CUET Mock Test

PHYSICS

Mathematical Methods

Calculus of single and multiple variables

Partial derivatives, Jacobian

Imperfect and perfect differentials

Taylor expansion, Fourier series

Vector algebra, Vector Calculus

Multiple integrals

Divergence theorem, green's theorem, Stokes' theorem

First order equations and linear second order differential equations with constant coefficients

Matrices and determinants

Algebra of complex numbers

Mechanics and General Properties of Matter

Newton's laws of motion and applications

Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems

Uniformly rotating frame, centrifugal and Coriolis forces

Motion under a central force, Kepler's laws

Gravitational Law and field

Conservative and non-conservative forces

System of particles, Center of mass

Conservation of linear and angular momentum, conservation of energy

Variable mass systems

Elastic and inelastic collisions

Rigid body motion, fixed axis rotations

Moments of Inertia and products of Inertia

Parallel and perpendicular axes theorem

Principal moments and axes

Kinematics of moving fluids

Equation of continuity, Euler's equation, Bernoulli's theorem

Oscillations, Waves and Optics

Differential equation for simple harmonic oscillator

Superposition of simple harmonic oscillators

Lissajous figures

Damped and forced oscillators, resonance

Wave equation, traveling and standing waves

Energy density and energy transmission in waves

Group velocity and phase velocity

Sound waves in media, Doppler Effect

Fermat's Principle

General theory of image formation

Thick lens, thin lens and lens combinations

Interference of light, optical path retardation

Fraunhofer diffraction

Rayleigh criterion and resolving power

Diffraction gratings

Polarization: linear, circular and elliptic polarization

Double refraction and optical rotation

Electricity and Magnetism

Coulomb's law, Gauss's law

Electric field and potential

Electrostatic boundary conditions

Solution of Laplace's equation for simple cases

Conductors, capacitors, dielectrics

Dielectric polarization, volume and surface charges

Electrostatic energy

Biot-Savart law, Ampere's law

Faraday's law of electromagnetic induction

Self and mutual inductance

Alternating currents

Simple DC and AC circuits with R, L and C components

Displacement current, Maxwell's equations

Plane electromagnetic waves, Poynting's theorem

Reflection and refraction at a dielectric interface

Transmission and reflection coefficients

Lorentz Force and motion of charged particles in electric and magnetic fields

Kinetic theory, Thermodynamics

Elements of Kinetic theory of gases

Velocity distribution and equipartition of energy

Specific heat of Mono-, di- and tri-atomic gases

Ideal gas, van-der-Waals gas and equation of state

Mean free path

Laws of thermodynamics

Zeroth law and concept of thermal equilibrium

First law and its consequences

Isothermal and adiabatic processes

Reversible, irreversible and quasi-static processes

Second law and entropy

Carnot cycle

Maxwell's thermodynamic relations

Thermodynamic potentials and their applications

Phase transitions and Clausius-Clapeyron equation

Ideas of ensembles

Maxwell-Boltzmann, Fermi-Dirac and Bose Einstein distributions

Modern Physics

Inertial frames and Galilean invariance

Postulates of special relativity

Lorentz transformations

Length contraction, time dilation

Relativistic velocity addition theorem

Mass energy equivalence

Blackbody radiation, photoelectric effect, Compton Effect

Bohr's atomic model, X-rays

Wave-particle duality, Uncertainty principle

The superposition principle

Calculation of expectation values

Schrödinger equation and its solutions

Reflection and transmission at a step potential

Pauli Exclusion Principle

Structure of atomic nucleus, mass and binding energy

Radioactivity and its applications

Laws of radioactive decay

Solid State Physics, Devices and Electronics

Crystal structure, Bravais lattices and basis

Miller indices

X-ray diffraction and Bragg's law

Intrinsic and extrinsic semiconductors

Variation of resistivity with temperature

Fermi level

p-n junction diode, I-V characteristics

Zener diode and its applications

BJT: characteristics in CB, CE, CC modes

Single stage amplifier, two stage R-C coupled amplifiers

Simple Oscillators: Barkhausen condition, sinusoidal oscillators

OPAMP and applications: Inverting and non-inverting amplifier

Boolean algebra: Binary number systems

Conversion from one system to another system

Binary addition and subtraction

Logic Gates AND, OR, NOT, NAND, NOR exclusive OR

Truth tables

Combination of gates

de Morgan's theorem

MATHEMATICS

Algebra

Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups

Normal subgroups, Lagrange's Theorem for finite groups

Group homomorphism and quotient groups

Rings, Subrings, Ideal, Prime ideal, Maximal ideals

Fields, quotient field

Vector spaces

Linear dependence and Independence of vectors

Basis, dimension, linear transformations

Matrix representation with respect to an ordered basis

Range space and null space, rank-nullity theorem

Rank and inverse of a matrix, determinant

Solutions of systems of linear equations, consistency conditions

Eigenvalues and eigenvectors

Cayley-Hamilton theorem

Symmetric, Skew symmetric, Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices

