IIT JEE Mathematics Study Plan 1. Sets

R.D. Sharma, Objective Mathematics, Chapter 1
Video Lectures


1.1 Sets
1.2 Description of a set
1.3 Types of sets
1.4 Subsets
1.5 Universal set
1.6 Power set
1.7 Venn diagrams
1.8 Operations on sets
1.9 Laws of algebra of sets
1.10 More results on operations on sets
1.11 Some important results on number of elements in sets

Sets Chapter - Study Plan

(1 May to 7 May)

Day 1 ( 1 May)

1.1 Sets
1.2 Description of a set
1.3 Types of sets
1.4 Subsets
1.5 Universal set
1.6 Power set
1.7 Venn diagrams

       Video Lectures - Sets 

Day 2  (2 May)

1.8 Operations on sets

___________________

___________________

      More Video Lectures on 1.8 Operations on Sets

1.9 Laws of algebra of sets

Day 3  (3 May)

1.10 More results on operations on sets

Day 4  (4 May)

1.11 Some important results on number of elements in sets

Day 5

Obj. Exercises 1 to 27

Day 6
Fill in the blanks 1 to 5
True/False 1 to 13

Day 7
Practice Exercises 1 to 21


For reviewing the concepts, formulas, and theorems of the chapters visit
Ch. 1. Sets - Concept Review


Updated   1 May 2016,  10 Apr 2016,  7 May 2015

IIT JEE Mathematics Study Plan 11. Matrices

11.1 Matrix
11.2 Types of matrices
11.3 Equality of matrices
11.4 Algebra of matrices
11.5 Multiplication of a matrix by a scalar (scalar multiplication)
11.6 Subtraction of matrices (definition)
11.7 Multiplication of matrices
11.8 Transpose of a matrix
11.9 Symmetric and skew symmetric matrices
11.10 Determinants
11.11 Singular matrix
11.12 Adjoint of a matrix
11.13 Inverse of a matrix
11.14 elementary transformations of elementary operations of a matrix
11.15 Orthogonal matrix
11.16 Submatrix
11.17 Rank of a matrix
11.18 Some theorems on rank of a matrix
11.19 Equivalent matrices
11.20 Echelon form of a matrix
11.21 System of simultaneous linear equations
11.22 Solution of a non-homogeneous system of linear equations
11.23 Rank method
11.24 Solution of a homogeneous system of linear equations


Study Plan


Day 1

11.1 Matrix
11.2 Types of matrices
11.3 Equality of matrices
11.4 Algebra of matrices

Day 2

11.5 Multiplication of a matrix by a scalar (scalar multiplication)
11.6 Subtraction of matrices (definition)
11.7 Multiplication of matrices

Day 3
11.8 Transpose of a matrix
Objective Types questins 1 to 6,
Practice Exercises 1 to 10

Day 4

11.9 Symmetric and skew symmetric matrices
Ex 1 to 8


Day 5

11.10 Determinants
11.11 Singular matrix
11.12 Adjoint of a matrix

Day 6

11.13 Inverse of a matrix
11.14 elementary transformations of elementary operations of a matrix

Day 7
11.15 Orthogonal matrix
11.16 Submatrix
11.17 Rank of a matrix
11.18 Some theorems on rank of a matrix

Day 8
11.19 Equivalent matrices
11.20 Echelon form of a matrix
Objective Type Exercises 8 to 20

Day 9
11.21 System of simultaneous linear equations
11.22 Solution of a non-homogeneous system of linear equations
11.23 Rank method


Day 10

11.24 Solution of a homogeneous system of linear equations
Revision of concepts in the chapter



Day 11
OTE 21 to 40

Day 12
OTE 41 to 60

Day 13
OTE 61 to 80

Day 14
OTE 81 to 91
Fill in the blanks 1 to 17

Day 15

True/false questions 1 to 30



Day 16
Practice Exercises 11 to 20

Day 17
Practice Exercises 21 to 33


Day 18
Revision - Theory, Formulas and Difficult Problems

Day 19
Revision - Theory, Formulas and Difficult Problems


Day 20
Revision - Theory, Formulas and Difficult Problems


Updated 1 May 2016,  7 Nov 2008

24. Increasing and Decreasing Functions - Study Plan

Sections in the Chapter

1 Increasing and Decreasing Functions - Definitions

2 Necessary and sufficient conditions for monotonicity of functions

3 Properties of monotonic functions

Study Plan

Day 1

1 Increasing and Decreasing Functions - Definitions

2 Necessary and sufficient conditions for monotonicity of functions

3 Properties of monotonic functions

Day 2

Illustrative Objective Type Examples: 1 to 15

Day 3

Objective Type Exercise: 1 to 20

Day 4
O.T.E.: 21 to 38

Day 5 Fill in the blanks type exercise 1 to 8
Practice Exercise 1 to 20

Revision period

Day 6
Concept review

Day 7
Formula review

Day 8
Difficult problem review

Day 9 and 10
Test paper problems



Revision Facilitator


Try to recollect relevant points on the topic.

If required right click on the topic and click on open in a new window to read the relevant material.

Close the window and come back.


