Integrate (x^4 +1)/(x^6 + 1) Problem for #jeemains #WBJEE #CBSE #ISC #mathematics

Problem for #jeemains #WBJEE #CBSE #ISC #mathematics 

Integration for JEE Mains

 Integrate sqrt ((cos x - cos^3 x)/(1 - cos^3 x) #jeemains #CBSE #wbjee #ISC #math

Integration for JEE Mains

 Integration for JEE Mains

Integration for JEE Mains

 Integration for JEE Mains

Trigonometry SN Dey Solved Problems - HS - Class XI

1. Trigonometric functions of Standard Angles [ 4 and 5 marks ]

2. Trigonometric functions of Associate Angles [ 4 and 5 marks ]

3. Trigonometric transformations of sums and products [ 4 and 5 marks]

4. Trigonometric functions of Compound Angles [ 4 and 5 marks]

5. Trigonometric functions of Multiple Angles [4 and 5 marks]

6. Trigonometric functions of Sub-multiple Angles [ 4 and 5 marks]

7. Trigonometric Equations  [ 4 and 5 marks]

Set Theory Solved Problems : Class XI

The concept of set serves as a fundamental part of the present day mathematics. Today this concept is being used in almost every branch of mathematics. Sets are used to define the concepts of relations and functions. The study of geometry, sequences, probability, etc. requires the knowledge of sets. The theory of sets was developed by German mathematician Georg Cantor (1845-1918). He first encountered sets while working on “problems on trigonometric series”. In this Chapter, we discuss some basic definitions and operations involving sets.

Empty Sets

The set with no elements or null elements is called an empty set. This is also called a Null set or Void set. It is denoted by {}.

For example: Let, Set X = {x:x is the number of students studying in Class 6th and Class 7th}

Since we know a student cannot learn simultaneously on two classes, therefore set X is an empty set.

Singleton Set

The set which has only one element is called a singleton set.

For example, Set X = { 2 } is a singleton set.

Finite and Infinite Sets

Finite sets are the one which has a finite number of elements, and infinite sets are those whose number of elements cannot be estimated, but it has some figure or number, which is very large to express in a set.

For example, Set X = {1, 2, 3, 4, 5} is a finite set, as it has a finite number of elements in it.

Set Y = {Number of Animals in India} is an infinite set, as there is an approximate number of Animals in India, but the actual value cannot be expressed, as the numbers could be very large.

Equal Sets

Two sets X and Y are said to be equal if every element of set X is also the elements of set Y and if every element of set Y is also the elements of set X. It means set X and set Y have the same elements, and we can denote it as;

X = Y

For example, Let X = { 1, 2, 3, 4} and Y = {4, 3, 2, 1}, then X = Y

And if X = {set of even numbers} and Y = { set of natural numbers} the X ≠ Y, because natural numbers consist of all the positive integers starting from 1, 2, 3, 4, 5 to infinity, but even numbers starts with 2, 4, 6, 8, and so on.

Subsets

A set X is said to be a subset of set Y if the elements of set X belongs to set Y, or you can say each element of set X is present in set Y. It is denoted with the symbol as X ⊂ Y.

We can also write the subset notation as;

X ⊂ Y if a ∊ X

a ∊ Y

Thus, from the above equation, “X is a subset of Y if a is an element of X implies that a is also an element of Y”.

Each set is a subset of its own set, and a null set or empty set is a subset of all sets.

Power Sets

The power set is nothing but the set of all subsets. Let us explain how.

We know the empty set is a subset of all sets and every set is a subset of itself. Taking an example of set X = {2, 3}. From the above given statements we can write,

{} is a subset of {2, 3}

{2} is a subset of {2, 3}

{3} is a subset of {2, 3}

{2, 3} is also a subset of {2, 3}

Therefore, power set of X = {2, 3},

P(X) = {{},{2},{3},{2,3}}

Universal Sets

A universal set is a set which contains all the elements of other sets. Generally, it is represented as ‘U’.

