AP EAMCET Mock Test 2025

ASPECT

DESCRIPTION

Name of the Examination

AP EAPCET: Andhra Pradesh Engineering, Agriculture, and Pharmacy Common Entrance Test (former name - AP EAMCET)

Exam Conducting Organization in 2024

Jawaharlal Nehru Technological University (JNTU), Kakinada

Frequency of the Exam

Annual (once a year)

Examination Level

State Level

Mode of the Exam

Online- Computer Based Test

Exam Duration

3 hours 

Number of Questions and their Type

• 160 questions
• Multiple-choice questions 

Courses Offered through AP EAPCET

• B.Tech: Bio-Technology, Dairy Technology, Agricultural Engineering, Food Science & Technology
• B.Sc.: Agriculture, Horticulture, B.V.Sc. & A.H., B.F.Sc.
• B. Pharmacy, and Pharma. D.
• B.Sc. Nursing 

SUBJECT

TOPICS

MATHEMATICS

ALGEBRA

Functions: Types of functions - Definitions - Inverse functions & Theorems - Domain, Range and Inverse.

Mathematical Induction: Principles of Mathematical Induction & Theorems - Applications of Mathematical Induction - Problems on divisibility.

Matrices: Types of matrices - Scalar multiple of a matrix and multiplication of matrices - Transpose of a matrix - Determinants - properties of determinants - Adjoint and Inverse of a matrix - Consistency and inconsistency of system of simultaneous equations - Rank of a matrix - Solution of simultaneous linear equations.

Complex Numbers: Complex numbers as an ordered pair of real numbers- fundamental operations - Representation of complex numbers in the form a+ib - Modulus and amplitude of complex numbers-Illustrations - Geometrical and Polar Representation of complex numbers in Argand plane-Argand diagram.

De Moivre's Theorem: De Moivre's theorem- Integral and Rational indices - n roots of unity-Geometrical Interpretations-Illustrations.

Quadratic Expressions: Quadratic expressions, equations in one variable - Sign of quadratic expressions - Change in signs- Maximum and minimum values - Quadratic Inequations.

Theory of Equations: The relation between the roots and coefficients in an equation - Solving equations when two or more roots of it are connected by a certain relation - Equation with real coefficients, the occurrence of complex roots in conjugate pairs and its consequences, Transformation of equations- Reciprocal equations.

Permutations and Combinations: Fundamental Principle of counting - linear and circular permutations- Permutations of 'n' dissimilar things taken 'r' at a time - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions- Combinations-definitions, certain theorems.

Binomial Theorem: Binomial theorem for positive integral index, Binomial theorem for rational Index - Approximations using Binomial theorem.

Partial fractions: Partial fractions of f(x)/g(x) when g(x) contains non-repeated linear factors - Partial fractions of f(x)/g(x) where both f(x) and g(x) are polynomials and when g(x) contains repeated and/or non-repeated linear factors - Partial fractions of f(x)/g(x) when g(x) contains irreducible factors.

TRIGONOMETRY

Trigonometric Ratios up to Transformations: Trigonometric ratios- Variation - Graphs and Periodicity of Trigonometric functions - Trigonometric ratios of Compound angles - Trigonometric ratios of multiple and sub-multiple angles - Transformations - Sum and Product rules.

Trigonometric Equations: General solutions of Trigonometric Equations - Simple Trigonometric Equations - Solutions.

Inverse Trigonometric Functions: To reduce a Trigonometric function into a bijective function - Graphs of Inverse Trigonometric functions - Properties of Inverse Trigonometric Functions.

Hyperbolic Functions: Definition of Hyperbolic Function - Graphs - Definition of Inverse Hyperbolic Functions - Graphs - Addition formulae of Hyperbolic Functions.

Properties of Triangles: Relation between sides and angles of a Triangle - Sine, Cosine, Tangent, and Projection rules- Half angle formulae and areas of a triangle - Incircle and Excircles of a Triangle.

VECTOR ALGEBRA

Addition of Vectors: Vectors as a triad of real numbers- Classification of vectors - Addition of vectors - Scalar multiplication - Angle between two non-zero vectors - The linear combination of vectors - Components of a vector in three dimensions - Vector equations of line and plane including their Cartesian equivalent forms.