1 Increasing and Decreasing Functions - Definitions

2 Necessary and sufficient conditions for monotonicity of functions

3 Properties of monotonic functions


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JEE Main Mathematics Study Plan Chapter 3. Functions

R.D. Sharma Objective Mathematics

3.1 Function
3.2 Domain, Co-Domain and range of a function
3.3 Description of a function
3.4 Equal function
3.5 Number of functions
3.6 Function as a relation
3.7 Kinds of functions
3.8 Composition of functions
3.9 Properties of composition of functions
3.10 Inverse of an element
3.11 Inverse of a function
3.12 Properties of inverse of a function

Study Plan

5 days main study - 5 days revision

Main study period 1 hour each day

Day 1

3.1 Function
3.2 Domain, Co-Domain and range of a function
3.3 Description of a function
3.4 Equal function


Day 2
3.5 Number of functions
3.6 Function as a relation
3.7 Kinds of functions
3.8 Composition of functions

Day 3


3.9 Properties of composition of functions
3.10 Inverse of an element
3.11 Inverse of a function
3.12 Properties of inverse of a function

Day 4
Objective Type Exercises 1 to 20

Revision Period 30 minutes each day

Day 5
O.T.E. 21 to 40

Day 6
O.T.E. 41 to 53


Day 7
Practice Exercise 1 to 20

33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions - Revision Facilitator

Sections in the chapter


33.1 Introduction
33.2 Some basic formulae
33.3 Domain and range of trigonometrical functions
33.4 Sum and difference formulae
33.5 Sum and difference into products
33.6 Product into sum or difference
33.7 T-ratios of the sum of three or more angles
33.8 Values of trigonometrical ratios some important angles and some important results.
33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.
33.10 Maximum and minimum values of trigonometrical functions

Study Plan


Day 1

33.1 to 33.4

33.1 Introduction
33.2 Some basic formulae
33.3 Doman and range of trigonometrical functions
33.4 Sum and difference formulae

Do objective type exercises 58,

Day 2

33.5 Sun and difference into products
33.6 product into sum and difference

Do objective type exercises 84,91, 92, 104, 115,

Day 3

33.7 T-ratios of the sum of three or more angles

Do objective type exercises 39, 44, 106, 113, 117,

Day 4

33.8 Values of trigonometric ratios of some important angles and some important results

Do objective type exercises 1,2,3,5,6,7,8,9,10,11

Day 5

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A

Do objective type exercises 12,13,14,15,16,17,19,20,21,22

Day 6

33.10 maximum and minimum values of trigonometrical functions

O.T.E.: 4,18,23-30

Day 7

O.T.E.: 31 to 50

Day 8

O.T.E.: 51 to 70

Day 9
O.T.E.: 71 to 90



Day 10
O.T.E.: 91 to 110

Revision Period

Day 11
O.T.E.: 111 to 120



Day 12
O.T.E.: 121 to 130


Day 13
O.T.E.: 131 to 140


Day 14
O.T.E.: 141 to 148


Day 15
Fill in the blanks type exercise: 1 to 10


Day 16
Fill in the blanks type exercise: 11 to 20


Day 17
Fill in the blanks type exercise: 21 to 30


Day 18
Fill in the blanks type exercise: 31 to 36


Day 19
True/false type exercise: 1 to 12


Day 20
Fill in the blanks type exercise: 13 to 25

Day 21
Practice Exercise: 1 to 10

Day 22
Practice Exercise: 11 to 20

Day 23
Practice Exercise: 21 to 32

Day 24
Formula Revision

Day 25
Formula Revision





Revision facilitator


33.1 Introduction
33.2 Some basic formulae
33.3 Domain and range of trigonometrical functions
33.4 Sum and difference formulae
33.5 Sum and difference into products
33.6 Product into sum or difference
33.7 T-ratios of the sum of three or more angles
33.8 Values of trigonometrical ratios some important angles and some important results.
33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.
33.10 Maximum and minimum values of trigonometrical functions

IIT JEE Mathematics Study Guide Ch.34 Properties of Triangles and circles connected with them - Revision Facilitator

Recollect and see how many things do you remember

34.1 Introduction
34.2 Sine rule
34.3 Cosine formulae
344 Projection formulae
34.5 Trigonometrical ratios of half of the angles of a triangle
34.6 Area of a triangle
34.7 Napier’s analogy
34.8 Circumcircle of a triangle
34.9 Inscribed circle or incircle of a triangle
34.10 Escribed circles of a triangle
34.11 Orthocentre and its distances from the angular points of a triangle
34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
34.13 Area of a cyclic quadrilateral
34.14 Ptolemy’s theorem
34.15 Circum-radius of a cyclic quadrilateral


Study Plan

Day 1

Study sections 34.1 to 34.5

34.1 Introduction
34.2 Sine rule
34.3 Cosine formulae
34.4 Projection formulae
34.5 Trigonometrical ratios of half of the angles of a triangle






Day 2

Study Sections 34.6, 34.7, 34.8, 34.9,

34.6 Area of a triangle
34.7 Napier’s analogy
34.8 Circumcircle of a triangle
34.9 Inscribed circle or incircle of a triangle



Attempt Objective Type Exercises 1 to 10


Day 3

34.10, 34.11

34.10 Escribed circles of a triangle
34.11 Orthocentre and its distances from the angular points of a triangle



Attempt objective type exercises 11 to 20


Day 4

Study 34.12 to 34.15

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
34.13 Area of a cyclic quadrilateral
34.14 Ptolemy’s theorem
34.15 Circum-radius of a cyclic quadrilateral





Attempt obj type exercises 21 to 30.


