Saple papers & marking Scheme Class 12
Sample Papers Class 12 CBSE 2020 || All Subjects – Download PDF

CBSE Sample Papers for March 2020 Exams has been recently released by the Central Board of Secondary Education. Sample Papers Class 12 CBSE 2020 are given to download in PDF form. CBSE Class 12 Marking Scheme 2020 for these Sample Papers is also available in this article for download in PDF format.

These CBSE Sample Papers 2020 are based on updated format of CBSE Class 12 Question Papers and are very important for the preparation of upcoming CBSE Board Exam 2020.

Sample Papers & Marking Scheme

SUBJECT

Sample Paper

Marking Scheme

English Core Download PDF Download PDF
Physics Download PDF Download PDF
Chemistry Download PDF Download PDF
Mathematics Download PDF  Download PDF
Biology Download PDF Download PDF
Physical Education Download PDF Download PDF

 

When it is about preparing for the exam efficiently, CBSE Sample Papers for Class 12 are one of the best resources. It benefits students to get prior practice before they attempt for the final exam. Also, they will get to know if they are prepared for the exam completely or not. They can test their knowledge for all these subjects and get confident about the answers. CBSE sample papers for class 12 help students to identify topics that need to be focused more, types of tricky questions, and much more.

Benefits of Practicing CBSE Class 12 Sample Papers

Time Management

By solving the CBSE 12 sample papers students get enough practice that they can solve the entire question paper on time. This helps them in managing the time during exams.

Examination Strategy

After practicing the sample papers students can make a strategy for the exam that which sections, they can solve first and which at the end, depending on their strong and weak points.

Helps in Self Evaluation

If you solve the sample CBSE Sample question paper it will help students to test themselves. They will get to know their current preparation level. Accordingly, they can work on them.

Helps to Identify Silly Mistakes

Solving CBSE Class 12 sample question papers will help students to identify silly mistakes. Note those points and try not to repeat them during the exam.

 

Keep learning and stay tuned for further updates on CBSE Exam. Download eSaral App and subscribe to YouTube Channel to access interactive Video tutorials for Class 10, 11, 12, JEE & NEET Exam preparation. Students can also check out the Complete Class 12 Notes of Physics, Chemistry, and Mathematics.

 

All The Best For 12th Board Exams 2020!

JEE Main April 2020 Dates Changed
JEE Main April 2020 Exam | Important Dates | Syllabus | Exam Pattern & Registration Process

JEE Main April 2020 Dates of Exam have been changed again by the National Testing Agency (NTA). JEE Main April 2020 Exam will be held from April 5 to April 11, 2020. Earlier, the Joint Entrance Examination Main April Attempt Exam was supposed to be held from 3rd – 9th April, 2020

According to the official notification, the online JEE Main 2020 application form for April Exam will release on February 7, 2020. Eligible candidates will be able to fill and submit their online application form until March 6, 2020. The scanned images can be uploaded and payment of the application fee can be done till March 8, 2020.

After the JEE Main 2020 April Attempt, the ranks of the qualified candidates will be released taking into consideration better of the both attempts of JEE Main 2020 scores of all candidates appeared in January 2020 and April 2020 examinations and will be made available on the official website of JEE Main.

CLICK HERE for JEE Main April 2020 Application Form !

IMPORTANT DATES FOR JEE Main 2020 – April Exam

JEE Main 2020 Important Dates – April Session

EVENTS

JEE Main 2020 Dates

Application form availability February 7, 2020
Last date to apply March 6, 2020
Last date to upload images and pay application fee March 8, 2020
Issue of admit card March 16, 2020
Exam date April 5 to April 11, 2020
Release date of answer key and recorded responses Second week of April, 2020
Release of answer key Last week of April, 2020: Paper 1
Second week of May, 2020: Paper 2 & 3
Declaration of result April 30, 2020
Announcement of NTA score Third week of May, 2020

 

Click Here for January JEE Main 2020 Exam Paper Analysis

 

NTA has declared JEE Main 2020 Result for January Session on January 17, 2020. Results for JEE Main April 2020 will be announced on April 30, 2020. Candidates can access their results by entering their date of birth and roll number, along with the declaration of the JEE Main Result, NTA has released the scorecard in online mode.

 

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JEE Main 2020 Exam Pattern

As per the eligibility criteria for, a few changes in the pattern of the question paper(s) and number of question(s) for B.E./B.Tech has been approved by the JEE Apex Board (JAB) for the conduct of JEE (Main)-2020 Examination.

 

Paper Subject with Number of Questions Type of Questions TIMING OF THE EXAMINATION(IST)
B.tech Mathematics – 25(20+5)

Physics – 25(20+5)

Chemistry – 25(20+5)

20 Objective Type – Multiple Choice Questions (MCQs) & 5 Questions with answer as numerical value, with equal weightage to Mathematics, Physics & Chemistry 1st Shift: 09:30 a.m. to 12:30 p.m.

2nd Shift: 02:30 p.m. to 05:30 p.m.

 

There is no age limit for the candidates to appear in JEE Main 2020 Examination. The candidates who have passed their 12th Examination in 2018, 2019 and appearing in 2020 are eligible to JEE Main Examination 2020.

Those candidates who cleared the class 12 exam in 2017 or before 2017 are not eligible to appear for JEE Main 2020 exam.

 

Educational Qualification

Candidates must have at least 5 subjects in class 12 exam or equivalent exam. Where Math, Physics and Chemistry are the essential subjects.

