Mind Maps for Trigonometric Ratio: Compound Angles Revision – Class 11, JEE

Get to learn all the formulae and important points of Trigonometric Ratio: Compound Angles in Mathematics Class 11 through this Mind Map. Download and share with your friends also.

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Physics Revision Series by Saransh Gupta Sir (AIR-41, IIT-BOMBAY)

Chemistry Revision Series by Prateek Gupta Sir  (IIT-BOMBAY, Metallurgy)

Maths Revision Series by N.K. Gupta Sir (eSaral Co-founder)

Mathematics: Vector Revision Video – Class 12, JEE

In this chapter, students deal with Vectors, scalars, magnitude and direction of vectors, direction cosines and direction ratios of vectors and many other concepts.

N.K Sir is explaining the important formulas and tips covering the entire chapter. The methodologies he developed in his journey of 30+ years in the education field, will help all the students to understand the chapter better and score wonderful marks in board and competitive examinations.

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### VECTORS PART – 2

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Physics Revision Series by Saransh Gupta Sir (AIR-41, IIT-BOMBAY)

Chemistry Revision Series by Prateek Gupta Sir  (IIT-BOMBAY, Metallurgy)

Maths Revision Series by N.K. Gupta Sir (eSaral Co-founder)

Mind Maps of 3D Geometry – Class 12, JEE

Get to learn all the formulae and important points of 3-D Geometry in Mathematics Class 12 through this Mind Map. Download and share with your friends also.

#### Prepare for JEE & NEET with the Kota’s Top IITian & Doctor Faculties !

Physics Revision Series by Saransh Gupta Sir (AIR-41, IIT-BOMBAY)

Chemistry Revision Series by Prateek Gupta Sir  (IIT-BOMBAY, Metallurgy)

Maths Revision Series by N.K. Gupta Sir (eSaral Co-founder)

Mind Maps for Vectors Revision – Class 12, JEE

Get to learn all the formulae and important points of Vectors in Mathematics Class 12 through this Mind Map. Download and share with your friends also.

#### Prepare for JEE & NEET with the Kota’s Top IITian & Doctor Faculties !

Physics Revision Series by Saransh Gupta Sir (AIR-41, IIT-BOMBAY)

Chemistry Revision Series by Prateek Gupta Sir  (IIT-BOMBAY, Metallurgy)

Maths Revision Series by N.K. Gupta Sir (eSaral Co-founder)

Mind Map for Logarithm Revision – Class 11, JEE

Get to learn all the formulae and important points of Logarithm through this Mind Map. Download and share with your friends also.

#### Prepare for JEE & NEET with the Kota’s Top IITian & Doctor Faculties !

Physics Revision Series by Saransh Gupta Sir (AIR-41, IIT-BOMBAY)

Chemistry Revision Series by Prateek Gupta Sir  (IIT-BOMBAY, Metallurgy)

Maths Revision Series by N.K. Gupta Sir (eSaral Co-founder)

Important Questions of Units and Measurement Class 11 Physics

Get important questions of Units and Measurement Class 11 Physics exams. View 11th Physics other chapters’ important questions for exam point of view. These important questions will play significant role in clearing concepts of the subject. This question bank is designed by top IITian Faculties keeping NCERT in mind and the questions are updated with respect to upcoming Board exams. You will get here all the important questions with answers for class 11 Physics Chapter Units and Measurement.

Click Here for Detailed Notes of Units and Measurements along with any chapter.

Q. What is a unit? Give an example.

Sol.

Q. What is the necessity of selecting some units as fundamental units?

Sol.

Q. Define the S.I. unit of solid angle.

Sol.

Q. Define light year.

Sol.

Q. Define a parsec.

Sol.

Q. What is the largest practical unit of mass?

Sol.

Q. What is lunar month?

Sol.

Q. How many shakes are there in 1 second?

Sol.

Q. What is a leap year?

Sol.

Q. The farthest objects in our universe are known as quasars (quasi-stellar radio sources). Much is not known about these objects. Electromagnetic wave emitted by quasars take billions of years to reach earth. Calculate distance of a quasar from which electromagnetic wave take three billion years to reach earth.

[NCERT]

Sol.

Q. The radius of the hydrogen atom is nearly 0.5 A.What is the total atomic volume in of a mole of hydrogen atoms?

[NCERT]

Sol.

Q. The moon is observed from two diametrically opposite points and on earth. The angle

subtended at the moon by the two directions of observation is ‘ Given the diameter of earthto be about . Calculate the distance of the moon form the earth.

[NCERT]

Sol.

Q. The sun’s angular diameter is measured to be 1920. The distance of the sun from the earth is What is the diameter of the sun?

[NCERT]

Sol.

Q. Give examples of three physical quantities which have the same dimensions.

Sol.

[esquestion] What is the unit of pressure if the unit of mass is

kg, the unit of length is metre and the unit of time is minute?

Q. Convert into erg.

Sol.

Q. Calculate the value of force 100 dynes on a system based on a metre, kilogram and minute as fundamental units.

Sol.

Q. What is a null vector?

Sol.

Q. What are co-initial and collinear vectors?

Sol.

Q. What is the significance of null vector?

Sol.

Q. Can three unequal forces add upto zero?

Sol.

Q. Under what condition the directions of sum and difference of two vectors will be same?

Sol.

Q. Point out the essential condition for the addition of vectors.

Sol.

Q. What is the difference between and

Sol.

Q. Which of the following quantities are independent of the choice of orientation of the co-ordinate axes? angle between and where is a scalar?

[NCERT]

Sol.

Q. A vector has magnitude and direction. Does it have a location in space? Will two equal vectors and at different locations in space necessarily have identical physical effects?