Day 5

Attempt obj type exercises 31 to 45.

Day 6

Attempt obj type exercises 46 to 60.

Day 7

Attempt obj type exercises 61 to 75.

Day 8

Attempt obj type exercises 76 to 90.

Day 9

Attempt fill in the blanks 1 to 15.

Day 10

Attempt fill in the blanks 16 to 31.

Day 11

Practice Exercise 1 to 21

Days 12 to 20

Revision

Ch. 37 Solution of Triangles - Revision Facilitator

Sections in the Chapter R D Sharma

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Study Plan

Day 1

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results


Day 2

Objective Type Exercises 1 to 20

Day 3
Revision











37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

a. Right angled triangle - orthocentre
b. Distance of midpoint of the hypotenuse of a right angled triangle from the vertices of the triangle.
c. Relation between mid-point of a right angled triangle and its circumcentre

Ch. 38 Heights and distances - Revision Facilitator

Sections in the chapter R D Sharma


38.1 Angle of elevation and depression of a point
38.2 Some useful results

Study Plan

Day 1

38.1 Angle of elevation and depression of a point
38.2 Some useful results

Day 2

Objective Type Exercises 1 to 20

IIT JEE Study Guide 2. Cartesian Product of Sets and Relations

Objective Mathematics by R D Sharma

Contents

2.1 Cartesian product of sets
2.2 Relations
2.3 Types of relations
2.4 Some results on relations
2.5 Composition of relations

Day 1

2.1 Cartesian product of sets

Day 2

2.2 Relations
2.3 Types of relations

Day 3
2.4 Some results on relations
2.5 Composition of relations

Day 4
Objective Exercises 1 to 37

Day 5
Fill in the blanks 1 to 8
True/False 1 to 13


Day 6
Practice exercises 1 to 27

Revision days


Day 7

Day 8

Day 9

Day 10

JEE Mathamatics Study Guide 4. Binary Operations - Revision Facilitator

4.1 Binary operations
4.2 Types of binary operation
4.3 Identity and inverse elements
4.4 Composition table

Study Plan

Day 1

4.1 Binary operations
4.2 Types of binary operation

Day 2

4.3 Identity and inverse elements
4.4 Composition table

Day 3
Objective type exercises 1 to 12
True/false type exercises 1 to 9

JEE Study Guide 5. Complex Numbers

Contents of the Chapter

5.1 Introduction
5.2 Integral powers of IOTA(i)
5.3 Imaginary quantities
5.4 Complex numbers
5.5 Equality of complex numbers
5.6 Addition of complex numbers
5.7 Subtraction of complex numbers
5.8 Multiplication of complex numbers
5.9 Division of complex numbers
5.10 Conjugate of a complex number
5.11 Modulus of a complex number
5.12 reciprocal of a complex number
5.13 Square roots of a complex number
5.14 Representation of a complex number
5.15 Argument or amplitude of a complex number z = x+iy for different signs of x and 5.16 Eulerian form of a complex number
5.17 Geometrical representations of fundamental operations
5.17B Modulus and argument of multiplication of two complex numbers
5.18 Modulus and argument of division of two complex numbers
5.19 Geometrical representation of conjugate of a complex number
5.20 Some important results on modulus and argument
5.21 Geometry of complex numbers
5.22 Affix of a point dividing the line segment joining points having affixes z1 and z2
5.23 Equation of the perpendicular bisector
5.24 Equation of a circle
5.25 Complex number as a rotating arrow in the argand plane
5.25B Some important results
5.26 Some standard loci in the argand plane
5.27 Equation of a straight line
5.28 De-moivere’s theorem
5.29 Roots of a complex number
5.30 Roots of unity
5.31 Cube roots of unity
5.32 Logarithm of a complex number


Study Plan

Day 1

5.1 Introduction
5.2 Integral powers of IOTA(i)
Example 1,2
5.3 Imaginary quantities
Ex 1 to 4
5.4 Complex numbers
Ex 1,2
5.5 Equality of complex numbers
Ex 1,2
5.6 Addition of complex numbers
Ex 1
5.7 Subtraction of complex numbers
Ex 1


Day 2

5.8 Multiplication of complex numbers
Ex 1, 2
5.9 Division of complex numbers
ex 1
5.10 Conjugate of a complex number
5.11 Modulus of a complex number
ex 1

Day 3
5.12 reciprocal of a complex number

5.13 Square roots of a complex number
ex 1 to 5

Day 4

Exercises


Day 5
5.14 Representation of a complex number

5.15 Argument or amplitude of a complex number z = x+iy for different signs of x and y
ex 1, 1 to 5

Day 6

5.16 Eulerian form of a complex number
ex. 1
5.17 Geometrical representations of fundamental operations
5.17B Modulus and argument of multiplication of two complex numbers
5.18 Modulus and argument of division of two complex numbers

Day 7

5.19 Geometrical representation of conjugate of a complex number
5.20 Some important results on modulus and argument


Day 8

5.21 Geometry of complex numbers
5.22 Affix of a point dividing the line segment joining points having affixes z1 and z2
ex 1 to 5