JEE Main 2020 Syllabus

 

FREE Revision Series For JEE | Quick Revision Videos 

👉Physics Revision Series

👉Chemistry Revision Series

👉Mathematics Revision Series

 

 

PHYSICS SYLLABUS CLASS 12
CBSE Class 12 Physics Syllabus 2019-20 | Download Detailed Syllabus

Here in this article the students can find the detailed CBSE Class 12 Physics Syllabus 2019-20. Each chapter is described topic wise. Students should follow this and prepare according to it for the exams.

 

CHAPTER                                                                                                                                  TOPICS
Chapter–1 Electric Charges and Fields

  • Electric Charges
  • Conservation of charge, Coulomb’s law-force between two point charges
  • Forces between multiple charges superposition principle and continuous charge distribution.
  • Electric field
  • Electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric fleld.
  • Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).
Chapter–2 Electrostatic Potential and Capacitance

  • Electric potential, potential difference, electric potential due to a point charge,
  • A dipole and system of charges
  • Equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.
  • Conductors and insulators, free charges and bound charges inside a conductor.
  • Dielectrics and electric polarisation, capacitors and capacitance
  • Combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates
  • Energy stored in a capacitor.
Chapter–3 Current Electricity

  • Electric current, flow of electric charges in a metallic conductor, drift velocity

mobility and their relation with electric current; Ohm’s law electrical resistance

  • V-I characteristics (linear and non-linear), electrical energy and

power, electrical resistivity and conductivity

  • Carbon resistors, colour code for carbon resistors
  • Series and parallel combinations of resistors
  • Temperature dependence of resistance.
  • Internal resistance of a cell, potential difference and emf of a cell
  • Combination of cells in series and in parallel
  • Kirchhoff’s laws and simple applications
  • Wheatstone bridge, metre bridge
  • Potentiometer – principle and its applications to measure potential difference and for comparing EMF of two cells; measurement of internal resistance of a cell
Chapter–4 Moving Charges and Magnetism

  • Concept of magnetic field, Oersted’s experiment
  • Biot – Savart law and its application to current carrying circular loop
  • Ampere’s law and its applications to infinitely long straight wire
  • Straight and toroidal solenoids (only qualitative treatment)
  • Force on a moving charge in uniform magnetic and electric fields, Cyclotron
  • Force on a current-carrying conductor in a uniform magnetic field
  • Force between two parallel current-carrying conductors-definition of ampere
  • Torque experienced by a current loop in uniform magnetic field
  • Moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter
Chapter–5 Magnetism and Matter

  • Current loop as a magnetic dipole and its magnetic dipole moment
  • Magnetic dipole moment of a revolving electron
  • Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis
  • Torque on a magnetic dipole (bar magnet) in a uniform magnetic field
  • Bar magnet as an equivalent solenoid, magnetic field lines; earth’s magnetic field and magnetic elements
  • Para-, dia- and ferro – magnetic substances, with examples
  • Electromagnets and factors affecting their strengths, permanent magnets
Chapter–6 Electromagnetic Induction

  • Electromagnetic induction
  • Faraday’s laws
  • induced EMF and current
  • Lenz’s Law
  • Eddy currents
  • Self and mutual induction
Chapter–7 Alternating Current

  • Alternating currents
  • Peak and RMS value of alternating current/voltage
  • Reactance and impedance
  • LC oscillations (qualitative treatment only)
  • LCR series circuit, resonance; power in AC circuits, power factor, wattless current
  • AC generator and transformer
Chapter–8 Electromagnetic Waves

  • Basic idea of displacement current
  • Electromagnetic waves, their characteristics, their Transverse nature (qualitative ideas only)
  • Electromagnetic spectrum (radio waves, microwaves, infrared, visible,

ultraviolet, X-rays, gamma rays) including elementary facts about their uses

Chapter–9 Ray Optics and Optical Instruments

  • Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and its applications, optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism
  • Scattering of light – blue colour of sky and reddish appearance of the sun at sunrise and sunset
  • Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers
Chapter-10 Wave Optics

  • Wave front and Huygen’s principle, reflection and refraction of plane wave at a plane surface using wave fronts
  • Proof of laws of reflection and refraction using Huygen’s principle
  • Interference, Young’s double slit experiment and expression for fringe width
  • Coherent sources and sustained interference of light
  • Diffraction due to a single slit, width of central maximum
  • Resolving power of microscope and astronomical telescope
  • Polarisation,
  • Plane polarised light
  • Brewster’s law, uses of plane polarised light and Polaroids
Chapter–11 Dual Nature of Radiation and Matter

  • Dual nature of radiation
  • Photoelectric effect
  • Hertz and Lenard’s observations
  • Einstein’s photoelectric equation-particle nature of light
  • Matter waves-wave nature of particles, de-Broglie relation
  • Davisson-Germer experiment (experimental details should be omitted; only conclusion should be

explained)

Chapter–12 Atoms

  • Alpha-particle scattering experiment
  • Rutherford’s model of atom
  • Bohr model,
  • Energy levels, hydrogen spectrum
Chapter–13 Nuclei

  • Composition and size of nucleus
  • Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law
  • Mass-energy relation, mass defect; binding energy per nucleon and its

variation with mass number; nuclear fission, nuclear fusion

Chapter–14 Semiconductor Electronics: Materials, Devices and Simple

Circuits

  • Energy bands in conductors, semiconductors and insulators (qualitative ideas

only)

  • Semiconductor diode – I-V characteristics in forward and reverse bias, diode as

a rectifier

  • Special purpose p-n junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics, zener diode as a voltage regulator

 

 

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Class 12 PHYSICS Complete Notes

 

Class 12 CHEMISTRY Complete Notes

 

Class 12 MATHEMATICS Complete Notes

 

CBSE Class 12 Syllabus of all subjects
Class 12 CBSE Syllabus 2019-20 for All Subjects | CBSE Exam Pattern | Chapter-wise Marks Distribution

Every year CBSE conducts board examination for class 10th and 12th. Class 12 CBSE Syllabus 2019-20 is released by Central Board of Secondary Education. But Class 12th Exam Pattern has been changed and the new pattern and marking scheme is introduced for the session 2019-20. So in this article get to know the changes for CBSE CLASS 12TH Exam Pattern with the marking scheme and syllabus.