[NCERT]

Sol.

Q. Pick out the two scalar quantities in the following list: Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

[NCERT]

Sol.

Q. Pick out only the vector quantities from the following list: Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

[NCERT]

Sol.

Q. Can you associate vectors with (i) length of a wire

bent into a loop (ii) a plane area (iii) a sphere?

[NCERT]

Sol.

Q. A vector has both magnitude and direction. Does that mean anything that has magnitude and direction is necessarily a vector? The rotation of a body can be specified by the direction of the axis of rotation and the angle of rotation about the axis. Does that make any rotation a vector?

[NCERT]

Sol.

Q. The position of a particle is given by
$\left.3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}\right)$

[NCERT]

Sol.

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Chapter 1- 13 Mathematics Notes for Class 12 and IIT JEE

eSaral brings you detailed maths notes for class 12. eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparations.

We hope Maths notes for class 12 will help you understand the important topics and remember the key points for the exam point of view.

Below are the direct links for detailed chapter-wise12th Maths study material.

Relation and Functions

Inverse Trigonometric Function

Matrices

Determinants

Continuity and Differentiability

Application of Derivatives

Integrals

Application of Integrals

Differential Equation

Vector Algebra

Three Dimension Geometry

Linear Programming

Probability

Mathematics Notes for Class 11

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Integration Class 12 Notes for JEE and Board Exam Preparation

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. Get Integration Class 12 Notes that will help in IIT JEE and boards preparation.

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE. Integration Class 12 Notes are divided into two parts:

• ### Definite Integral Notes for Class 12 & IIT JEE

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

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Application of Derivatives Class 12 Notes || IIT JEE

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the Application of Derivatives Class 12 Notes that will help in IIT JEE and boards preparation.

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE. Application of Derivatives Class 12 Notes are broken into three topics:

• ### Tangent & Normal

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

Chapter 1 – 16 Mathematics Notes for Class 11 & IIT JEE

eSaral brings you detailed Mathematics Notes for Class 11. eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparations.

We hope Mathematics Notes for Class 11 will help you understand the important topics and remember the key points for the exam point of view.

Below are the direct links for detailed chapter-wise Mathematics Notes for Class 11.

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Our eSaral application contains around 5,00,000 questions to practice for IIT JEE, NEET and Board Exams.

Continuity and Differentiation Notes for Class 12 & IIT JEE

eSaral provides you complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the detailed Continuity and Differentiation Class 12 Notes with Important Questions that will also help in IIT JEE and boards preparation.

Measures of Central Tendency & Dispersion Notes for Class 12 & IIT JEE

eSaral provides you complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the detailed notes on Measures of Central Tendency & Dispersion with Important Questions that will also help in IIT JEE and boards preparation.

Indefinite Integral Notes for Class 12 & IIT JEE

eSaral provides you complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the detailed notes on Indefinite Integral Class 12 with Important Questions that will also help in IIT JEE and boards preparation.

Definite Integral Notes for Class 12 & IIT JEE

eSaral provides you complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the detailed Notes with the help of Definite Integral Examples with Important Questions that will also help in IIT JEE and boards preparation.

Vector Algebra Class 12 Notes for IIT JEE & Board Exams

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the Vector Algebra Class 12 Notes to prepare for boards and JEE

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE.

### Vector Algebra Class 12 Notes

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

Differential Equations Class 12 Notes for IIT JEE

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. Here are the Differential Equations Class 12 Notes to prepare for boards and JEE

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE.

### Differential Equations Class 12 Notes

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

Application of Integrals Class 12 Notes for IIT JEE

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. Application of Integrals Class 12 Notes to help in IIT JEE and boards preparation.

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE.

### Application of Integrals Class 12 Notes

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

3D Geometry Class 12 Notes for IIT JEE and Boards

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 12 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. 3D Geometry Class 12 Notes to prepare for boards and JEE

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 12 Maths.

These Notes have been designed in the most simple and precise format covering almost all the Domains like Differential Calculus, Algebra, Trigonometry, and Coordinate Geometry. These Notes will also be helpful to those who are preparing for competitive Exams like JEE.

### 3D Geometry Class 12 Notes

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 12 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 12 Mathematics Notes

At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

Probability Notes for Class 11 & IIT JEE

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 11 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination.So here are Probability Notes for Class 11 & IIT JEE Exam preparation.

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### Probability Notes for Class 11

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 11 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 11 Mathematics Notes

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At eSaral we are offering a complete platform for IIT-JEE & NEET preparation. The main mission behind eSaral is to provide education to each and every student in India by eliminating the Geographic and Economic factors, as a nation’s progress and development depends on the availability of quality education to each and every one. With the blend of education & technology, eSaral team made the learning personalized & adaptive for everyone.

eSaral Making Learning affordable, Accessible, and thoughtful for all.

Permutations and Combinations Class 11 Notes for IIT JEE

eSaral provides detailed Notes of Physics, Chemistry, Mathematics and Biology Notes for class 11, and 12. So here you will get class 11 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorem etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. So here Permutations and Combinations Class 11 Notes for IIT JEE Exam preparation.

With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 11 Maths.

### Permutations and Combinations Class 11 Notes

eSaral helps the students by providing you an easy way to understand concepts and attractive study material for IIT JEE which includes the video lectures & Study Material designed by expert IITian Faculties of KOTA.

eSaral provides a series of detailed chapter wise notes for all the Subjects of class 11th and 12th.  These notes will also help you in your IIT JEE preparation.

We hope these Mathematics Notes for Class 11 will be helpful for you to understand the important topics and help in remembering the key points for the exam point of view.

Get Complete Class 11 Mathematics Notes

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