Day 9

5.23 Equation of the perpendicular bisector
5.24 Equation of a circle
Ex 1 to 10.

Day 10

5.25 Complex number as a rotating arrow in the argand plane
ex 1 to 11
5.25B Some important results
ex 1 to 4

Day 11

5.26 Some standard loci in the argand plane
ex 1,2
5.27 Equation of a straight line
ex 1,1

Day 12

5.28 De-Moivere’s theorem
x 3 to 9

Day 13

5.29 Roots of a complex number
ex 1 to 3
5.30 Roots of unity
5.31 Cube roots of unity
ex 1 to 7

Day 14

5.32 Logarithm of a complex number
ex 1,2

Day 15
Illustrative Obj type Examples 1 to 15


From Day 16 take it as revision period

Day 16
I.O.T.E. 16 to 25


Day 17
I.O.T.E. 26 to 35

Day 18
I.O.T.E. 36 to 45


Day 19
46 to 55


Day 20
Objective Type Exercises 1 to 10


Day 21
O.T.E. 11 to 20

Day 22
O.T.E. 21 to 30

Day 23
O.T.E. 31 to 40

Day 24
O.T.E. 41 to 50

Day 25
O.T.E. 51 to 60

Day 26
O.T.E. 61 to 80 do only odd numbered problems

Day 27
O.T.E. 81 to 100

Day 28
O.T.E. 101 to 120

Day 29
O.T.E. 121 to 140

Day 30
O.T.E. 141 to 160

Still the book has many many probles. You have to do these problems as a special task and also as a revision whenever you find extra time.

IIT JEE Mathematics Study Plan 6. Sequences and Series

Sections in Chapter

6.1 Sequence
6.2 Arithmetic progression
6.3 General term of an A.P.
Selection of terms in an A.P.
6.5 Sum of n terms of an A.P.
6.6 Properties of arithmetical progressions
6.7 Insertion of arithmetic means

6.8 Geometric Progression
6.9 The nth or general term of a G.P.
6.10 Selection of terms in G.P.
6.11 Sum of n terms of a G.P.
6.12 Sum of an Infinite G.P.
6.13 Properties of geometric progressions
6.14 Insertion of geometric means between two given numbers
6.15 Some important properties of arithmetic and geometric means between two given quantities

6.16 Arithmetico-geometric sequence
6.17 Sum of n terms of an arithmetico-geometric sequence
6.18 Sum to n terms of some special sequences
6.19 Miscellaneous sequences and series

6.20 Harmonic progression
6.21 Properties of arithmetic, geometric, and harmonic means between two given numbers.

Study Plan

Day 1

6.1 Sequence
6.2 Arithmetic progression
Ex. 1 to 7
6.3 General term of an A.P.
Ex. 1 to 7

Day 2

6.4 Selection of terms in an A.P.
6.5 Sum of n terms of an A.P.
Ex. 1 to 12
6.6 Properties of arithmetical progressions
Ex. 1 to 4

Day 3
6.7 Insertion of arithmetic means
Ex. 1 to 5
Revision of A.P.

Day 4

6.8 Geometric Progression
Ex. 1 to 3
6.9 The nth or general term of a G.P.
Ex. 1 to 10
6.10 Selection of terms in G.P.
Ex. 1

Day 5
6.11 Sum of n terms of a G.P.
Ex. 1 to 11
6.12 Sum of an Infinite G.P.
Ex. 1 to 11

Day 6
6.13 Properties of geometric progressions
Ex. 1 to 6
6.14 Insertion of geometric means between two given numbers
Ex. 1,2

Day 7
6.15 Some important properties of arithmetic and geometric means between two given quantities
Ex. 1 to 5


Day 8
6.16 Arithmetico-geometric sequence
Ex. 1 to 3
6.17 Sum of n terms of an arithmetico-geometric sequence
Ex. 1 to 6

Day 9
6.18 Sum to n terms of some special sequences
Ex. 1 to 13
6.19 Miscellaneous sequences and series
Ex. 1

Day 10

6.20 Harmonic progression
Ex. 1 to 3
6.21 Properties of arithmetic, geometric, and harmonic means between two given numbers.

Day 11
Chapter 6
Illustrative Objective Type Questions 1 to 20

Day 12
Chapter 6
I.O.T.P.: 21 to 40

Day 13
Chapter 6
I.O.T.P.: 41 to 48
Objective Type questions 1 to 10

Day 14
Chapter 6
O.T.P. 11 to 30

Day 15
Chapter 6
O.T.P. 31 to 50


Day 15
Chapter 6
O.T.P. 51 to 70

Day 16
Chapter 6 Revision
O.T.P. 71 to 80


Day 17
Chapter 6 Revision
O.T.P. 81 to 90


Day 18
Chapter 6 Revision
O.T.P. 91 to 100


Day 19
Chapter 6 Revision
O.T.P. 101 to 110

Day 20
Chapter 6 Revision
O.T.P. 111 to 120


Day 21
Chapter 6 Revision
O.T.P. 121 to 130

Day 22
Chapter 6 Revision
O.T.P. 131 to 140

Day 23
Chapter 6 Revision
O.T.P. 141 to 150

Day 24
Chapter 6 Revision
O.T.P. 151 to 160

Day 25
Chapter 6 Revision
O.T.P. 161 to 163
Formula revision


Day 26
Chapter 6 Revision
Fill in the blanks 1 to 20

Day 27
Chapter 6 Revision
True or false 1 to 12

Day 28
Chapter 6 Revision
Practice Exercises 1 to 20 even problems

Day 29
Chapter 6 Revision
Practice Exercises 21 to 40 even problems

Day 30
Chapter 6 Revision
Practice Exercises 41 to 67 even problems

Special task remaining problems

IT JEE Mathematics Study Guide 7. Quadratic Equations and Expressions - Revision Facilitator