CBSE Exam Pattern of Class 12

 

Internal Assessment Earlier the internal assessment was not considered for all subjects. But in March 2020 exams, it is mandatory for all the subjects. From now 25% marks are allotted as internal assessments [20 out of 100]. So from March 2020 exams, the final exams will be conducted for 80 marks. However, some fine arts and science stream subjects will follow the same ratio of 70-30.
Multiple Choice/Objective Type Questions Recently MCQs or objective type questions are included in all the exams. CBSE will ask 25% of the questions as MCQs. So it is clear that at least 20 marks in each exam are covered by these objective type questions. Rest marks will be covered by the subjective and theory questions.
Choice in Questions As per the trend of 2019, CBSE will give option for choice to the students in 33% of the questions.

 

So, here is the Class 12 CBSE Syllabus 2019-20 for All Subjects with Unit wise weightage:

CBSE Class 12 Physics Syllabus 2020 with Unit Wise Weightage

Marking
Unit–I Electrostatics 16
Chapter–1: Electric Charges and Fields
Chapter–2: Electrostatic Potential and
Unit-II Current Electricity
Chapter–3: Current Electricity
Unit-III Magnetic Effects of Current and Magnetism 17
Chapter–4: Moving Charges and Magnetism
Chapter–5: Magnetism and Matter
Unit-IV Electromagnetic Induction and Alternating

Currents

Chapter–6: Electromagnetic Induction
Chapter–7: Alternating Current
Unit–V Electromagnetic Waves 18
Chapter–8: Electromagnetic Waves
Unit–VI Optics
Chapter–9: Ray Optics and Optical Instruments
Chapter–10: Wave Optics
Unit–VII Dual Nature of Radiation and Matter 12
Chapter–11: Dual Nature of Radiation and

Matter

Unit–VIII Atoms and Nuclei
Chapter–12: Atoms
Chapter–13: Nuclei
Unit–IX Electronic Devices  

7

Chapter–14: Semiconductor Electronics:

Materials, Devices and Simple Circuits

TOTAL MARKS 70

 

CLICK HERE FOR THE DETAILED SYLLABUS OF PHYSICS CLASS 12

CBSE Class 12 Chemistry Syllabus 2020 with Unit Wise Weightage

 

 

Unit No.

 

Title

 

Marks

 

Unit I

 

Solutions

 

 

 

23

 

Unit II

 

Electrochemistry

 

Unit III

 

Chemical Kinetics

 

Unit IV

 

Surface Chemistry

 

Unit V

 

General Principles and Processes of Isolation of Elements

 

 

 

 

 

19

 

Unit VI

 

p -Block Elements

 

Unit VI

 

d -and f -Block Elements

 

Unit VII

 

Coordination Compounds

 

Unit VIII

 

Haloalkanes and Haloarenes

 

 

 

 

 

 

28

 

Unit IX

 

Alcohols, Phenols and Ethers

 

Unit X

 

Aldehydes, Ketones and Carboxylic Acids

 

Unit XI

 

Organic Compounds containing Nitrogen

 

Unit XII

 

Biomolecules

 

Unit XIII

 

Polymers

 

Unit XIV

 

Chemistry in Everyday Life

 

Total

 

70

 

CBSE Class 12 Mathematics Syllabus 2020 with Unit Wise Weightage

No. Units Marks
I. Relations and Functions 08
II. Algebra  

10

III. Calculus  

35

IV. Vectors and Three – Dimensional Geometry  

14

V. Linear Programming  

05

VI. Probability  

08

Total  

80

Internal Assessment  

20

 

CLICK HERE FOR THE DETAILED SYLLABUS OF MATHEMATICS CLASS 12

 

CBSE Class 12 Biology Syllabus 2020 with Unit Wise Weightage

 

Unit Title Marks
VI Reproduction 14
VII Genetics and Evolution 18
VIII Biology and Human Welfare 14
IX Biotechnology and its Applications 10
X Ecology and Environment 14
Total 70

 

 CLICK HERE FOR THE DETAILED SYLLABUS OF BIOLOGY CLASS 12

CBSE Class 12 English Syllabus 2020 with Unit Wise Weightage

Typology Testing

Competencies

Objective Type Question including MCQs(1 mark each) Short Answer Questio ns

(2 marks each)

Short Answer Question (4 marks each) Long Answer Question

120150

words

(6 marks each)

Very Long Answer Question

150200

words (HOTS) (10 marks each)

Total marks
Comprehension Conceptual understanding, decoding, Analyzing, inferring, interpreting, appreciating, literary, conventions and vocabulary, summarizing and using appropriate format/s  

 

 

 

MCQ = 5

Objective Type Questions

= 7

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20

Writing Skills Reasoning, appropriacy of style and tone, using appropriate format and fluency, inference, analysis, evaluation and creativity  

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

1

 

 

 

 

2

 

 

 

 

30

Literature Textbooks  and Supplementary Reading Text Recalling, reasoning, appreciating literary convention, inference, analysis, creativity

with fluency

8

Objective Type Questions (4 from1 prose and

4 from 1 poetry extract)

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

30

 

TOTAL

 

1×20=20

 

2×5=10

 

4×3=12

 

6×3=18

 

10×2=20

 

80

Assessment                      of Listening                      and Speaking Skills  

 

 

 

 

 

 

 

 

 

 

 

20

GRAND TOTAL 100

 

CBSE Class 12 Physical Education Syllabus 2020

 

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Class 12 PHYSICS Complete Notes

 

Class 12 CHEMISTRY Complete Notes

 

Class 12 MATHEMATICS Complete Notes

 

Mind Map of Nuclear Physics | Class 12, JEE & NEET – Download from here

Nuclear Physics in Class 12 comprises variety of cases with important formulae and key points. So here is the mind map to help you in remembering all the formulas and important key concepts on finger tips.