Product of Vectors: Scalar or dot product of two vectors- Geometrical Interpretations - orthogonal projections - Properties of dot product - Expression of the dot product in i, j, k system - Angle between two vectors - Geometrical Vector methods - Vector equations of a plane in normal form-Angle between two planes- Vector product of two vectors and properties- Vector product in i, j, k system- Vector Areas - Scalar triple product - Vector equation of a plane different forms, skew lines, shortest distance - plane, condition for coplanarity, etc. - vector triple product - results.

MEASURES OF DISPERSION AND PROBABILITY

Measures of Dispersion - Range - Mean deviation - Variance and standard deviation of ungrouped/grouped data, coefficient of variation, and analysis of frequency distributions with equal means but different variances.

Probability: Random experiments and events - Classical definition of probability, Axiomatic approach and addition theorem of probability - Independent and dependent events - conditional probability- multiplication theorem and Baye's theorem.

Random Variables and Probability Distributions: Random Variables - Theoretical discrete distributions - Binomial and Poisson Distributions.

COORDINATE GEOMETRY

Locus: Definition of locus-Illustrations-To find equations of locus-Problems connected to it.

Transformation of Axes: Transformation of Axes - Rules, derivations, and illustrations Rotation of Axes - Derivations - Illustrations.

The Straight Line: Revision of fundamental results - Straight line - Normal form Illustrations - Straight line - Symmetric form - Straight line - Reduction into various forms - Intersection of two Straight Lines - Family of straight lines - Concurrent lines - Condition for

Concurrent lines - Angle between two lines - Length of perpendicular from a point to a Line - Distance between two parallel lines - Concurrent lines - properties related to a triangle.

Pair of Straight lines: Equations of a pair of lines passing through the origin - angle between a pair of lines - Condition for perpendicular and coincident lines, bisectors of angles - Pair of

bisectors of angles - Pair of lines - second-degree general equation - Conditions for parallel lines - the distance between them, Point of the intersection of pair of lines - Homogenising a second-degree equation with a first-degree equation in x and y.

Circle: Equation of circle -standard form-center and radius - Equation of a circle with a given

line segment as diameter & equation of a circle through three non-collinear points - parametric equations of a circle - Position of a point in the plane of a circle - the power of a point definition of tangent-length of a tangent - Position of a straight line in the plane of a circle-conditions for a line to be tangent - chord joining two points on a circle - equation of the tangent at a point on the circle-point of contact-equation of normal-Chord of contact-pole and polar-conjugate points and conjugate lines- equation of chord with given middle point, Relative position of two circles- circles touching each other externally, internally common tangents -centers of similitude-equation of pair of tangents from an external point.

System of circles: Angle between two intersecting circles -condition for orthogonality - Radical axis of two circles- properties- Common chord and common tangent of two circles - radical center - Intersection of a line and a Circle.

Parabola: Conic sections -Parabola- equation of parabola in standard form-different forms of parabola- parametric equations, Equations of tangent and normal at a point on the parabola

(Cartesian and Parametric)- conditions for a straight line to be a tangent.

Ellipse: Equation of ellipse in standard form Parametric equations, Equation of tangent and normal at a point on the ellipse (Cartesian and parametric)- condition for a straight line to be a Tangent.

Hyperbola: Equation of hyperbola in standard form- Parametric equations - Equations of tangent and normal at a point on the hyperbola (Cartesian and parametric) - conditions for a straight line to be tangent-Asymptotes.

Three-Dimensional Coordinates: Coordinates - Section formulae - Centroid of a triangle and tetrahedron.

Direction Cosines and Direction Ratios: Direction Cosines -Direction Ratios.

Plane: Cartesian equation of a Plane-Simple Illustrations.

CALCULUS

Limits and Continuity: Intervals and neighborhoods - Limits Standard Limits-Continuity.

Differentiation: Derivative of a function - Elementary Properties - Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function-Derivatives - Methods of Differentiation - Second Order Derivatives.

