Sunday, November 30, 2014

JEE Main 2015 Mathematics Syllabus

JEE MAIN 2015 SYLLABUS FOR MATHEMATICS:




1 Sets, Relations And Functions

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations,functions;.
One-one, into and onto functions, composition of functions


2 Complex Numbers and Quadratic Equations

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality,
Quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.

3 Matrices And Determinants

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

4 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

5 Mathematical Induction

Principle of Mathematical Induction and its simple applications

6 Binomial Theorem And Its Simple Applications

Binomial theorem for a positive integral index, general term and middle term,properties of Binomial coefficients and simple applications

7 Sequences And Series

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers.
Relation between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric progression

8 Limit, Continuity And Differentiability

Real valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions.
Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions.
Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two.
Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of
quantities, monotonic increasing and decreasing functions,
Maxima and minima of functions of one variable, tangents and normals

9 Integral Calculus

Integral as an anti derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.
Integral as limit of a sum. Fundamental Theorem of Calculus.
Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form

Evaluation of simple integrals of the type:


10 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 homogeneous and linear differential
equations of the type

11 Coordinate Geometry

Cartesian system of rectangular coordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

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.

Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, 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 a circle, equation of
the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

12 Three Dimensional Geometry

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a
plane, coplanar lines

13 Vector Algebra

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

14 Statistics And Probability

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

15 Trigonometry

Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances

16 Mathematical Reasoning

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction,
converse and contrapositive

Saturday, November 29, 2014

JEE Main 2015 Information Booklet

Submission of Online Application Form: 07.11.2014 – 18.12.2014
Joint Entrance Examination (Main) - 2015
I N F O R M A T I O N I N F O R M A T I O N B U L L E T I N B U L L E T

http://jeemain.nic.in/webinfo/pdf/JEE_Main_Bulletin%202015.pdf

JEE 2014 Advanced Mathematics Paper



49. From a point P(lambda, lambda, lambda), perpendiculars PQ and PR are drawn respectively on the lines
y = x,  z = 1 and y  = -x and  z = − 1. If P is such that ∠QPR is a right angle, then the possible
value(s) of lambda is (are)
A) SQRT (2) B) 1         C) -1           D) − SQRT (2)


JEE 2014 Advanced Paper Analysis

Saturday, April 20, 2013

JEE (Advanced) 2013 Mathematics Syllabus



Mathematics
Algebra: Algebra of complex numbers,
addition, multiplication, conjugation, polar
representation, properties of modulus and
principal argument, triangle inequality, cube
roots of unity, geometric interpretations.
Quadratic equations with real coefficients,
relations between roots and coefficients,
formation of quadratic equations with given
roots, symmetric functions of roots.
Arithmetic, geometric and harmonic
progressions, arithmetic, geometric and
harmonic means, sums of finite arithmetic and
geometric progressions, infinite geometric
series, sums of squares and cubes of the first n
natural numbers.
Logarithms and their properties.

Permutations and combinations, Binomial
theorem for a positive integral index, properties
of binomial coefficients.

Matrices as a rectangular array of real
numbers, equality of matrices, addition,
multiplication by a scalar and product of
matrices, transpose of a matrix, determinant of
a square matrix of order up to three, inverse of
a square matrix of order up to three, properties
of these matrix operations, diagonal, symmetric
and skew-symmetric matrices and their
properties, solutions of simultaneous linear
equations in two or three variables.

Addition and multiplication rules of probability,
conditional probability, Bayes Theorem,
independence of events, computation of
probability of events using permutations and
combinations.

Trigonometry: Trigonometric functions, their
periodicity and graphs, addition and subtraction
formulae, formulae involving multiple and submultiple angles, general solution of
trigonometric equations.
Relations between sides and angles of a
triangle, sine rule, cosine rule, half-angle
formula and the area of a triangle, inverse
trigonometric functions (principal value only).