Download Mind Map  

Nuclear Physics mind Map

Class 12 CBSE Date Sheet 2020 Released | Download PDF Here

Class 12 CBSE Date Sheet 2020 Released by the CBSE on 17 December 2019. However, Class 12th Examination is going to held from 15 February 2020. Schedule for Arts, Science, Commerce has been released by the CBSE Board. CBSE is the most important board in India as lakhs of students are enrolled in the Central Board of Secondary Education. As per the news, CBSE has ordered the affiliated schools to start the practical exams from 01 January 2020. The schools affiliated to CBSE are supposed to upload the marks before February 2020. CBSE 12th Time Table 2020 is important for students appearing in CBSE board schools.

Class 12 CBSE Date Sheet Science Stream

CBSE XII Time Table (SCIENCE)
Date & Time Subject Code Subject Name
MONDAY,24TH FEB 2020 
10:30 AM – 1:30 PM 048 PHYSICAL EDUCATION
SATURDAY,27TH FEB 2020 
10:30 AM – 1:30 PM 001 ENGLISH ELECTIVE-N
101 ENGLISH ELECTIVE-C
301 ENGLISH CORE
MONDAY,02ND MAR 2020 
10:30 AM – 1:30 PM 042 PHYSICS
625 APPLIED PHYSICS
SATURDAY,07TH MAR 2020 
10:30 AM – 1:30 PM CHEMISTRY
SATURDAY,14TH MAR 2020 
10:30 AM – 1:30 PM 044 BIOLOGY
TUESDAY,17TH MAR 2020 
10:30 AM – 1:30 PM 041 MATHEMATICS
840 APPLIED MATHEMATICS
FRIDAY,20TH MAR 2020 
10:30 AM – 1:30 PM 002 HINDI ELECTIVE
302 HINDI CORE

 

CBSE Class XII Time Table – Download PDF 

 

For Arts & Commerce Class 12th Exam Dates – Click HERE 

The CBSE affiliated schools can download the admit cards of their respective students from CBSE official website from 30 January 2020. Furthermore, CBSE circulated the link for downloading of Admit Cards/Centre Material for Class XII & X examination 2020.

CBSE has also released some important points along with the examination schedule.

  • Duration of time for each paper has been indicated in the data-sheet.
  • Duration of time for each subject / paper as given on the question paper be followed meticulously.
  • Answer books would be distributed to candidates between 10.00 – 10.15 A.M.
  • Candidates would write their particulars on the answers book.
  • Particulars shall be checked & signed by Assistant Superintendent (s).
  • Question paper will be distributed at 10.15 A.M. From 10.15 A.M – 10.30 A.M (15 Minutes), Candidates shall read the question paper.
  • Candidates would plan proper strategy to write the answers.
  • At 10.30 A.M candidates will start writing the answers.

 

Board Exam Preparation Tips:

  • Make your Revision Time table: CBSE ha released Exam dates for Class 12th, so its time to ace up your preparation. Students can plan their revision as per accordance. Students are advised to provide equal time to every subjects to secure good percentage in Board Exams. Also focus on NCERT, as in board Exams questions are asked directly from the textbooks of students.
  • Exam will be conducted in the Morning session from 10:30AM to 1:30 AM, so answer sheets will be distributed at 10:00AM and the students will get question paper at 10:15.
  • Students will be advised to spent 15 minutes in reading question paper carefully and prepare plan on how to approach Exam papers.

Tip: Once the exam starts, it is advised to begin with the easiest questions and then move forward  towards difficult ones! With this approcah you can save extra time to attempt long questions.

  • Don’t take stress stay calm and positive. Even if you don’t know the answers of the questions, don’t stressed out!!!
  • Attempt easy questions first, that will help you in building confidence.
Class X Board Exam Dates - CLICK HERE 

All the Best Students!!!

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Bihar Board Model Paper 2020 for Class 10th – Download PDF
Bihar Board  Model Paper 2020 for Class 10

BSEB has released Bihar Board class 10 model papers 2020 for all Subjects. Students preparing for board exams must practice Bihar Board Model Paper 2020, released by BSEB to get familiar with the exam pattern, marking scheme and the different types of questions. Besides, by solving these Bihar Board 10th model papers 2020 within the given time helps in improving problem-solving speed. This, therefore, helps students learn to manage their time and prepares them for the real and the bigger Bihar Board 10th exams. Students can download the subject-wise Bihar 10th model paper 2020 pdf from below given links.

SUBJECTS DOWNLOAD LINKS
English CLICK HERE
Hindi CLICK HERE 
Mathematics  CLICK HERE
Science CLICK HERE
Social Science CLICK HERE
Sanskrit CLICK HERE

 

BSEB 10th Model Questions Papers are the handiest and easily available online question paper bank that can be used by students to solve questions while preparing for the 10th board examination.

Detailed Syllabus of Class 10th for All Subjects  👈Click Here 

MODEL PAPERS BENEFITS:

The sample papers of BSEB 10th provides numerous benefits. They give a fair idea of exam pattern and marking scheme followed in the exam.

While solving them, students can devise their own strategies for solving it. They can plan which questions to answer first.

