Maxima and minima)

• Integral as anti-derivative, 
• Standard integrals, 
• Integration by substitution, parts & partial fractions, Fundamental theorem of calculus, 
• Definite integrals properties, 
• Area bounded by curves.

• Ordinary differential equations, 
• Order and degree, 
• Solution by separation of variables, 
• Homogeneous & linear differential equations.

• Cartesian system, 
• Straight lines (forms, slopes, intersection, centroid, orthocentre, circumcentre), 
• Conic sections (Circle, Parabola, Ellipse, Hyperbola) in standard forms.

• Coordinates in space, 
• Distance formula, 
• Section formula, 
• Direction cosines & direction ratios, 
• Equation of a line, 
• Skew lines & shortest distance.

• Vectors and scalars, 
• Vector components, 
• Scalar (dot) and vector (cross) products.

• Measures of dispersion (Mean, median, mode, standard deviation, variance), 
• Probability axioms, 
• Addition & multiplication rules, 
• Bayes’ theorem, 
• Probability distributions.

• Trigonometrical identities & functions,
• Inverse trigonometrical functions and their properties.

• SI Units,
•  Fundamental & derived units, 
• Least count, 
• Significant figures, 
• Errors in measurements, 
• Dimensional analysis.

• Motion in a straight line & plane, 
• Graphs (v−t,x−tv-t, x-tv−t,x−t), 
• Uniformly accelerated motion,
•  Relative velocity, Projectile motion, 
• Uniform circular motion.

• Newton’s laws, 
• Momentum,
• Impulse, 
• Law of conservation of momentum, 
• Friction (static, kinetic, rolling), 
• Centripetal force, Banking of roads.

• Work-energy theorem, 
• Kinetic & potential energy, 
• Conservative forces, 
• Collisions (elastic & inelastic in 1D & 2D).

• Centre of mass, 
• Torque, 
• Angular momentum & its conservation, 
• Moment of inertia, 
• Parallel & perpendicular axes theorems,
•  Rigid body rotation.

• Universal law of gravitation, 
• Acceleration due to gravity (ggg) variations, 
• Kepler’s laws, 
• Orbital velocity, 
• Escape velocity, 
• Satellite motion.

• Hooke’s Law, 
• Moduli of elasticity, 
• Pascal’s law, 
• Viscosity, 
• Stoke’s law, 
• Bernoulli’s principle, 
• Surface tension, 
• Capillary rise, 
• Heat & calorimetry, 
• Heat transfer.

• Thermal equilibrium, 
• Zeroth, 
• First and Second laws of thermodynamics,
• Isothermal & adiabatic processes, 
• Reversible & irreversible processes.

• Equation of state, 
• Kinetic interpretation of temperature, 
• RMS speed, 
• Degrees of freedom, 
• Law of equipartition of energy, 
• Mean free path.

• Simple Harmonic Motion (S.H.M.), 
• Simple pendulum, 
• Wave motion, 
• Progressive & standing waves, 
• Resonance, 
• Beats, 
• Harmonics in pipes & strings.

• Coulomb’s law, 
• Electric field & dipole, 
• Gauss’s law applications, 
• Electric potential, 
• Capacitors (series & parallel), 
• Energy stored in capacitors.

• Ohm’s law, 
• Drift velocity, 
• Electrical resistivity, 
• Series-parallel resistor circuits, 
• Kirchhoff’s laws, 
• Wheatstone bridge, 
• Metre bridge.

• Biot-Savart law, 
• Ampere’s circuital law, 
• Force on moving charge, 
• Moving coil galvanometer, 
• Magnetic dipoles, 
• Dia, para & ferromagnetic materials.

• Faraday’s & Lenz’s laws, 
• Self & mutual inductance, 
• Alternating currents, Peak & RMS values, 
• LCR series circuit, Resonance, 
• AC generator & transformer.

• Displacement current, 
• Characteristics of EM waves, 
• Electromagnetic spectrum and applications.

• Reflection,
•  Refraction, 
• Lens maker formula, 
• Total internal reflection (TIR), 
• Prism, Microscope & Telescope, 
• Wave optics (Interference, Diffraction, Polarization).

• Photoelectric effect, 
• Einstein’s equation, de-Broglie relation,
•  Matter waves.

• Rutherford & Bohr models, 
• Hydrogen spectrum, 
• Nuclear composition, 
• Mass defect, Binding energy, 
• Fission and fusion.

• Semiconductors, 
• p−np-np−n junction diode characteristics, 
• Rectifiers, 
• Zener diode, 
• Logic gates (OR, AND, NOT, NAND, NOR).