Real Analysis

Sequences and series of real numbers

Convergent and divergent sequences, bounded and monotone sequences

Convergence criteria for sequences of real numbers, Cauchy sequences

Absolute and conditional convergence

Tests of convergence for series of positive terms

Functions of one variable: limit, continuity, differentiation

Rolle's Theorem, Cauchy's Taylor's theorem

Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets

Completeness of R

Power series (of real variable) including Taylor's and Maclaurin's

Functions of two real variable: limit, continuity, partial derivatives, differentiability

Maxima and minima, Method of Lagrange multipliers

Homogeneous functions including Euler's theorem

Complex Analysis

Functions of a complex Variable

Differentiability and analyticity, Cauchy Riemann Equations

Power series as an analytic function

Properties of line integrals

Goursat Theorem, Cauchy theorem

Consequence of simply connectivity, index of a closed curves

Cauchy's integral formula

Morera's theorem, Liouville's theorem

Fundamental theorem of Algebra

Harmonic functions

Integral Calculus

Integration as the inverse process of differentiation

Definite integrals and their properties

Fundamental theorem of integral calculus

Double and triple integrals, change of order of integration

Calculating surface areas and volumes using double integrals

Calculating volumes using triple integrals

Differential Equations

Ordinary differential equations of the first order of the form y'=f(x,y)

Bernoulli's equation, exact differential equations, integrating factor

Orthogonal trajectories

Homogeneous differential equations-separable solutions

Linear differential equations of second and higher order with constant coefficients

Method of variation of parameters

Cauchy-Euler equation

Vector Calculus

Scalar and vector fields, gradient, divergence, curl and Laplacian

Scalar line integrals and vector line integrals

Scalar surface integrals and vector surface integrals

Green's, Stokes and Gauss theorems and their applications

Linear Programming

Convex sets, extreme points, convex hull

Hyper plane & polyhedral Sets

Convex function and concave functions

Concept of basis, basic feasible solutions

Formulation of Linear Programming Problem (LPP)

Graphical Method of LPP

Simplex Method

STATISTICS

Sequences and Series

Convergence of sequences of real numbers

Comparison, root and ratio tests for convergence of series of real numbers

Differential Calculus

Limits, continuity and differentiability of functions of one and two variables

Rolle's Theorem, mean value theorems, Taylor's theorem

Indeterminate forms

Maxima and minima of functions of one and two variables

Integral Calculus

Fundamental theorems of integral calculus

Double and triple integrals

Applications of definite integrals

Arc lengths, areas and volumes

Matrices

Rank, inverse of a matrix

Systems of linear equations

Linear transformations, eigenvalues and eigenvectors

Cayley‐Hamilton theorem

Symmetric, skew‐symmetric and orthogonal matrices

Differential Equations

Ordinary differential equations of the first order of the form y' = f(x,y)

Linear differential equations of the second order with constant coefficients

Descriptive Statistics and Probability

Measure of Central tendency

Measure of dispersion, skewness and Kurtosis

Elementary analysis of data

Axiomatic definition of probability and properties

Conditional probability, multiplication rule

Theorem of total probability

Bayes' theorem and independence of events

Random Variables

Probability mass function, probability density function and cumulative distribution functions

Distribution of a function of a random variable

Mathematical expectation, moments and moment generating function

Chebyshev's inequality

Standard Distributions

Binomial, negative binomial, geometric, Poisson, hyper-geometric, uniform, exponential, gamma, beta and normal distributions

Poisson and normal approximations of a binomial distribution

Chi-square distribution, t-distribution and F-distribution

Joint Distributions

Joint, marginal and conditional distributions

Distribution of functions of random variables

Product moments, correlation, simple linear regression

Independence of random variables

Limit Theorems

Weak law of large numbers

Central limit theorem (i.i.d. with finite variance case only)