Also, they can be downloaded as many times as one wants for perfect practice.

Students can learn time management while solving the BSEB model papers within the given time schedule.

Solving Bihar 10th Model question papers helps in improving the calculation speed.

Download eSaral App for Free Learning

Bihar Board Syllabus class 10th
Bihar Board 10th Syllabus 2020 | All Subjects PDF Download

Bihar Board 10th Syllabus 2020: eSaral is providing the students of Bihar board with latest information regarding the BSEB 10th class 2020 syllabus. The syllabus for Matric students in the new pattern is available here in PDF format.

Students looking for most recent released 10th class syllabus for 2020 year can now download it easily. All the direct links to download these syllabus pdf files are given below.

Students the details of BSEB 2020 Syllabus of all subjects for class 10th is given in this page. Read this page thoroughly and make sure you don’t miss out the important links that we have listed for you. We know that having a proper knowledge about syllabus matters a lot and plays a significant role in order to prepare for board exams hence we are providing you the 10th class latest pattern syllabus. Download BSEB Matric Syllabus 2020 and begin your preparations.

 

Subjects  Download Link
English CLICK HERE
Hindi CLICK HERE
Mathematics CLICK HERE
Science CLICK HERE
Social Science CLICK HERE
Sanskrit CLICK HERE

 

BSEB conducts both secondary and senior secondary board examinations twice (regular and supplementary) in a year. Candidates can download the syllabus as PDF, subject wise syllabus is released for Hindi, English, Mathematics, Science, Social Science and other optional subjects. 

EXAM PREPARATION TIPS FOR BOARD EXAMS:

  • Get all your doubts cleared with the help of seniors, friends or teachers as better clarity leads to good preparation.
  • Refer to the Bihar Board 10th time table 2020 and make a suitable study schedule that accommodates all subjects, time for self-evaluation and contains sufficient breaks in between.
  • After the release of the Bihar Board 10th time table 2020, start solving the model papers. Practice previous years’ Bihar Board 10th papers and sample papers are available online to improve speed and accuracy. Solving sample papers/ model papers also helps in understanding the main concepts that are asked in the examination and the difficulty level of the exam.
  • Make short notes while studying and use them later when revising.
  • Group study is very effective as it will help you analyse your preparation level.

Download eSaral App for Free Learning

 

model papers 12th board
Bihar Board Model Paper 2020 Released for Class 12th – Download PDF
Bihar Board  Model Paper 2020 for Class 12

BSEB has released Bihar Board class 12 model papers 2020 for all the streams including Arts, Science and Commerce. Students preparing for board exams must practice Bihar Board Model Paper 2020, released by BSEB to get familiar with the exam pattern, marking scheme and the different types of questions. Besides, by solving these Bihar Board 12th model papers 2020 within the given time helps in improving problem-solving speed. This, therefore, helps students learn to manage their time and prepares them for the real and the bigger Bihar Board 12th exams. Students can download the subject-wise Bihar 12th model paper 2020 pdf from below given links.

SUBJECTS DOWNLOAD LINKS
English CLICK HERE 
Hindi CLICK HERE
Chemistry CLICK HERE
Physics CLICK HERE
Mathematics CLICK HERE
Biology CLICK HERE

 

BSEB Intermediate 12th Model Questions Papers are the handiest and easily available online question paper bank that can be used by students to solve questions while preparing for the 12th board examination.

Get to know the Detailed Syllabus of Class 12th for Science Stream. 

MODEL PAPERS BENEFITS:

The sample papers of BSEB 12th provides numerous benefits. They give a fair idea of exam pattern and marking scheme followed in the exam.

While solving them, students can devise their own strategies for solving it. They can plan which questions to answer first.

Also, they can be downloaded as many times as one wants for perfect practice.

Students can learn time management while solving the BSEB model papers within the given time schedule.

Solving Bihar 12th Model question papers helps in improving the calculation speed.

Download eSaral App for Free Learning

Bihar board timetable 2020 class 12th
Bihar Board Time Table 2020 for Class 12 Announced – Download PDF

The final Bihar Board 12th Time Table for Science, Comerce and Arts Stream has been released by Bihar School Examination Board (BSEB) on November 18, 2019. Bihar Board Exams 2020 for Class 12th will start from February 3 and will end on February 13, 2020. Bihar Board time table 2020 contains all the important exam dates and instructions to be followed while appearing in the exam.

Bihar Board 12th Exams 2020 will be conducted in two sittings.

As per the Bihar Board 12th time table, the timings of the first sitting are 9:30 am to 12:45 pm and that for the second sitting are 1:45 pm to 5:00 pm. According to the Bihar Intermediate time table 2020, students will be given 15 minutes prior to the beginning of the exam to read the question paper. Therefore, students should complete their exam preparation until the last week of December 2019. Students are suggested to refer to the Bihar Board Time Table for 12th boards given below:

Download 12th timetable 2020
Bihar Board Time Table 2020

According to the Bihar Board class 12 time table, the practical examination/ internal assessment will be conducted from January 10, 2020, to January 21, 2020. To know the Bihar Board 12th time table 2020.

 

 

EXAM PREPARATION TIPS FOR BOARD EXAMS:

  • Get all your doubts cleared with the help of seniors, friends or teachers as better clarity leads to good preparation.
  • Refer to the Bihar Board 12th time table 2020 and make a suitable study schedule that accommodates all subjects, time for self-evaluation and contains sufficient breaks in between.
  • After the release of the Bihar Board 12th time table 2020, start solving the model papers. Practice previous years’ Bihar Board 12th papers and sample papers are available online to improve speed and accuracy. Solving sample papers/ model papers also helps in understanding the main concepts that are asked in the examination and the difficulty level of the exam.
  • Make short notes while studying and use them later when revising.
  • Group study is very effective as it will help you analyse your preparation level.

