Admission Test for IcfaiTech (ATIT ICFAI)

Sets and their representations

Sets and their representations

Union

Intersection and complements of sets

Their algebraic properties

Relations

Equivalence relations

Mappings

One-one into and onto mappings ralation

Composition of mappings into ralation

Complex numbers

Complex numbers in the form a+ib and their representation in a plane

Argand diagram

Algebra of complex numbers

Cube roots of unity

Triangle inequality

Matrices and determinants

Determinants and matrices of order two and three

Properties of determinants

Evaluation of determinants

Area of triangles using determinants

Addition multiplication of matrices

Adjoint and inverse of matrix

Quadratic equations

Relation between roots and co-efficients

Nature of roots

Symmetric functions of roots

Equations reducible to quadratic equations

Application to practical problems

Permutations and combinations

Fundamental principle of counting

Permutation as an arrangement and combination as selection

Meaning of p(n,r) and c(n,r)

Simple applications

Binomial theorem and its applications - mathematical induction and its applications

Binomial theorem for a positive integral index

General term and middle term

Binomial theorem for any index

Properties of binomial co-efficients

Simple applications for approximations

Sequences and series

Arithmetic

Geometric and harmonic progressions

Insertion of arithmetic geometric and harmonic means between two given numbers

Relation between a.m. g.m. and h.m special series

Sn, sn2, sn3

Arithmetico and geometric series

Exponential and logarithmic series

Differential calculus

Polynomials

Rational

Trigonometric

Logarithmic and exponential functions

Inverse functions

Graphs of simple functions

Limits

Continuity

Differentiation of the sum

Difference

Product and quotient of two functions

Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions

Rational, trigonometric, inverse trigonometric, exponential and logarithmic functions

Logarithmic

Exponential

Composite and implicit functions

Derivatives of order up to two

Applications of derivatives

Rate of change of quantities

Monotonic

Increasing and decreasing functions

Maxima and minima of functions of one variable

Tangents and normals

Rolle's and Lagrange's mean value theorems

Integral calculus

Integral as an anti-derivative

Fundament alintegrals involving algebraic

Trigonometric

Exponential and logarithmic functions

Integration by substitution

By parts and by partial fractions

Integration using trigonometric identities

Integralas limit of a sum

Properties of definite integrals

Evaluation of definite integrals

Determining areas of the regions bounded by simple curves

Differential equations

Ordinary differential equations

Their order and degree

Formation of differential equations

Solution of differential equations by the method of separation of variables

Solution of differential equations by the method of separations of variables,solution of homogeneous and linear differential equations of the type : dy/dx+p(x)y=q(x)

Two dimensional geometry

Recall of cartesian system of rectangular co-ordinates in a plane

Distance formula

Area of a triangle

Condition for the collinearity of three points and section formula

Translation of axes

Slope of a line

Parallel and perpendicular lines

Intercepts of a line on the coordinate axes

Two dimensional geometry - the straight line and pair of straight lines

Various forms of equations of a line

Intersection of lines

Angles between two lines

Conditions for concurrence of three lines

Distance of a point from a line equations of internal and external bisectors of angles between two lines

Coordinates of centroid

Orthocentre and circumcentre of a triangle

Equation of family of lines passing through the point of intersection of two lines

Homogeneous equation of second in x and y

Angles between a pair of lines through the origin

Combined equation of he bisectors of the angles between a pair of lines

Condition for the general second degree equation to represent a pair of lines

Point of intersection and angle between two lines

Two dimensional geometry - circles and family of circles

Standard form of equation of a circle

General form of the equation of a circle

Its radius and centre

Equation of a circle in the parametric form

Equation of a circle when the end points of a diameter are given

Points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle

Length of the tangent

Equation of the tangent

Equation of a family of circles through the intersection of two circles

Two dimensional geometry - conic sections

Sections of cones

Equations of conic sections of parabola, ellipse and hyperbola in standard forms

Condition for y = mx + c to be a tangent and point(s) of tangency

Three dimensional geometry

Coordinates of a point in space

Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin

Section formula

Section formula and direction cosines angle between two intersecting lines

Skew lines

The shortest distance between them and its equation

Intersection of a line and a plane

Coplanar lines

Its centre and radius

Diameter form of the equation of a sphere

Vector algebra

Vectors and scalars

Addition of vectors

Scalar and integral calculus

Scalar and vector products

Scalar and vector triple product

Measures of central tendency and dispersion

Calculation of mean

Median and mode of grouped and ungrouped data

Calculation of standard deviation

Variance and mean deviation for grouped and ungrouped data

Probability

Conditional probability

Bayes' theorem

Probability distribution of a random variate

Binomial and poisson distributions and their properties

Trigonometry

Inverse trigonometric functions and their properties

Properties of triangles, including centroid, incentre, circum- centre and orthocentre, solution of triangles.

Heights and distances

Statics

Introduction

Basic concepts and basic laws of mechanics

Force

Resultant of forces acting at a point

Parallelogram law of forces

Resolved parts of a force

Equilibrium of a particle under three concurrent forces

Triangle law of forces and its converse

Lami's theorem and its converse

Like parallel forces

Unlike parallel forces

Couple and its moment

Dynamics

Speed and velocity

Average speed dynamics

Instantaneous speed dynamics

Acceleration and retardation

Resultant of two velocities

Motion of a particle along a line is moving with constant acceleration

Motion under gravity

Laws of motion and projectile motion