Analytical geometry (2 dimensions):

Cartesian coordinates, distance between two
points, section formulae, shift of origin.
Equation of a straight line in various forms,
angle between two lines, distance of a point
from a line; Lines through the point of
intersection of two given lines, equation of the
bisector of the angle between two lines,
concurrency of lines; Centroid, orthocentre,
incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations
of tangent, normal and chord.
Parametric equations of a circle, intersection of
a circle with a straight line or a circle, equation
of a circle through the points of intersection of
two circles and those of a circle and a straight
line.

Equations of a parabola, ellipse and hyperbola
in standard form, their foci, directrices and
eccentricity, parametric equations, equations of
tangent and normal.
Locus Problems.

Analytical geometry (3 dimensions):

Direction cosines and direction ratios, equation
of a straight line in space, equation of a plane,
distance of a point from a plane.

Differential calculus: Real valued functions of
a real variable, into, onto and one-to-one
functions, sum, difference, product and
quotient of two functions, composite functions,
absolute value, polynomial, rational,
trigonometric, exponential and logarithmic
functions.

Limit and continuity of a function, limit and
continuity of the sum, difference, product and
quotient of two functions, L’Hospital rule of
evaluation of limits of functions.

Even and odd functions, inverse of a function,
continuity of composite functions, intermediate
value property of continuous functions.
Derivative of a function, derivative of the sum,
difference, product and quotient of two
functions, chain rule, derivatives of polynomial,
rational, trigonometric, inverse trigonometric,
exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up
to order two, geometrical interpretation of the
derivative, tangents and normals, increasing
and decreasing functions, maximum and
minimum values of a function, Rolle’s Theorem
and Lagrange’s Mean Value Theorem

Integral calculus: Integration as the inverse
process of differentiation, indefinite integrals of
standard functions, definite integrals and their
properties, Fundamental Theorem of Integral
Calculus.

Integration by parts, integration by the methods
of substitution and partial fractions, application
of definite integrals to the determination of
areas involving simple curves.

Formation of ordinary differential equations,
solution of homogeneous differential equations,
separation of variables method, linear first
order differential equations.

Vectors: Addition of vectors, scalar
multiplication, dot and cross products, scalar
triple products and their geometrical
interpretations.

Monday, April 15, 2013

Eulerian form of a complex number





Eulerian form of a complex number

    eθ  = cosθ + i sinθ  and e = cos θ  - i sin θ

These two are called Eulerian forms of a complex number.

Monday, April 30, 2012

Using Logarithmic Tables

Using Logarithmic Tables

Using Logarithmic Tables

Express the given number "n" in the form of m * 10p       where 1≤m<10 and p is an integer(positive or negative whole number).
 
For example number 2 is expressed as 2*100
 
log n become equal to p + log m
 
log 2 becomes equal to 0 + log 2
 
p is called the characeristic and log m is called the mantissa. Mantissa is read from the logarithmic tables.
 
Logarithmic tables are show three sets of columns
i) the first set of column on the extreme left contains numbers from 10 to 99.
ii) in the seocnd set there 10 columns headed by 0,1,2,...,9
iii) after this, in the third set there 9 more columns headed by 1,2,3...9. These are known as mean differences.
 
As 1≤m<10, the mantissa is for a number between 1 and 10. Hence the interpretation of the first set of column in the table is 1.0 to 9.9, If you add the digit in the second set one more digit is added to the number. Which mean 1.0 becomes 1.01. If we add a digit in the third column on more digit is added to the number. Which means 1.01 becomes 1.011.
 
Hence log 2 = 0 + 0.3010 = 0.3010
 
How to see its antilogarithm.
 
Antilogaritm tables are written from .00. If mantissa of a logarithm is .00, then antilogarithm is 1.000
Antilogarithm of .3010 is equal to 2.000
As the characteristic of the number is 0 the number is 2.0*100. Which is equal to 2.
 
Suppose the problem is to find 2^(1/6). It is 2 to the power (1/6).
 
When we take logarithms, it becomes (1/6)* log 2 which is equal to (1/6)*(0.3010) = 0.0617 (rounded)
 
What is antilogarithm of 0.0617 = 1.153*100. = 1.153
 
So the answer of 2^(1/6) is equal to 1.153.