Estimation

Unbiasedness, consistency and efficiency of estimators

Method of moments and method of maximum likelihood

Sufficiency, factorization theorem

Completeness, Rao‐Blackwell and Lehmann‐Scheffe theorems

Uniformly minimum variance unbiased estimators

Rao‐Cramer inequality

Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions

Testing of Hypotheses

Basic concepts

Applications of Neyman‐Pearson Lemma for testing simple and composite hypotheses

Likelihood ratio tests

Sampling and Designs of Experiments

Simple random sampling, stratified sampling and Cluster sampling

One-way, two-way analysis of variance

CRD, RBD, LSD and 2² and 2³ factorial experiments

CHEMISTRY

Gaseous State

Behavior of real gases

van der Waals equation of state

Kinetic molecular model of a gas

Maxwell distribution

Liquid State

Structure and physical properties of liquids

Vapour pressure, surface tension, viscosity

Effect of addition of various solutes

Structure of water

Ionic Equilibria

Strong, moderate and weak electrolytes

Ionization of weak acids and bases

Salt hydrolysis

Buffer solutions

Solubility and solubility product

Brönsted-Lowry concept of acid-base reactions

Lewis acid-base concept

Solid State

Nature of the solid state

X-ray diffraction

Various types of defects in crystals

Glasses and liquid crystals

Thermodynamics

First law of thermodynamics

Thermochemistry

Second Law of thermodynamics

Third law of thermodynamics

Free Energy Functions

Partial molar quantities

Gibbs-Duhem equation

Chemical potential of ideal mixtures

Dilute solutions or Colligative Properties

Dilute solutions

Raoult's and Henry's Laws

Colligative properties

Molecular Spectroscopy & Photochemistry

Interaction of electromagnetic radiation with molecules

Rotation spectroscopy

Vibrational spectroscopy

Raman spectroscopy

Electronic spectroscopy

Photophysical and photochemical processes

Chemical Kinetics

Order and molecularity of a reaction

Rate laws

Temperature dependence of reaction rates

Collision theory of reaction rates

Catalysis

Types of catalyst

Mechanisms of catalyzed reactions

Enzyme catalysis

Surface chemistry

Physical adsorption, chemisorption

Adsorption isotherms

BET theory

Adsorption in solution

Phase Equilibria

Gibbs Phase Rule

Phase diagrams

Binary solutions

Nernst distribution law

Introduction to Quantum Chemistry

Wave function and Schrödinger equation

Simple harmonic oscillator model

Rigid rotator model

Hydrogen atom and hydrogen-like ions

Valence bond and molecular orbital approaches

Conductance

Arrhenius theory of electrolytic dissociation

Conductivity and molar conductivity

Kohlrausch law

Applications of conductance measurement

Electrochemistry

Faraday's laws of electrolysis

Chemical cells

Electromotive force

Concentration cells

Potentiometric titrations

Atomic Structure

Bohr's theory

Wave mechanics

Quantum numbers

Shapes of orbitals

Pauli's Exclusion Principle

Hund's rule

Aufbau's principle

Periodicity of Elements

s, p, d, f block elements

Periodic properties

Chemical Bonding

Ionic bond

Covalent bond

Molecular orbital theory

Metallic bonding and Weak chemical forces

Metallic Bond

Weak Chemical Forces

Oxidation-Reduction and general principle of metallurgy

Redox equations

Standard Electrode Potential

Ellingham diagrams

Methods of purification of metals

Chemistry of s and p Block Elements

Inert pair effect

Allotropy and catenation

Hydrides

Oxides and oxoacids

Inter-halogen compounds

Noble Gases

Occurrence and uses

Preparation and properties of xenon compounds

Bonding in noble gas compounds

Inorganic Polymers

Types of inorganic polymers

Silicones and siloxanes

Borazines, silicates, phosphazenes, polysulphates

Coordination Chemistry

Werner's theory

Valence bond theory

Crystal field theory

IUPAC nomenclature

Isomerism in coordination compounds

Transition Elements

General group trends

Stability of various oxidation states

Chemistry of Ti, V, Cr Mn, Fe and Co

Lanthanoids and Actinides

Electronic configuration

Oxidation states

Lanthanide contraction

Separation of lanthanides

Bioinorganic Chemistry

Metal ions in biological systems

Geochemical effect on distribution of metals

Toxicity of metal ions

Iron and its application in biosystems

Organometallic Compounds

Definition and classification

Metal carbonyls

General methods of preparation

Structures of mononuclear and binuclear carbonyls

Basics of Organic Chemistry

Classification and Nomenclature

Hybridization

Electronic Displacements

Organic acids and bases

Reaction intermediates

Types of organic reactions

Stereochemistry

Concept of asymmetry

Geometrical isomerism

Optical Isomerism

Relative and absolute configuration

Chemistry of Aliphatic Hydrocarbons

Chemistry of alkanes

Chemistry of alkenes and alkynes

Elimination reactions

Addition reactions

Cycloalkanes and Conformational Analysis

Cycloalkanes and stability

Conformation analysis

Aromatic Hydrocarbons

Aromaticity

Electrophilic aromatic substitution

Chemistry of Halogenated Hydrocarbons

Alkyl halides

Aryl halides

Organometallic compounds

Alcohols, Phenols, Ethers and Epoxides

Alcohols: preparation and properties

Phenols: preparation and properties

Ethers and Epoxides: preparation and reactions

Carbonyl Compounds

Structure, reactivity and preparation

Nucleophilic additions

Condensation reactions

Oxidations and reductions

Active methylene compounds

Carboxylic Acids and their Derivatives

Preparation and reactions of carboxylic acids

Reactions of acid derivatives

Comparative study of nucleophilic substitution at acyl group

Sulphur containing compounds

Preparation and reactions of thiols, thioethers and sulphonic acids

Nitrogen Containing Functional Groups

Nitro compounds, nitriles and isonitriles

Amines

Diazonium salts

Polynuclear Hydrocarbons

Reactions of naphthalene phenanthrene and anthracene

Structure and derivatives of naphthalene and anthracene

Heterocyclic Compounds

Classification and nomenclature

Synthesis and reactions of various heterocycles

Structure elucidation of indole, quinoline, and isoquinoline

Alkaloids

Natural occurrence and general structural features

Isolation and physiological action

Structure elucidation and synthesis of specific alkaloids

Terpenes

Occurrence and classification

Isoprene rule

Elucidation of structure and synthesis of specific terpenes

Organic Spectroscopy

UV Spectroscopy

IR Spectroscopy

NMR Spectroscopy

Mass Spectrometry

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