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All Subjects - PCM
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Overview
NCERT Maths Class 12 Chapters are mentioned below:
Chapter 1 Relations and Functions
Chapter 2 Inverse Trigonometric Functions
Chapter 3 Matrices
Chapter 4 Determinants
Chapter 5 Continuity and Differentiability
Chapter 6 Application of Derivatives
Chapter 7 Integrals
Chapter 8 Application of Integrals
Chapter 9 Differential Equations
Chapter 10 Vector Algebra
Chapter 11 Three Dimensional Geometry
Chapter 12 Linear Programming
Chapter 13 Probability
TERM I MCQ TYPES ( 2021 -2022)
Unit-I: Relations and Functions 1. Relations and Functions Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. 2. Inverse Trigonometric Functions Definition, range, domain, principal value branch. Unit-II: Algebra 1. Matrices Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices, Invertible matrices; (Here all matrices will have real entries). 2. Determinants Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. Unit-III: Calculus 1. Continuity and Differentiability Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. 2. Applications of Derivatives Applications of derivatives: increasing/decreasing functions, tangents and normals, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations). Unit-V: Linear Programming 1. Linear Programming Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
TERM II MCQ TYPES (2021 -2022)
Unit-III: Calculus
1. Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by
partial fractions and by parts, Evaluation of simple integrals Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation
of definite integrals.
2. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, parabolas; area of circles /ellipses
(in standard form only) (the region should be clearly identifiable).
3. Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. Solution of
differential equations by method of separation of variables, solutions of homogeneous differential
equations of first order and first degree of the type: 𝑑𝑦
𝑑𝑥
= 𝑓(y/x). Solutions of linear differential equation
of the type:
dy
dx + py = q, where p and q are functions of x or constant.
Unit-IV: Vectors and Three-Dimensional Geometry
1. Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a
vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point,
negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar,
position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation,
properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.
2. Three - dimensional Geometry
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation
of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation
of a plane. Distance of a point from a plane.
Unit-VI: Probability
1. Probability
Conditional probability, multiplication theorem on probability, independent events, total probability,
Bayes’ theorem, Random variable and its probability distribution.
Free Courses
Chemistry
The CBSE syllabus for Class 12 Chemistry has both Theory and Practical. The Theory Exam is conducted for 70 marks whereas the Practical Exam is held for 30 marks. In this article, we will cover the CBSE Class 12 Chemistry syllabus of both Theory and Practical.
Physics
Unit 1 – Electrostatics
Unit 2 – Current Electricity
Unit 3 – Magnetic Effects of Electric Current and Magnetism
Unit 4 – Electromagnetic Induction and Alternating Currents
Unit 5 – Electromagnetic Waves
Unit 6 – Optics
Unit 7 – Dual Nature of Radiation and Matter
Unit 8 – Atoms and Nuclei
Unit 9 – Electronic Devices
Term 1 Syllabus
Unit I: Electrostatics
Chapter–1: Electric Charges and Fields Electric Charges; Conservation of charge, Coulomb's law-force between two-point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss's theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet
Chapter–2: Electrostatic Potential and Capacitance Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two-point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.
Unit II: Current Electricity
Chapter–3: Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm's law, electrical resistance, V-I characteristics (linear and nonlinear), electrical energy and power, electrical resistivity and conductivity; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff's laws and simple applications, Wheatstone bridge, metre bridge(qualitative ideas only). Potentiometer - principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell (qualitative ideas only)
Unit III: Magnetic Effects of Current and Magnetism
Chapter–4: Moving Charges and Magnetism Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long straight wire. Straight and toroidal solenoids (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields. Force on a current-carrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.
Chapter–5: Magnetism and Matter Current loop as a magnetic dipole and its magnetic dipole moment, magnetic dipole moment of a revolving electron, bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic elements.
Unit IV: Electromagnetic Induction and Alternating Currents
Chapter–6: Electromagnetic Induction Electromagnetic induction; Faraday's laws, induced EMF and current; Lenz's Law, Eddy currents. Self and mutual induction.
Chapter–7: Alternating Current Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits. AC generator and transformer.
Term 2 Syllabus
Unit V: Electromagnetic waves
Chapter–8: Electromagnetic Waves Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
Unit VI: Optics
Chapter–9: Ray Optics and Optical Instruments Ray Optics: Refraction of light, total internal reflection and its applications, optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lensmaker's formula, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Chapter–10: Wave Optics Wave optics: Wave front and Huygen's principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light, diffraction due to a single slit, width of central maximum
Unit VII: Dual Nature of Radiation and Matter
Chapter–11: Dual Nature of Radiation and Matter Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation-particle nature of light. Experimental study of photoelectric effect Matter waves-wave nature of particles, de-Broglie relation
Unit VIII: Atoms and Nuclei
Chapter–12: Atoms Alpha-particle scattering experiment; Rutherford's model of atom; Bohr model, energy levels, hydrogen spectrum.
Chapter–13: Nuclei Composition and size of nucleus Nuclear force Mass-energy relation, mass defect, nuclear fission, nuclear fusion.
Unit IX: Electronic Devices
Chapter–14: Semiconductor Electronics: Materials, Devices and Simple Circuits Energy bands in
conductors, semiconductors and insulators (qualitative ideas only) Semiconductor diode - I-V
characteristics in forward and reverse bias, diode as a rectifier; Special purpose p-n junction diodes:
LED, photodiode, solar cell.
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