CLICK TO KNOW THE DETAILED SYLLABUS OF BIHAR BOARD FOR CLASS 12th.

We hope the detailed article on Bihar Board 12th Time Table is helpful. If you have any doubt regarding this article or Bihar Board 12th Routine, drop your comments below and we will get back to you as soon as possible. 

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UP Board Exam
UP Board Exam 10th Class | Syllabus, Timetable & Sample Papers

UP Board Exam 2020 for Class 10th and 12th will begin from February 18, 2020. Check complete details including schedule of Exam, Time Table, Exam pattern and complete syllabus of Exam. UP Board Exam 10th Class Time Table 2020 has been released. Uttar Pradesh Madhyamiuk Shiksha Parishad (UPMSP) has released the class 12 time table on its official website- upmsp.edu.in. While a direct link to download UP Board Class 10 Time Table 2020 has been provided on this page. According to the UP Board 10th Date Sheet 2020, the exams are going to commence from February 18, 2020. The aspiring students can go through the entire page to know the class 10 time table, syllabus and other information in detail.

UP Board Exam 2020 Timetable for Class 10th 

Date of Examination Subject/s Timings
February 18, 2020 Hindi 8 am to 11:15 am
February 19, 2020 Pali, Arabic, Persian 8 am to 11:15 am
Music Singing 2 pm to 5:15 pm
February 20, 2020 Home Science 8 am to 11:15 am
February 22, 2020 English 8 am to 11:15 am
February 24, 2020 Urdu, Gujarati, Punjabi, Bangla, Marathi, Assamese, Odiya, Kannada, Tamil, Sindhi, Telugu, Malayalam, Nepali

 

8 am to 11:15 am
February 25, 2020 Mathematics

 

8 am to 11:15 am
February 26, 2020 Stitching 8 am to 11:15 am
Commercial 2 pm to 5:15 pm
February 27, 2020 Social Science 8 am to 11:15 am
Agriculture 2 pm to 5:15 pm
February 28, 2020 Sanskrit 8 am to 11:15 am
February 29, 2020 Science 8 am to 11:15 pm
March 2, 2020 Painting, Ranjan Arts 8 am to 11:15 am
Computer

 

2 pm to 5:15 pm
March 3, 2020 Human Science

Retail Trade Security Automobile ITO/ITES

8 am to 11:15 am

 

Download Exam Timetable for all streams of Class 10th. Link given below:

Download UP Board Time table 2020
 

UP Board 10th Model Test Papers 

UP Board Class 10th Model Test Papers will help you to get a better overview of the UP Board 10th exam pattern. You will understand the Exam as well as the question pattern and will be able to prepare for exams in a better way.

Syllabus of UP Board 2020 Exam Class 10th 

Here is the Direct Link to Download UP Board Class 12th Syllabus for 2020. Click on the button below to download pdf of class 10th Syllabus.

Download Class 10th UP Board Syllabus
 
Download eSaral App for free Video Tutorials for Class 10th | JEE | NEET & Olympiad Preparation. 

 

sample papers up board
UP Board Model Paper 10th | Download PDF of Sample Papers Class X

Uttar Pradesh Board Has Issued UPMSP Uttar Pradesh Madhyamik Shiksha Parishad UP Board Model Paper 2020 Exam Intermediate to all Subjects. These Have Been Released in PDF Format. Students can See the UP Board Model Paper 10th for 2020 given below in this post.

eSaral brings UP Board Model Papers 2020 for Class 10th students for all subject. These sample question papers are provided by the official website of UP Board. All students of UP Board are allowed to download these papers in pdf format for free.

Get the Model papers of all the important subjects in this page. And also you can download papers in PDF for all group  on this page. The provided model papers are completely  based on the latest NCERT Pattern of UP Board. These  papers will help you to score high and get better ranks in the UP Board exam session 2019-20.

 

Download English Model Paper 2020

Download Hindi Model Paper 2020

Download Mathematics Model paper 2020

Download Science Model paper 2020

Download Social Science Model Paper 2020

 

Every year lakhs of students appear for class 10 &12 board exams from across the state. The Board holds the examinations and prepares the results of lakh of students.
Side-by-side, students also prepare for competitive entrance exams like JEE Main, JEE Advanced, and NEET for admission to engineering and medical courses in various colleges.

Uttar Pradesh Board Syllabus-

Contenders should download the latest revised UP Board 12th Syllabus in PDF Form by pressing the following Link –

 

Download Class 10th UP Board Syllabus
Download eSaral App for free Video Tutorials. 

UP Board Exam
Class 12th UP Board Exam 2020 | Syllabus, Timetable & Model Papers

UP Board Exam 2020 for Class 10th and 12th will begin from February 18, 2020. Check complete details including schedule of Exam, Time Table, Exam pattern and complete syllabus of Exam.

UP Board Class 12 Time Table 2020 has been released. A total of 25,86,247 students have successfully registered themselves for the examination. Uttar Pradesh Madhyamiuk Shiksha Parishad (UPMSP) has released the class 12 time table on its official website- upmsp.edu.in. While a direct link to download UP Board Class 12 Time Table 2020 has been provided on this page. According to the UP Board 12th Date Sheet 2020, the exams are going to commence from February 18, 2020. The aspiring students can go through the entire page to know the class 12 time table, syllabus and other information in detail.