R.D. Sharma Objective Mathematics

7.1 Some definitions and results
7.2 Some results on roots of an equation
7.3 Position of roots of a polynomial equation
7.4 Descartes rule of signs
7.5 Relations between roots and coefficients
7.6 Formation of a polynomial equation from given roots.
7.7 Transformation of equations
7.8 Roots of a quadratic equation with real coefficients
7.9 Quadratic expression and its graph
7.10 Sign of a quadratic expression for real values of the variable
7.11 Solution of inequations
7.12 Position of roots of a quadratic equation
7.13 Common roots
7.14 Values of a rational expression P(x)/Q(x) for real values of x, where P(x) and Q(x) are quadratic expressions
7.15 Condition for resolution into linear factors of a quadratic function
7.16 Algebraic interpretation of Rolle’s theorem


Study Plan

Always circle difficult concepts or difficult problems. You need to revise them later on more intensively and make them easy (Any difficult issue becomes easy as you understand the concept and related concepts better.)

Day 1

7.1 Some definitions and results
7.2 Some results on roots of an equation
7.3 Position of roots of a polynomial equation
Ex. 1
7.4 Descartes rule of signs
Ex. 1 to 3

Day 2

7.5 Relations between roots and coefficients
Ex. 1 to 3
7.6 Formation of a polynomial equation from given roots.
7.7 Transformation of equations
Ex. 1 to 4

Day 3

7.8 Roots of a quadratic equation with real coefficients

7.9 Quadratic expression and its graph
7.10 Sign of a quadratic expression for real values of the variable

Day 4

7.11 Solution of inequations
Ex. 1,2 and Ex 1,2

7.12 Position of roots of a quadratic equation
EX. 1 to 4



Day 5

7.13 Common roots
Ex. 1 to 3

Day 6
7.14 Values of a rational expression P(x)/Q(x) for real values of x, where P(x) and Q(x) are quadratic expressions
Ex. 1 to 3

7.15 Condition for resolution into linear factors of a quadratic function
Ex. 1 ro 2

Day 7

7.16 Algebraic interpretation of Rolle’s theorem
Ex. 1,2
Illustrative Objective Type Questions: 1 to 10


Day 8
I.O.T.Q.: 11 to 30


Day 9
I.O.T.Q.: 31 to 50

Day 10.
I.O.T.Q.: 51 to 64

Day 11
Objective Type Questions: 1 to 20


Day 12
O.T.P.: 21 to 60 odd numbered questions
(Persons who can do more problems can do more problems)

Day 13
O.T.P.: 61 to 100 even numbered questions
(Persons who can do more problems can do more problems)


Day 14
O.T.P.: 101 to 140 odd numbered questions
(Persons who can do more problems can do more problems)


Day 15
O.T.P.:141 to 184 even numbered questions
(Persons who can do more problems can do more problems)


Revision Period

Day 16
Fill in the blanks exercises: 1 to 20


Day 17
True or false exercises: 1 to 13


Day 18
Practice Exercises: 1 to 10


Day 19
Practice Exercises:11 to 20


Day 20
Practice Exercises: 21 to 30


Day 21
Practice Exercises: 31 to 40

Day 22
Practice Exercises: 41 to 50

Day 23
Practice Exercises: 51 to 60

Day 24
Practice Exercises: 61 to 63

Day 25
Revision of concepts of the chapter

Day 26
O.T.P.: 21 to 60 even numbered questions


Day 27
O.T.P.: 61 to 100 odd numbered questions

Day 28
O.T.P.: 101 to 140 even numbered questions

Day 29
O.T.P.:141 to 184 odd numbered questions

Day 30
Revision of some difficult problems

IIT JEE Mathematics Study Plan 8. Permutations and Combinations - Revision Facilitator

Chapters in the R.D. Sharma Book


8.1 The factorial
8.2 Exponent of prime p in n!
8.3 Fundamental principles of counting
8.4 Permutations
8.5 Permutations under certain conditions
8.6 Permutations of objects not all distinct
8.7 Permutations when objects can repeat
8.8 Circular permutations
8.9 combinations
8.10 Practical problems on combinations
8.11 Mixed problems on permutations and combinations
8.12 Selection of one or more items
8.13 Division of items into groups
8.14 Division of identical objects into groups
8.15 Some important results


Study plan

Day 1

1. The Factorial
2. Exponent of Prime p in n!
3. Fundamental principles of counting

Day 2

8.4 Permutations
4 theorems and 20 examples

8.5 Permutations under certain conditions
Three theorems and 20 examples

Day 3

8.6 Permutations of Objects not all Distinct
Theorem 1, 11 examples

8.7 Permutations when Objects can Repeat
1 theorem, 6 examples

8.8 Circular Permutations

1 theorem, 10 examples

Day 4

8.9 Combinations
Theorem 1,
Remarks 3
Properties 7
Examples 6

8.10 Practical Problems on Combinations
24 examples

8.11 Mixed Problems on Combinations and Permutations

Examples 6

Total examples for the day 36

Day 5

8.12 Selection of one or more items
Sub topics

Selection from different items
Selection from identical items
Selection of items from a group containing both identical and different items.