For example; set X = {1, 2, 3}, set Y = {3, 4, 5, 6} and Z = {5, 6, 7, 8, 9}

Then, we can write universal set as, U = {1, 2, 3, 4, 5, 6, 7, 8, 9,}

Note: From the definition of the universal set, we can say, all the sets are subsets of the universal set. Therefore,

X ⊂ U

Y ⊂ U

And Z ⊂ U

Union of sets

A union of two sets has all their elements. It is denoted by ⋃.

For example, set X = {2, 3, 7} and set Y = { 4, 5, 8}

Then union of set X and set Y will be;

X ⋃ Y = {2, 3, 7, 4, 5, 8}

Properties of Union of Sets:

X ⋃ Y = Y ⋃ X ; Commutative law

(X ⋃ Y) ⋃ Z = X ⋃ (Y ⋃ Z)

X ⋃ {} = X ; {} is the identity of ⋃

X ⋃ X = X

U ⋃ X = U

Intersection of Sets

Set of all elements, which are common to all the given sets, gives intersection of sets. It is denoted by the symbol ⋂.

For example, set X = {2, 3, 7} and set Y = {2, 4, 9}

So, X ⋂ Y = {2}

Difference of Sets

The difference of set X and set Y is such that, it has only those elements which are in the set X and not in the set Y.

i.e. X – Y = {a: a ∊ X and a ∉ Y}

In the same manner, Y – X = {a: a ∊ Y and a ∉ X}

For example, if set X = {a, b, c, d} and Y = {b, c, e, f} then,

X – Y = {a, d} and Y – X = {e, f}

Disjoint Sets

If two sets X and Y have no common elements, and their intersection results in zero(0), then set X and Y are called disjoint sets.

It can be represented as; X ∩ Y = 0

WBJEE MATHEMATICS PAPER 2021 SOLVED

 The West Bengal Joint Entrance Examinations Board

The West Bengal Joint Entrance Examinations Board (WBJEEB) was established in 1962 by Government of West Bengal in exercise of the powers conferred under article 162 of the Constitution of India in pursuant to No. 828-Edn(T), dated 02.03.1962.

Subsequently in 2014, the Government of West Bengal enacted the West Bengal Act XIV of 2014 to form The West Bengal Joint Entrance Examinations Board and empowered it to conduct Common Entrance Examinations for selection of candidates for admission to undergraduate and postgraduate Professional, Vocational and General Degree Courses in the State of West Bengal and to conduct on-line counselling process or otherwise adopting a single-window approach.

WBJEEB has been instrumental in the admission process based on online application and allotment through e-Counselling since 2012. It advocates fairness and transparency, ensures no-error, and adopts state-of-the-art technology.

WBJEE 2022 Mathematics Syllabus

S.No.	Topics
1	Algebra Arithmetic Progression G.P., H.P Sets, Relations and Mappings Logarithms Complex Numbers Permutation and combination Polynomial equation Principle of mathematical induction Matrices Binomial theorem (positive integral index) Statistics and Probability
2	Trigonometry
3	Coordinate geometry of two dimensions
4	Coordinate geometry of three dimensions
5	Differential calculus Calculus Integral calculus Application of Calculus Differential Equations Vectors

WBJEE MATHEMATICS PAPER 2020 SOLVED

 The West Bengal Joint Entrance Examinations Board

The West Bengal Joint Entrance Examinations Board (WBJEEB) was established in 1962 by Government of West Bengal in exercise of the powers conferred under article 162 of the Constitution of India in pursuant to No. 828-Edn(T), dated 02.03.1962.

Subsequently in 2014, the Government of West Bengal enacted the West Bengal Act XIV of 2014 to form The West Bengal Joint Entrance Examinations Board and empowered it to conduct Common Entrance Examinations for selection of candidates for admission to undergraduate and postgraduate Professional, Vocational and General Degree Courses in the State of West Bengal and to conduct on-line counselling process or otherwise adopting a single-window approach.

WBJEEB has been instrumental in the admission process based on online application and allotment through e-Counselling since 2012. It advocates fairness and transparency, ensures no-error, and adopts state-of-the-art technology.