• Vernier calipers, Screw gauge, 
• Simple pendulum, 
• Metre scale, 
• Young’s modulus, 
• Surface tension, 
• Viscosity, 
• Speed of sound, 
• Specific heat capacity, 
• Metre bridge, 
• Ohm’s law, 
• Galvanometer resistance, 
• Mirror/lens focal length, 
• Prism, Glass slab refractive index, 
•  curves.

• Matter, 
• Laws of chemical combination,
• Mole concept,
• Molar mass, 
• Empirical & molecular formulae, Stoichiometry

• Bohr model,
•  Dual nature of matter,
• Heisenberg uncertainty principle, 
• Quantum numbers, 
• Shapes of orbitals, 
• Aufbau principle, 
• Pauli’s rule, 
• Hund’s rule

• Ionic & covalent bonding,
• Electronegativity, 
• VSEPR theory, 
• Hybridization, 
• Molecular Orbital Theory (MOT), 
• Hydrogen bonding।

• First & second laws of thermodynamics, 
• Enthalpies of reactions,
• Spontaneity, S and G,
• Standard Gibbs free energy

• Concentration expressions,
• Raoult’s law, Colligative properties (Elevation of BP,
• Depression of FP, Osmotic pressure), 
• Van ‘t Hoff factor

• Dynamic equilibrium, 
• Le Chatelier’s principle,
• Equilibrium constants, 
• Ionic equilibrium (Acids, bases, pH, 
• Buffer solutions, 
• Solubility product)

• Oxidation number, 
• Balancing redox equations,
• Electrolytic & Galvanic cells,
• Nernst equation, 
• Conductance, 
• Kohlrausch’s law, 
• Batteries

• Rate of reaction,
•  Order & molecularity, 
• Rate law, 
• Zero & first-order reactions,
• Arrhenius equation, 
• Activation energy

• Periodic trends (atomic/ionic radii, ionization enthalpy, electron gain enthalpy, oxidation states)

• Groups 13 to 18 electronic configuration,
• General trends, 
• Anomalous behaviour of first elements

• Transition elements trends,
• Lanthanoids & Actinoids,
• Contraction, Preparation and properties of K2Cr2O7 & KMnO4

• Werner’s theory, 
• Ligands,
• IUPAC nomenclature,
• Isomerism,
• Valence Bond Theory (VBT),
• Crystal Field Theory (CFT)

• Crystallization, 
• Distillation, 
• Chromatography, 
• Qualitative analysis (N, S, P, halogens), 
• Empirical/molecular formulae calculations

• IUPAC nomenclature,
• Carbocations, 
• Carbanions, 
• Free radicals,
• Inductive/electromeric effects,
• Resonance, Hyperconjugation

• Alkanes,
• Alkenes, 
• Alkynes, 
• Aromatic hydrocarbons (Benzene, Electrophilic substitution,Friedel-Crafts reaction)

• Alkyl & aryl halides,
• Nucleophilic substitution (SN1,SN2),
•  Environmental effects of chloroform, freons, DDT

• Alcohols, 
• Phenols, 
• Ethers, 
• Aldehydes, 
• Ketones, 
• Carboxylic acids (Reimer-Tiemann, Aldol condensation, Cannizzaro)

• Amines (Classification, 
• Basic character, Separation),
• Diazonium salts in synthetic organic chemistry

• Carbohydrates (Aldoses,
• ketoses, glucose, fructose),
• Proteins, 
• Vitamins, 
• Nucleic acids (DNA, RNA),
• Hormones

• Functional group detection,
• Salt analysis (Cations & Anions), 
• Inorganic & Organic preparations, 
• Titrimetric exercises

Sets, 

Complex Numbers, 

Matrices, 

Permutations, 

Binomial, 

Sequences, 

Calculus, 

Coordinate Geometry, 

Vectors, 

3D, 

Probability, 

Trigonometry

• Architectural awareness, 
• Famous buildings, 
• Materials, 
• Textures, 
• Visualizing 3D from 2D drawings, 
• Mental ability & analytical reasoning

• 3D perception, 
• Proportions, 
• Color texture harmony,
• Geometrical patterns, 
• Form transformation (union, subtraction, rotation),
• Plan/elevation/3D views

• Sketching scenes from memory (Urbanscapes,
• Public spaces, 
• Festivals, 
• Monuments, 
• Landscapes, 
• Rural life)

• Government development schemes, 
• Famous cities, 
• Urban infrastructure issues

• Nationalism, 
• Resources & development,
• Industries, 
• Agriculture, 
• Human settlements,
• Constitution of India,
• Urbanization & poverty