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KEAM - Syllabus

Kerala Engineering, Architecture, Medical Entrance Examination

Exam Date: 05 Aug 2021

Pen & Paper Mode

Updated On - June 19 2021 by Anusha Pachauri

Given below the complete syllabus for KEAM 2021. Candidate can check the important topics and subjects from the below-given section. The exam paper will consist of two papers i.e.

- Paper I: Chemistry and Physics
- Paper-II: Mathematics

Candidates must note that they have to appear for both papers if applied for engineering admission. For pharmacy, admission candidate has to appear in only 1 paper.

**Sets, Relations and Function**

Sets and their Representations, Finite and Infinite sets, Empty set, Equal sets, Subsets, Power set, Universal set, Venn Diagrams, Complement of a set, Operations on Sets (Union, Intersection and Difference of Set), Applications of sets, Ordered Pairs, Cartesian Product of Two Sets, Relations, Domain, Co-domain and Range, Functions, into, on to, one – one in to, one-one on to Functions, Constant Function, Identity Function, composition of Functions, Invertible Functions, Binary Operations.

**Complex Numbers**

Complex Numbers in the form a + ib, Real and Imaginary Parts of a Complex Number, Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane, Modulus and Argument of a Complex Number, Algebra of Complex Numbers, Triangle Inequality.

**Quadratic Equations**

The solution of a Quadratic Equation in the Complex Number System by (i) Factorization (ii) Using Formula, Relation between Roots and Coefficients, Nature of Roots, Formation of Quadratic Equations with given Roots, Equations Reducible to Quadratic Forms.

**Sequences and Series**

Sequence and Examples of Finite and Infinite Sequences, Arithmetic Progression (A.P), First Term, Common Difference, nth Term and sum of n terms of an A.P., Arithmetic Mean (A.M), Insertion of Arithmetic Means between any Two given Numbers; Geometric Progression (G.P), first Term, Common Ratio and nth term, Sum to n Terms, Geometric Mean (G.M), Insertion of Geometric Means between any two given Numbers.

**Permutations, Combinations, Binomial Theorem and Mathematical Induction**

Fundamental Principle of Counting, The Factorial Notation, Permutation as an Arrangement, Meaning of P(n, r), Combination, Meaning of C(n,r), Applications of Permutations and Combinations. Statement of Binomial Theorem, Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method, General and Middle Terms in Binomial Expansions, Properties of Binomial Coefficients, Binomial Theorem for any Index (without proof), Application of Binomial Theorem. The Principle of Mathematical Induction, simple Applications.

**Matrices and Determinants**

Concept of a Matrix, Types of Matrices, Equality of Matrices (only real entries may be considered), Operations of Addition, Scalar Multiplication and Multiplication of Matrices, Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only, Determinant of a Square Matrix, Minors and Cofactors; singular and non-singular Matrices, Applications of Determinants in (i) finding the Area of a Triangle (ii) solving a system of Linear Equations (Cramer’s Rule), Transpose, Adjoint and Inverse of a Matrix, Consistency and Inconsistency of a system of Linear Equations, Solving System of Linear Equations in Two or Three variables using Inverse of a Matrix (only up to 3X3 Determinants and Matrices)

**Linear Inequations**

Solutions of Linear Inequation in one variable and its Graphical Representation; solution of the system of Linear Inequations in one variable, Graphical solutions of Linear inequations in two variables, solutions of the system of Linear Inequations in two variables.

**Mathematical Logic and Boolean Algebra**

Statements, use of Venn Diagram in Logic, Negation Operation, Basic Logical Connectives and Compound Statements including their Negations.

**Trigonometric functions and Inverse Trigonometric functions**

Degree measures and Radian measure of positive and negative angles, the relation between degree measure and radian measure, the definition of trigonometric functions with the help of a unit circle, periodic functions, the concept of periodicity of trigonometric functions, the value of trigonometric functions of x.

**Introduction and Measurement**

Physics – Scope and excitement, Physics with science, society and technology – inventions, names of scientists and their fields, Nobel prize winners and topics, current developments in physical sciences and related technology. Units for measurement – systems of units, S.I units, conversion from other systems to S.I units. Fundamental and derived units. Measurement of length, mass and time, least count in measuring instruments (eg. vernier callipers, screw gauge etc), Dimensional analysis and applications, the order of magnitude, Accuracy and errors in measurement, random and instrumental errors, Significant figures and rounding off principles.

**Description of Motion in 1D**

Objects in motion in one dimension – Motion in a straight line, uniform motion – its graphical representation and formulae; speed and velocity – instantaneous velocity; ideas of relative velocity with expressions and graphical representations, Uniformly accelerated motion, position-time graph, velocity-time graph and formulae. Elementary ideas of calculus – differentiation and integration – applications to motion.