UP Board Exam 2020 Timetable for Class 12th Science

Exam Date Subject Name Exam Timings
18 फरवरी मंगलवार Hindi/हिंदी 2:00 pm to 5:15 pm
20 फरवरी सोमवार Physics/भौतिक विज्ञान 2:00 pm to 5:15 pm
22 फरवरी सोमवार Chemistry/रसायन विज्ञान 2:00 pm to 5:15 pm
26 फरवरी बुधवार English/अंग्रेजी 2:00 pm to 5:15 pm
29 फरवरी शनिवार Biology/जीव विज्ञान, Maths/गणित 2:00 pm to 5:15 pm

 

Download Exam Timetable for all streams of Class 12th. Link given below:

Download UP Board Time table 2020
 

UP Board 12th Model Test Papers 

UP Board Class 12th Model Test Papers will help you to get a better overview of the UP Board 12th exam pattern. You will understand the Exam as well as the question pattern and will be able to prepare for exams in a better way.

Syllabus of UP Board 2020 Exam Class 12th 

Here is the Direct Link to Download UP Board Class 12th Syllabus for 2020. Click on the button below to download pdf of class 12th Syllabus.

Download Class 12th UP Board Syllabus
 
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UP board Exam syllabus 12
UP Board Class 12 Syllabus 2020 | Download PDF

UP Board has finally opted for the NCERT Syllabus for UP Board Class 9th-12th from 2018. This syllabus brings a bit of change in the Exam Pattern of class 12th UP Board. UP Board will now follow the single paper pattern. Earlier UP Board used to take 2 papers in almost every subject in order to conduct exams. Now UP Board will follow the pattern as of CBSE. This pattern has reduced the month of exams to almost half. This new Exam Pattern for UP Board 12th Class may create troubles for the students as they have to pursue a completely different UP Board Class 12 SyllabusOn the other hand, the new exam pattern will help students to get themselves prepared for competition exams.

UP Board Class 12th Exams – Weightage:

  • Theoretical Paper- 70 Marks
  • Practical/Project/Internals – 30 Marks

Students should be focused in Internal exams as well as project work as it carries weightage of 30% in the UP Board 12th Exams Syllabus.

Download Class 12th UP Board Syllabus
 

Advantages of NCERT pattern for UP Board students:

  • The revised Syllabus of UP Board is more beneficial for students and it will assist them to manage up with current demands.
  • This can be turned as an opportunity for the students who wish to simultaneously prepare for the competitive examination through the NCERT syllabus.
  • NCERT books offers in-depth knowledge in easy language.

Students should understand the fact that the syllabus acts as the course planning tool. It describes the course goals; explains the course structure and assignments, exams, review sessions, and other activities required for students to learn the material more effectively. So, it’s very essential for students to go through the syllabus of each subject before they move ahead with their studies.

With NCERT Books and CBSE Pattern, UP Board has also introduced a single paper pattern. Earlier there were 2 papers for every subject now UP board has cut down it to only 1 paper which will reduce no. of exams to almost half.

UP Board 12th Model Test Papers 

UP Board Class 12th Model Test Papers will help you to get a better overview of the UP Board 12th exam pattern. You will understand the Exam as well as the question pattern and will be able to prepare for exams in a better way.

 

Download eSaral App for free Video Tutorials for JEE | NEET | Olympiad Preparation. 

UP Board Model Paper 2020 for Class 12 | Download Pdf

Uttar Pradesh Board Has Issued UPMSP Uttar Pradesh Madhyamik Shiksha Parishad UP Board Model Paper 2020 Exam Intermediate to all Subjects. These Have Been Released in PDF Format. Students can See the UP Board Class 12th Model Paper 2020 given below in this post.

eSaral brings UP Board Model Papers 2020 for Class 12th students for all subject. These sample question papers are provided by the official website of UP Board. All students of UP Board are allowed to download these papers in pdf format for free.

Get the Model papers of Subjects like Mathematics, Hindi, English, Physics, Chemistry, and Biology. And also you can download papers in pdf for all group  on this page. The provided model papers are completely  based on the latest NCERT Pattern of UP Board. These papers will help you to score high and get better ranks in the UP Board exam session 2019-20.

Download English Model Papers 2020

Download Hindi Model Paper 2020

Download Physics Model paper 2020

Download Chemistry Model paper 2020

Download Math Model Paper 2020

Download Biology Model Paper 2020

Every year lakhs of students appear for class 12 board exams from across the state. The Board holds the examinations and prepares the results of lakhs of students.
Side-by-side, students also prepare for competitive entrance exams like JEE Main, JEE Advanced, and NEET for admission to engineering and medical courses in various colleges.
These exams too follow the CBSE syllabus of class 11 and 12 .

Uttar Pradesh Board Syllabus-

Contenders should download the latest revised UP Board 12th Syllabus in PDF Form by pressing the following Link –

 

Download Class 12th UP Board Syllabus
Download eSaral App for free Video Tutorials. 

Rajasthan Board Class 12th – Syllabus | Timetable | Previous Year Question Papers

If you are looking for Rajasthan Board Class 12th Exam 2020 Timetable, then we are here to inform you that as per the news, RBSE will soon release12th Time Table 2020 in a pdf format. Last year RBSE 12th Exam Dates were announced on December 21. So this year we can expect the time table by the end of December. As per last year Rajasthan Board class 12th exam timings are from 8:30 am to 11:45 am.

Important dates related Class 12th RBSE 2020 Exams:

RBSE 12th Exam Date 2020 Important Dates
Availability of Time Table 3rd week of Dec
Start of Examination 1st week of Mar 2020
End of Examination 1st week of Apr 2020

 

Official Website RBSE  http://rajeduboard.rajasthan.gov.in/

 

SYLLABUS

Download PDF – Rajasthan Board (RBSE) Syllabus Class 12 

 

RBSE MODEL PAPERS 

RBSE 12th Model Papers for the preparation of upcoming board exams will be available soon for download in PDF format.