WBJEE 2022 Mathematics Syllabus

S.No.	Topics
1	Algebra Arithmetic Progression G.P., H.P Sets, Relations and Mappings Logarithms Complex Numbers Permutation and combination Polynomial equation Principle of mathematical induction Matrices Binomial theorem (positive integral index) Statistics and Probability
2	Trigonometry
3	Coordinate geometry of two dimensions
4	Coordinate geometry of three dimensions
5	Differential calculus Calculus Integral calculus Application of Calculus Differential Equations Vectors

Solved Problems on Differentiation

Hundreds of solved problems at 10+2 level or the final year at school from the topic of differentiation. The aim of the document to help students from different boards (ISC, CBSE and other State Boards) studying at Higher Secondary level to get access to wide variety of problems, that too solved!

This should not be substituted for classroom teaching neither this documents aims to teach the theories of differentiation. Students are requested to go through the theory and the rules before looking at the problems. Any error in the document can be reported at: prime.maths@hotmail.com

First Order Differentiation, Implicit Functions, Parametric Differentiation, Differentiation of Logarithmic Functions, Second Order Differentiation, Chain Rule, Composite functions.

If you have any query, don't forget to comment below.

Click below the links to download the files:

LIMITS Solved Problems on Limits

File 1 Basic Differentiation Problems 

File 2 Derivatives of Logarithmic Functions

File 3 Derivatives of Parametric Equations 

File 4 Long Answer Type ( First Order Mixed Problems)

File 5 Second Order Differentiation 

More solved problems to follow. Keep visiting this space.

Sum of squares of 5 consecutive natural numbers!

Here's a difficult problem of proving that a given expression is not a perfect square. A direct approach will be a nightmare ( even not sure it can be proved) but use of a simple property of perfect squares will ease the problem. We know that any perfect squares leaves a remainder either 1 or 0 when being divided by 3 or 4. This simple result would be used to solve the problem.

Comple Number_Inequality

Here is the download link http://sdrv.ms/16cXtED

or

http://kolkatamaths.yolasite.com/problems-for-isi.php

Quadratic Equation & Locus

Collection some good problems on Quadratic Equation & Locus for boards and other competitive exams.
 Click here to go to download page.

Pigeon Hole Principle and Divisibility

Here is a good problem Pigeon Hole Principle and Divisibility of integers. These type of problems are important for  Olympiads, Indian Statistical Institute (ISI) and  Chennai Mathematical Institute (CMI) .
Get the pdf file here. Please leave your comment.

Test Paper

Test Sheet on Infinite Series and Properties of Triangles for WBJEE,AIEEE and IIT. Chapters Included Properties of Triangles,Infinite Series,logarithmic,Exponential & Binomial.


Download here

Tangent and Normal

Solved Problems on Tangent and Normal mainly for IIT,WBJEE and AIEEE. Click here to download For more problems visit http://kolkatamaths.yolasite.com/xi-xii.php

Solved Problems on Definite Integrals

Few difficult problems on Definite Integrals which I have solved partially. Click here to download These problems are important for understanding the application of the properties of the definite integrals which are commonly asked in boards and exams like IIT, AIEEE, WBJEE and other exams of same nature.

CBSE BOARD PROBLEMS

CBSE BOARD PROBLEMS & PROBLEMS FROM ENTRANCE EXAM ON SYSTEM OF LINEAR EQUATION & MATRICES Download For more problems visit http://kolkatamaths.yolasite.com/xi-xii.php

LIMITS

Problems on LIMIT for entrance exams like ISI,IIT,WBJEEE,AIEEE and other various engineering entrance exams.Click here to download

AIEEE Mock Test Paper 2011

Get the AIEEE Mock Test Paper 2011 now! and much more click here to go to the downlaod page. Materials for CBSE,ISC,WBJEE,IIT and other exams and board are also avilable

Problem for Entrance Exams

Download here. Practice Problem for entrance exam ISC, CBSE, WBHS, AIEEE, WBJEE, IIT and other entrance exam