Question Banks Readily Available for the following Subjects. CBSE Class 12th standard subject for all groups in both tamil and english medium. Class 10th Standard all subjects. [ except tamil and english subjects ]. Buy both medium and prepare same set of question paper with single click. Our Database includes CBSE Class 10 and Class 12 subjects.

**1. Relations and Functions**

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

**2. Inverse Trigonometric Functions**

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

1058Downloads

**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 and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

**2. Determinants**

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

322Downloads

**1. Continuity and Differentiability**

Continuity and differentiability, derivative of composite functions, chain rule, derivatives 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. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

**2. Applications of Derivatives**

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, 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 real-life situations).

**3. 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 of the following types and problems based on them.

\(\int { \frac { dx }{ { x }^{ 2 }\pm { a }^{ 2 } } \int { \frac { dx }{ \sqrt { { x }^{ 2 }\pm { a }^{ 2 } } } } \int { \frac { dx }{ \sqrt { { a }^{ 2 }-{ x }^{ 2 } } } } } ,\int { \frac { dx }{ { ax }^{ 2 }+bx+c } } ,\int { \frac { dx }{ \sqrt { { ax }^{ 2 }+bx+c } } } \)

\(\int { \frac { px+q }{ { ax }^{ 2 }+bx+c } } dx,\int { \frac { px+q }{ \sqrt { { ax }^{ 2 }+bx+c } } } dx,\int { \sqrt { { a }^{ 2 }\pm { x }^{ 2 } } } dx,\sqrt { { x }^{ 2 }-{ a }^{ 2 } } dx\)

\(\int { \sqrt { { ax }^{ 2 }+bx+c } } dx,\int { (px+q) } \sqrt { { ax }^{ 2 }+bx+c } dx\)

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

4. **Applications of the Integrals**

Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

**5. Differential Equations **

Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type

368Downloads

**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, scalar triple 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.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.

1748Downloads

**1. Linear Programming**

introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions(bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

828Downloads

**1. Probability**

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

506Downloads

Introduction-Types of Relations-Types of Functions-Composition of Functions and Invertible Function-Binary Operations

1058Downloads

Introduction-Basic Concepts-Properties of Inverse Trigonometric Functions

1426Downloads

Introduction-Matrix-Types of Matrices-Operations on Matrices-Transpose of a Matrix-Symmetric and Skew-SymmetricMatrices-Elementary Operation Transformation of a Matrix-Invertible Matrices

368Downloads

Introduction-Determinant-Properties of Determinants-Area of a Triangle-Minors and Cofactors-Adjoint and Inverse of a Matrix-Applications of Determinants and Matrices

552Downloads

Introduction-Continuity-Differentiability-Exponential and Logarithmic Functions-Logarithmic Differentiation-Derivatives of Functions in Parametric Forms-Second Order Derivative-Mean Value Theorem

1472Downloads

Introduction-Rate of Change of Quantities-Increasing and Decreasing Functions-Tangents and Normals-Approximations-Maxima and Minima

1196Downloads

Introduction-Integration as an Inverse Process of Differentiation-Methods of Integration-Integrals of some Particular Functions-Integration by Partial Fractions-Integration by Parts-Definite Integral-Fundamental Theorem of Calculus-Evaluation of Definite Integrals by Substitution-Some Properties of Definite Integrals

414Downloads

Introduction-Area under Simple Curves-Area between Two Curves

1104Downloads

Introduction-Basic Concepts-General and Particular Solutions of a Differential Equation-Formation of a Differential Equation whose General Solution is given-Methods of Solving First order, First Degree Differential Equations

1012Downloads

Introduction-Some Basic Concepts-Types of Vectors-Addition of Vectors-Multiplication of a Vector by a Scalar-Product of Two Vectors

644Downloads

Introduction-Direction Cosines and Direction Ratios of a Line-Equation of a Line in Space-Angle between Two Lines-Shortest Distance between Two Lines-Plane-Coplanarity of Two Lines-Angle between Two Planes-Distance of a Point from a Plane-Angle between a Line and a Plane

1196Downloads