4 examples

8.13 Division of Items into Groups
Division of items into groups of unequal size
Division of items into groups of equal size

5 examples

8.14 Division of Identical Objects into groups

3 results and 7 examples

8.15 Some important results

4 results

Day 6

Illustrative objective type questions 1 to 10

Attempt objective type exercises 1 to 10

Attempt Practice exercises (given at the end of the chapter)

1 to 4 and 6


Day 7

Illustrative objective type questions 11 to 20

Attempt objective type exercises 11 to 20

Attempt Practice exercises (given at the end of the chapter)
8,23,24,25,28,29

Day 8

Illustrative objective type questions 21 to 40

Attempt objective type exercises 21 to 50

Attempt Practice exercises (given at the end of the chapter)
51 to 55

Day 9

Illustrative objective type questions 41 to 53

Attempt objective type exercises 51 to 80

Attempt Practice exercises (given at the end of the chapter)
56 to 60

Day 10

81-120

Attempt objective type exercises 51 to 80

Attempt Practice exercises (given at the end of the chapter)
31 to 35

Revision period

Day 11

Do 121 – 130 in Objective type exercises.

Day 12

Do 131 – 141 in Objective type exercises.

Day 13

Do the Fill in the blanks type exercise questions 1 to 5

Day 14

Do the Fill in the blanks type exercise questions 6 to 15

Day 15

From Permutations chapter

Do the Fill in the blanks type exercise questions 16 to 20

Day 16

Do the Fill in the blanks type exercise questions 21 to 25

Day 17

Do the Fill in the blanks type exercise questions 26 to 33

Day 18 to 30
Attempt all the practice questions and test paper questions

IIT JEE Mathematics Study Guide 9. Binomial Theorem

Text Book R D Sharma Objective Mathematics

Day 1

Go through 9.1, 9.2 and 9.3 today

Day 2

Go through
9.3 Multinomial theorem
9.4 Middle terms in a Binomial expansion
9.5 Some important results

Day 3

Go through
9.6 Some problems on applications of Binomial theorem
9.7 Greatest term in the expansion of (x+a)n
9.8 S Properties of the binomial coefficients

Day 4

Go through
9.9 Binomial Theorem for any index
9.10 synopsis

Day 5

Do illustrative objective type examples

1 to 20

Do practice exercises (at the end of the chapter) 1 to 5

Day 6

Do illustrative objective type examples

21 to 40
Do practice exercises (at the end of the chapter) 6 to 10

Day 7

Do illustrative objective type examples

41 to 52

In this, past IIT problems are
45, 52,

Do practice exercises (at the end of the chapter) 11 to 15


Day 8

Do objective type exercises

1 to 20


Do practice exercises (at the end of the chapter) 16 to 20

Q. 19 is a past IIT question.


Day 9

Do objective type exercises

21 to 40


Do practice exercises (at the end of the chapter) 21 to 25

Day 10

Do objective type exercises

41 to 60


Do practice exercises (at the end of the chapter) 26 to 30

Revision Period

Day 11

61-70 in objective exercises

Day 12

71-80 in objective exercises

Day 13

81-90 in objective exercises

day 14

91-100 in objective exercises

Day 15

100-110 in objective exercises

Day 16

111-120 in objective exercises

Day 17

121-130 in objective exercises

Day 18

131-135 in objective exercises

Day 19

Practice exercise problems 1 to 5
Fill in the blank type exercises 1 to 5


Day 20

Practice exercise problems 6 to 15
Do True or False Questions 1 to 7


Day 21

Practice exercise problems 16 to 20 (There are a total of 57 problems in this exercise)

Day 22

Practice exercise problems 21 to 25 (There are a total of 57 problems in this exercise)

Day 23

In the previous chapter Binomial theorem do problems

Practice exercise problems 26 to 30 (There are a total of 57 problems in this exercise)

Day 24

Practice exercise problems 31 to 35

Day 25

Practice exercise problems 36 to 40

Day 26






Concept Revision Facilitator



Try to recollect relevant points on the topic.

If required right click on the topic and click on open in a new window to read the relevant material.

Close the window and come back.




1 Pascal’s Triangle of Binomial coefficients

2 Binomial theorem for positive integral index.

3 Some Deductions from Binomial Theorem

4 Different version of Binomial theorem

5 Multinomial theorem

6 Middle terms in a binomial expansion

7 Results related to Binomial Coefficieints

8 Some problems on applications of binomial theorem

9 Finding greatest term in the expansion of (x+a)^n

10 Properties of the binomial coefficients

11. Binomial theorem for any index



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IIT JEE Mathematics Study Guide 12. Determinants

12.1 Definition
12.2 Singular matrix
12.3 Minors and cofactors
12.4 Properties of determinants
12.5 Evaluation of determinants
12.6 Evaluation of determinants by using factor theorem
12.7 Product of determinants
12.8 Differentiation of determinants
12.9 Applications of determinants to coordinate geometry
12.10 Applications of determinants in solving a system of linear equations