**Description of Motion in 2D and 3D**

Vectors and scalars, vectors in two and three dimensions, unit vector, addition and multiplication, resolution :of the vector in a plane, rectangular components, scalar and vector products. Motion in two dimensions – projectile motion, ideas of uniform circular motion, linear and angular velocity, the relation between centripetal acceleration and angular speed.

**Laws of Motion**

Force and inertia, the first law of motion, momentum, the second law of motion, forces in nature, impulse, the third law of motion, conservation of linear momentum, examples of variable mass situation, rocket propulsion, the equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication. Inertial and non-inertial frames (elementary ideas), Dynamics of uniform circular motion – centripetal and centrifugal forces, examples: banking of curves and centrifuge.

**Work, Power and Energy**

Work done by a constant force and by a variable force, units of work – Energy – kinetic and potential forms, power, work-energy theorem. Elastic and inelastic collisions in one and two dimensions. Gravitational potential energy and its conversion to kinetic energy, spring constant, the potential energy of a spring, Different forms of energy, mass-energy equivalence (elementary ideas), conservation of energy, conservative and non-conservative forces.

**Laws of chemical combination**

Law of conservation of mass. Law of definite proportion. Law of multiple proportions. Gay-Lussac’s law of combining volumes. Dalton’s atomic theory. Mole concept. Atomic, molecular and molar masses. Chemical equations. Balancing and calculation based on chemical equations.

**Atomic structure**

Fundamental particles, Rutherford model of the atom, Nature of electromagnetic radiation, The emission spectrum of the hydrogen atom. Bohr model of the hydrogen atom. Drawbacks of Bohr model. Dual nature of matter and radiation. de Broglie relation. Uncertainty principle. Wave function (mention only). Atomic orbitals and their shapes (s, p and d orbitals only). Quantum numbers. Electronic configurations of elements. Pauli’s exclusion principle. Hund’s rule. Aufbau principle.

**Bonding and Molecular Structure**

Kossel and Lewis approach of bonding. Ionic bond, the covalent character of an ionic bond, Lattice energy. Born-Haber cycle. Covalent bond. Lewis structure of covalent bond. Concept of orbital overlap. VSEPR theory and geometry of molecules. The polarity of a covalent bond. Valence bond theory and hybridization (sp, sp^{2}, sp^{3}, dsp^{2}, d^{2}sp^{3} and sp^{3}d^{2}). Resonance. Molecular orbital method. Bond order. Molecular orbital diagrams of homodiatomic molecules. Bond strength and magnetic behaviour. Hydrogen bond. Coordinate bond. Metallic bond.

**Gaseous state**

Boyle’s law. Charles’ law. Avogadro’s hypothesis. Graham’s law of diffusion. The absolute scale of temperature. Ideal gas equation. Gas constant and its values. Dalton’s law of partial pressure. Aqueous tension. Kinetic theory of gases. Deviation of real gases from ideal behaviour. Intermolecular interaction, van der Waals equation. Liquefaction of gases. Critical temperature.

**Liquid state**

Properties of liquids. Vapour pressure and boiling point. Surface tension. Viscosity.

For covering the more topics of KEAM syllabus, candidates are advised to refer to class XII Books.

Candidate must be aware of the exam pattern to get an idea of the exam paper. Given below the Section wise distribution of marks:

Paper | Subjects | Time Allotted | Number of Questions | Total Marks |
---|---|---|---|---|

I | Physics and Chemistry | 180 minutes | 60 | 240 |

II | Mathematics | 180 minutes | 60 | 240 |

Total |
| 180 minutes | 120 questions | 480 marks |

Candidate can go through the below-given books to prepare for KEAM 2021 entrance exam.

- 16 Years’ (2000-2015) Solved Papers: Kerala Engineering Entrance Exam.
- Topic-wise Solved Papers for Engineering Entrance 2nd Edition.
- 16 years Solved Papers Kerala CEE Engineering Entrance Exam.
- NCERT Physics, Chemistry, Mathematics (PCM) Books Set.

Follow the below given KEAM 2021 Preparation Tips to score well in the exam:

- Candidates must go through the whole syllabus to avoid last moment burden.
- Applicants are advised to make notes.
- Revise the hard topics daily.
- Solve previous year papers and mock test to get an idea of the exam.
- Analyse the KEAM 2021 exam pattern to know about which topic has maximum weightage.

01 Jun 2021

26 Jun 2021

05 Aug 2021

₹ 700

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