Applications of Derivatives: Errors & Approximations - Geometrical Interpretation of a derivative - Equations of tangents and normal to a curve Lengths of Tangent, Normal, Subtangent and subnormal - Angles between two curves and condition for orthogonality of curves - Derivative as a rate of change - Rolle's theorem and Lagrange's Mean value theorem - Increasing and decreasing functions - Maxima and Minima.

Integration: Integration as the inverse process of differentiation- Standard forms -properties of integrals - Method of substitution- integration of Algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions - Integration by parts - Integration by the method of substitution - Integration of algebraic and trigonometric functions - Integration by parts - Integration of exponential, logarithmic, and inverse trigonometric functions - Integration - Partial fractions method - Reduction formulae.

Definite Integrals: Definite Integral as the limit of sum, Interpretation of Definite Integral as an area. Fundamental theorem of Integral Calculus. Properties, Reduction formulae, Application of Definite integral to areas.

Differential equations: Formation of differential equation- degree and order of an ordinary differential equation - Solving differential equation by i) Variables separable method, ii) Homogeneous differential equation, iii) Non Homogeneous differential equation iv) Linear differential equations.

PHYSICS

PHYSICAL WORLD: What is physics? Scope and excitement of physics. Physics, technology, and society, Fundamental forces in nature, and the Nature of physical laws.

UNITS AND MEASUREMENTS: The international system of units, Measurement of Length, Measurement of Large Distances, Estimation of Very Small Distances, Size of a Molecule, Range of Lengths, Measurement of Mass, Range of Masses, Measurement of time, Accuracy, precision of instruments and errors in measurement, Systematic errors, random errors, least count error, Absolute Error, Relative Error and Percentage Error, Combination of Errors, Significant figures, Rules for Arithmetic Operations with Significant Figures, Rounding off the Uncertain Digits, Rules

for Determining the Uncertainty in the Results of Arithmetic Calculations, Dimensions of Physical Quantities, Dimensional Formulae and dimensional equations. Dimensional Analysis and its Applications, Checking the Dimensional Consistency of Equations, Deducing Relation among the Physical Quantities.

MOTION IN A STRAIGHT LINE: Position, path length and displacement, average velocity and average speed, instantaneous velocity, and speed, acceleration, and kinematic equations for uniformly accelerated motion, relative velocity.

MOTION IN A PLANE: Scalars and vectors, position and displacement vectors, equality of vectors, multiplication of vectors by real numbers, addition and subtraction of vectors - graphical method, resolution of vectors, vector addition - analytical method, motion in a plane, position vector and displacement, velocity, acceleration, motion in a plane with constant acceleration, relative velocity in two dimensions, projectile motion, equation of path of a projectile, time of maximum height, maximum height of a projectile, horizontal range of projectile, uniform circular motion.

LAWS OF MOTION: Aristotle's fallacy, Laws of inertia, Newton's first law of motion, Newton's second law of motion- momentum, impulse, Newton's third law of motion, conservation of momentum, Equilibrium of a particle, Common forces in mechanics, friction, types of friction, static, kinetic and rolling frictions, Circular motion, Motion of a car on a level road, Motion of a car on a banked road, solving problems in mechanics.

WORK, ENERGY AND POWER: The Scalar Product, Notions of work and kinetic energy, The work-energy theorem, Work, Kinetic energy, Work done by a variable force, The work-energy theorem for a variable force, The concept of Potential Energy, The conservation of Mechanical Energy, The Potential Energy of a spring, Various forms of energy, Heat, Chemical Energy, Electrical Energy, The Equivalence of Mass and Energy, Nuclear Energy, The Principle of Conservation of Energy, Power, Collisions, Elastic and Inelastic Collisions, Collisions in one dimension, Coefficient of Restitution and its determination, Collisions in Two Dimensions.