Study Plan

Day 1

12.1 Definition
There are three examples in this section
12.2 Singular matrix
12.3 Minors and cofactors

Day 2


12.4 properties of determinants
12.5 Evaluation of Determinants


Day 3



Do all the 19 example problems

Day 4

Study sections

12.6 Evaluation of Determinants using Factor Theorem
2 examples

12.7 Product of determinants
5 examples


Day 5

Do illustrative obj type examples 1 to 20

Day 6

12.8 Differentiation of determinants
12.9 Applications of determinants to coordinate geometry

Day 7
12.10 Applications of determinants in solving a system of linear equations

Day 8
I.O.T.E. 21 to 28
Objective Type Exercises 1 to 10

Day 9
O.T.E. 11 to 30

Day 10
O.T.E. 331 to 50

Day 11
O.T.E. 51 to 72

Day 11
Fill in the blansk 1 to 24

Day 12
True or false 6


Day 13 to 30
Revision Concepts and test paper problems

IIT JEE Study Guide 13. Cartesian System of Coordinates and Straight Lines - Revision Facilitator

1. Introduction

2. Catesian coordinate system

3. Distance between two points

4. Area of a triangle

5. Section Formulae

6. coordinates of the centroid, in-centre, and ex centre of a triangle

7. Locus and equation to a locus

8. Shifting of origin

9. Rotation of axes

10. Definition of a straight line

11. Slope (Gradient) of a straight line

12. Angle between two straight lines

13. Intercepts of a line on the axes

14. Equations of lines parallel to the coordinate axes

15. Different forms of the equation of a straight line

16. Transformation of general equation in different standard forms

17. point of intersection of two lines

18. Coordination of concurrency of three lines

19. Lines parallel and perpendicular to a given line

20. Angle between two straight lines when their equations are given.

21. Distance of a point from a line

22. Positions of points relative to a line

23. Equations of straight lines passing through a given point and making a given angle with a given line

24. Equations of the bisectors of the angles between two straight lines

25. Some important points of a triangle

26. Family of lines through the intersection of two given lines



Study Plan

Day 1

1. Introduction

2. Catesian coordinate system

3. Distance between two points

Day 2

4. Area of a triangle

5. Section Formulae

6. coordinates of the centroid, in-centre, and ex centre of a triangle

Day 3

7. Locus and equation to a locus

8. Shifting of origin


Day 4

9. Rotation of axes

10. Definition of a straight line

11. Slope (Gradient) of a straight line

12. Angle between two straight lines

Day 5

13. Intercepts of a line on the axes

14. Equations of lines parallel to the coordinate axes

15. Different forms of the equation of a straight line

Day 6

16. Transformation of general equation in different standard forms

17. point of intersection of two lines

18. Coordination of concurrency of three lines

Day 7

19. Lines parallel and perpendicular to a given line

20. Angle between two straight lines when their equations are given.

21. Distance of a point from a line

Day 8

22. Positions of points relative to a line

23. Equations of straight lines passing through a given point and making a given angle with a given line

Day 9

24. Equations of the bisectors of the angles between two straight lines

25. Some important points of a triangle

26. Family of lines through the intersection of two given lines - Up to Example 10

Day 10
26. Family of lines through the intersection of two given lines - Examples 21 to 30

Day 11
Illustrative Objective Type Examples 1 to 19

Day 12
Objective Type Exercise 1 to 20


Day 13
O.T.E. 21 to 40


Day 14
O.T.E. 41 to 60

Day 15
O.T.E. 61 to 80


Revision Period - 30 minutes a day

Day 16
O.T.E. 81 to 90


Day 17
O.T.E. 91 to 100


Day 18
O.T.E. 101 to 110


Day 19
O.T.E. 111 to 120



Day 20
O.T.E. 121 to 130



Day 21
O.T.E. 131 to 142


Day 22
Fill in the blanks type exercise 1 to 10


Day 23
Fill in the blanks type exercise 11 to 20


Day 24
Fill in the blanks type exercise 21 to 30

Day 25
Fill in the blanks type exercise 31 to 40


Day 26
True of False Exercise 1 to 19

Day 27
Practice Exercise 1 to 10

Day 28
Practice Exercise 11 to 20

Day 29
Practice Exercise 21 to 30

Day 30
31 to 41

Should you compulsorily do every problem. Not necessary. If you feel, you know how to do it, you can always skip some problems. But make a note of all difficult problems. You may have to a relook at them sometimes more to remember the complication or complexity in that problem.











Try to recollect relevant points on the topic.

If required right click on the topic and click on open in a new window to read the relevant material.

Close the window and come back.


Euclidean Geometry and Analytic Geometry - Difference

Distance between two points

Area of a triangle

Section Formulae

coordinates of the centres related to triangle

Definition of a straight line

Slope (Gradient) of a straight line

Angle between two straight lines

Intercepts of a line on the axes

Joint equation of a pair of straight lines

IIT JEE Mathematics Study Plan 14. The Family of Lines - - Revision Facilitator

14.1 Introduction
14.2 Joint equation of a pair of straight lines
14.3 Pair of straight lines through the origin
14.4 Angle between pair of lines given by ax² +2hxh+by² = 0
14.5 Bisectors of the angle between the lines given by a homogeneous equation
14.6 General equation of a second degree
14.7 Equations of the bisectors of the angles between the lines represented by the equation ax² +2hxh+by²+2gx+2fy+c = 0
14.8 Lines joining the origin to the points of intersection of a line and curve

Study Plan

10 Days for both main study and revision

Day 1

14.1 Introduction
14.2 Joint equation of a pair of straight lines
14.3 Pair of straight lines through the origin

Day 2

14.4 Angle between pair of lines given by ax² +2hxh+by² = 0
14.5 Bisectors of the angle between the lines given by a homogeneous equation
14.6 General equation of a second degree