RBSE 12th Model Papers 2020 will release soon. 

Board of Secondary Education, Rajasthan has not released the model papers for the 2020 board exams. The board might shortly release the RBSE 12th Model Papers 2020. Till then students can take help of previous Rajasthan Board papers or 2019 Model Papers given below. These papers are important resources and important for the preparation of upcoming Rajasthan Board Exams 2020.

RBSE Model Papers (2019)
English Compulsory 
English Literature
Physics
Chemistry
Mathematics
Hindi Literature
Hindi Compulsory 

 

The above model papers includes blueprint and complete details of question paper design. Each model papers is published by the Board of Secondary Education, Rajasthan itself and also provided with answers to all the questions.

Answers are provided in each model paper itself. With these help of these model papers, students preparing for RBSE 12th board exams will get an idea about the design of the questions paper and will also understand the level of questions which can be asked in upcoming RBSE 12th exams.

Rajasthan Board Class 12 Previous Year Question Papers HERE

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Rajasthan Board Class 12th | Last 5 years question Papers

Rajasthan Board Class 12th Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ Rajasthan Board Higher Secondary School Papers of all subjects of Class 12th (English, Mathematics, Physics, Chemistry & Hindi).

Previous year question papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ Rajasthan board Higher secondary school (HSC) question papers. These papers will act as the practicing tests for Class 12th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 12th) from the link provided in the given table below:

 

Subjects PDF Download Link 
ENGLISH CLICK HERE
PHYSICS CLICK HERE
CHEMISTRY CLICK HERE
MATHEMATICS CLICK HERE
HINDI CLICK HERE

 

RBSE Previous years question papers are quite useful as they help students familiarise with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

 

 GET FREE Study Material, Download eSaral APP. 

Rajasthan Board Class 12th Physics: Last 5 years Question Papers

Rajasthan Board Class 12th Physics Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ Rajasthan Board Higher Secondary School Papers of all subjects of Class 12th (English, Mathematics, Physics, Chemistry & Hindi).

 

RBSE Mathematics Class 12th Previous Year Question Papers
RBSE-Class-12-Board-Paper-2014-Mathematics 
RBSE-Class-12-Board-Paper-2015-Mathematics
RBSE-Class-12-Board-Paper-2016-Mathematics
RBSE-Class-12-Board-Paper-2017-Mathematics
RBSE-Class-12-Board-Paper-2018-Mathematics

 

Download Previous Year Question Papers of:

Previous year question papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ Rajasthan board Higher secondary school (HSC) Mathematics question papers. These papers will act as the practicing tests for class 12th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 12th) from the link provided in the given table below:

 

RBSE Previous years question papers are quite useful as they help students familiarise with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

 

 GET FREE Study Material, Download eSaral APP. 

Rajasthan Board Class 12th Mathematics: Last 5 years Question Papers

Rajasthan Board Class 12th Mathematics Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ Rajasthan Board Higher Secondary School Papers of all subjects of Class 12th (English, Mathematics, Physics, Chemistry & Hindi).

 

RBSE PHYSICS Class 12th Previous Year Question Papers
RBSE-Class-12-Board-Paper-2014-PHYSICS
RBSE-Class-12-Board-Paper-2015-PHYSICS
RBSE-Class-12-Board-Paper-2016-PHYSICS
RBSE-Class-12-Board-Paper-2017-PHYSICS
RBSE-Class-12-Board-Paper-2018-PHYSICS

 

 

Download Previous Year Question Papers of:

 

Previous year question papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ Rajasthan board Higher secondary school (HSC) Physics question papers. These papers will act as the practicing tests for class 12th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 12th) from the link provided in the given table below:

 

RBSE Previous years question papers are quite useful as they help students familiarise with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

 

 GET FREE Study Material, Download eSaral APP. 

CBSE Syllabus for Class 12 Mathematics
CBSE Syllabus for Class 12 Mathematics

Here is the detailed syllabus of Class 12 Mathematics for CBSE Boards:

Get the detailed CBSE Syllabus for Class 12 Mathematics. This syllabus contains Unit and Chapterwise distribution for Mathematics.

You can also get Syllabus of Physics and Chemistry.

Unit-I : Relations and Functions

1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

2. Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Unit-II : Algebra

1. Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III : Calculus

1. Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

2. Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

$$\int {{{dx} \over {{x^2} \pm {a^2}}}} ,\,\,\int {{{dx} \over {\sqrt {{x^2} \pm {a^2}} }},\,\int {{{dx} \over {{a^2} – {x^2}}}} } ,$$$$\int {{{dx} \over {a{x^2} + bx + c}}} ,\,\,\int {{{dx} \over {\sqrt {a{x^2} + bx + c} }}} $$

$$\int {{{px + q} \over {a{x^2} + bx + c}}dx,\,\,} \int {{{px + q} \over {\sqrt {a{x^2} + bx + c} }}dx,\,\,\int {\sqrt {{a^2} \pm {x^2}} \,dx,\,\,} \,\int {\sqrt {{x^2} – {a^2}} \,dx} } $$

$$\int {\sqrt {a{x^2} + bx + c} } \,\,dx,\,\int {(px + q)\,\sqrt {a{x^2} + bx + c} \,\,} dx$$

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

5. Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

$${{dy} \over {dx}} + py = q$$ , where p and q are functions of x or constants.

$${{dx} \over {dy}} + px = q$$, where p and q are functions of y or constants

Unit-IV : Vectors and Three-Dimensional Geometry

1. Vectors

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

2. Three – dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Unit-V: Linear Programming

1. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI : Probability

1. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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