SYSTEM OF PARTICLES AND ROTATIONAL MOTION: Rigid body motion, Centre of mass, Centre of Gravity, Motion of center of mass, Linear momentum of a system of particles, Vector product of two vectors, Angular velocity and its relation with linear velocity, Angular acceleration, Kinematics of rotational motion about a fixed axis, Moment of force (Torque), Angular momentum of a particle, Torque and angular momentum for a system of particle conservation of angular momentum, Equilibrium of a rigid body, Principle of moments, Moment of inertia, Dynamics of rotational motion about a fixed axis, Angular momentum in case of rotation about a fixed axis - conservation of angular momentum, Rolling motion, Kinetic Energy of Rolling Motion.

OSCILLATIONS: Periodic and oscillatory motions, Period and frequency, Displacement, Simple harmonic motion (S.H.M.), Simple harmonic motion and uniform circular motion, Velocity and acceleration in simple harmonic motion, Force law for Simple harmonic Motion, Energy in simple harmonic motion, some systems executing Simple Harmonic Motion, Oscillations due to a spring. The Simple Pendulum, damped simple harmonic motion, Forced oscillations, and resonance.

GRAVITATION: Kepler's laws, Universal law of gravitation, central forces, the gravitational constant, Acceleration due to gravity of the earth, Acceleration due to gravity below and above the surface of the earth, Gravitational potential energy, Escape speed, Orbital Speed, Earth satellites, Energy of an orbiting satellite, Geostationary and polar satellites, Weightlessness.

MECHANICAL PROPERTIES OF SOLIDS: Elastic behavior of solids, Stress and strain, Hooke's law, Stress-strain curve, Elastic moduli, Young's Modulus, Determination of Young's Modulus of the Material of a Wire, Shear Modulus, Bulk Modulus, Poisson's ratio, Elastic potential energy in a stretched wire, Applications of elastic behavior of materials.

MECHANICAL PROPERTIES OF FLUIDS: Pressure, Pascal's Law, Variation of Pressure with Depth, Atmospheric Pressure and Gauge Pressure, Hydraulic Machines, Archimedes' Principle, Streamline flow, Bernoulli's principle, Speed of Efflux, Torricelli's Law, Venturi- meter, Blood Flow and Heart Attack, Dynamic Lift, Viscosity, Variation of Viscosity of fluids with temperature, Stokes' Law, Reynolds number, Critical Velocity, Surface tension and Surface Energy, Angle of Contact, Drops and Bubbles, Capillary Rise, Detergents and Surface Tension.

THERMAL PROPERTIES OF MATTER: Temperature and heat, Measurement of temperature, Ideal-gas equation and absolute temperature, Thermal expansion, Specific heat capacity, Calorimetry, Change of state, Triple Point, Regelation, Latent Heat, Heat transfer Conduction, convection and radiation, Black body Radiation, Greenhouse Effect, Newton's law of cooling and its experimental verification.

THERMODYNAMICS: Thermal equilibrium, Zeroth law of thermodynamics, Heat, Internal Energy and work, First law of thermodynamics, Specific heat capacity, Specific heat capacity of

water, Thermodynamic state variables and equation of State, Thermodynamic processes, Quasi-

static process, Isothermal Process, Adiabatic Process, Isochoric Process, Isobaric process, Cyclic process, Heat engines, Refrigerators and heat pumps, Second law of thermodynamics, Reversible and irreversible processes, Camot engine, Camot's theorem.

KINETIC THEORY: Molecular nature of matter, Behaviour of gases, Boyle's Law, Charles' Law, Kinetic theory of an ideal gas, Pressure of an Ideal Gas, Kinetic interpretation of temperature, Law of equipartition of energy, Specific heat capacity, Monatomic Gases, Diatomic Gases, Polyatomic Gases, Specific Heat Capacity of Solids, Specific Heat Capacity of Water, Mean free path.

WAVES: Transverse and longitudinal waves, wave displacement relation in a progressive wave, amplitude and phase, wavelength and angular wave number, period, angular frequency and frequency, the speed of a traveling wave, the speed of a transverse wave on a stretched string, the speed of a longitudinal wave (speed of sound), the principle of superposition of waves, reflection of waves, standing waves, and normal modes, beats, Doppler effect - source moving & Observer stationary, an observer moving and source stationery, both observer and source are moving, applications of Doppler effect.