Day 3

14.7 Equations of the bisectors of the angles between the lines represented by the equation ax² +2hxh+by²+2gx+2fy+c = 0
14.8 Lines joining the origin to the points of intersection of a line and curve

Day 4
Illustrative Objective Type Examples 1 to 7
Objective Type Exercise 1 to 10

Day 5
O.T.E. 11 ro 32

day 6
Fill in the blanks type Exercise 1 to 5
practce exercise 1 to 10

Day 7
Practice exercise 11 to 28

Day 8 to 10 Revision
Concepts, Formulas, and test paper problems

IIT JEE Mathematics Study Plan 15. The Circle

Sections in the chapter

1. Definition
2. Standard equation of a circle
3. Some particular cases of the central form of the equation of a circle
4. General equation of a circle
5. Equation of a circle when the co-ordinates of end points of a diameter are given
6. Intercepts on the axis
7. Position of a point with respect to a circle
8. Equation of a circle in parametric form
9. Intersection of a straight line and a circle
10. The length of the intercept cut off from a line by a circle
11. Tangent to a circle at a given point.
12. Normal to a circle at a given point
13. Length of the tangent from a point to a circle
14. Pair of tangents drawn from a point to a given circle
15. Combined equation of pair of tangents
16. Director circle and its equation
17. Chord of contact of tangents
18. Pole and polar
19. Equation of the chord bisected at a given point
20. Diameter of a circle
21. Common tangents to two circles
22. Common chord of two circles
23. Angle of intersection of two curves and the condition of orthogonality of two circles.
24. Radical axis
25. Equation of a circle through the intersection of a circle and line
26. Circle through the intersection of two circles
27. Coaxial system of circles

Study Plan

Sections in the chapter

Day 1

1. Definition
2. Standard equation of a circle
3. Some particular cases of the central form of the equation of a circle
4. General equation of a circle

Day 2

5. Equation of a circle when the co-ordinates of end points of a diameter are given
6. Intercepts on the axis
7. Position of a point with respect to a circle
8. Equation of a circle in parametric form

Day 3

9. Intersection of a straight line and a circle
10. The length of the intercept cut off from a line by a circle
Illustrative Objective Type Examples: 1 to 8

Day 4

11. Tangent to a circle at a given point.
12. Normal to a circle at a given point
13. Length of the tangent from a point to a circle

day 5

14. Pair of tangents drawn from a point to a given circle
15. Combined equation of pair of tangents
16. Director circle and its equation
17. Chord of contact of tangents

Day 6

18. Pole and polar
19. Equation of the chord bisected at a given point
20. Diameter of a circle
21. Common tangents to two circles

Day 7
Concept revision
I.O.T.E. 7 to 25 (If some problems cannot be understood leave them for later days)

Day 8

22. Common chord of two circles
23. Angle of intersection of two curves and the condition of orthogonality of two circles.
24. Radical axis

Day 9
25. Equation of a circle through the intersection of a circle and line
26. Circle through the intersection of two circles
27. Coaxial system of circles

Day 10
I.O.T.E. 26 to 53

Revision Period

Day 11

Objective Type Exercises 1 to 10

Day 12
Objective Type Exercises 11 to 20

Day 13
Objective Type Exercises 21 to 30

Day 14
Objective Type Exercises 31 to 40


Day 15
Objective Type Exercises 41 to 50


Day 16
Objective Type Exercises 51 to 60


Day 17
Objective Type Exercises 61 to 70


Day 18
]Objective Type Exercises 71 to 80


Day 19
Objective Type Exercises 81 to 90


Day 20
Objective Type Exercises 91 to 100

Special task remaining problems

IIT JEE Mathematics Study Plan 16. Parabola - Revision Facilitator

Ch. 16. Parabola-RDS-
Sections



1. Conic sections: Definition

2. The parabola

3. Equation of parabola in its standard form

4. Some other standard forms of parabola

5. Position of a point with respect to a parabola

6. Equation of a parabola in parametric form

7. Equation of the chord joining any two points on the parabola

8. Intersection of a straight line and a parabola

9. Equation of tangent in different forms

10. Equation of normal in different forms

11 Number of normals drawn from a point to a parabola

12. Some results in conormal points

13 Number of tangents drawn from a point to a parabola

13a. Equation of the pair of tangents from a point to a parabola


14. Equation of the chord of contacts of tangents to a parabola

15. Equation of the chord bisected at a given point

16. Equation of diameter of a parabola

17. Length of tangent, subtangent, normal and subnormal

18. Pole and Polar

19. Some important results at a glance

Study Plan





1. Conic sections: Definition

2. The parabola

3. Equation of parabola in its standard form

4. Some other standard forms of parabola

5. Position of a point with respect to a parabola

6. Equation of a parabola in parametric form

7. Equation of the chord joining any two points on the parabola

8. Intersection of a straight line and a parabola

9. Equation of tangent in different forms

10. Equation of normal in different forms

11 Number of normals drawn from a point to a parabola

12. Some results in conormal points

13 Number of tangents drawn from a point to a parabola

13a. Equation of the pair of tangents from a point to a parabola


14. Equation of the chord of contacts of tangents to a parabola

15. Equation of the chord bisected at a given point

16. Equation of diameter of a parabola

17. Length of tangent, subtangent, normal and subnormal

18. Pole and Polar

19. Some important results at a glance