NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8

NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8 - Application of Integrals

Edited By Ramraj Saini | Updated on Dec 03, 2023 10:26 PM IST | #CBSE Class 12th

Upcoming Event

CBSE Class 12th Exam Date : 15 Feb' 2025 - 15 Feb' 2025

NCERT Solutions For Class 12 Maths Chapter 8 Exercise 8.2

NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8 Application of Integrals are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 is similar to the exercise 8.1. Also it has linkages with the previous chapter. Exercise 8.2 Class 12 Maths consists of questions related to areas bounded by two different curves. NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 can be solved easily if the concept is understood from initial few questions. All other questions have the same concept used. Similar questions which are in this exercise are asked in Physics also, hence this exercise becomes more important.

New: CBSE Class 12 Date Sheet 2025 Declared; Direct Link

Sample Papers 2025: English-Core | English-Elective | Hindi-Core | Hindi-Elective | History

This Story also Contains

NCERT Solutions For Class 12 Maths Chapter 8 Exercise 8.2
Access NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2
Application of Integrals Class 12 Chapter 8 Exercise: 8.2
More About NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2
Also Read| Application of Integrals Class 12 Notes
Benefits of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2
Key Features Of NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8
Also see-
NCERT Solutions Subject Wise
Subject Wise NCERT Exemplar Solutions

12th class Maths exercise 8.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

Pearson | PTE

Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 31st DEC'24! Trusted by 3,500+ universities globally

Apply

Access NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2

Download PDF

Application of Integrals Class 12 Chapter 8 Exercise: 8.2

Question: 1 Find the area of the circle $\small 4x^2+4y^2=9$ which is interior to the parabola $\small x^2=4y$ .

Answer:

The area bounded by the circle $\small 4x^2+4y^2=9$ and the parabola $\small x^2=4y$ .
1594727818345
By solving the equation we get the intersecting point $D(-\sqrt{2},\frac{1}{2})$ and $B(\sqrt{2},\frac{1}{2})$
So, the required area (OBCDO)=2 times the area of (OBCO)
Draw a normal on the x-axis (M = $\sqrt{2},0$ )

Thus the area of OBCO = Area of OMBCO - Area of OMBO

$\\\int_{0}^{\sqrt{2}}\sqrt{\frac{(9-4x^2)}{4}}dx-\int_{0}^{\sqrt{2}}{\frac{x^2}{4}}dx\\ =\frac{1}{2}\int_{0}^{\sqrt{2}}\sqrt{9-4x^2}-\frac{1}{4}\int_{0}^{\sqrt{2}}x^2dx\\ =\frac{1}{4}[x\sqrt{9-4x^2}+\frac{9}{2}\sin^{-1}\frac{2x}{3}]_0^{\sqrt{2}}-\frac{1}{4}[\frac{x^3}{3}]_0^{\sqrt{2}}\\ =\frac{1}{4}[\sqrt{2}+\frac{9}{8}\sin^{-1}\frac{2\sqrt{2}}{3}]-\frac{1}{12}(\sqrt{2})^3\\ =\frac{\sqrt{2}}{12}+\frac{9}{8}\sin^{-1}\frac{2\sqrt{2}}{3}\\ =\frac{1}{2}(\frac{\sqrt{2}}{6}+\frac{9}{4}\sin^{-1}\frac{2\sqrt{2}}{3})$
S0, total area =
$\\=2\times \frac{1}{2}(\frac{\sqrt{2}}{6}+\frac{9}{4}\sin^{-1}\frac{2\sqrt{2}}{3})\\ =\frac{\sqrt{2}}{6}+\frac{9}{4}\sin^{-1}\frac{2\sqrt{2}}{3}$

Question:2 Find the area bounded by curves $\small (x-1)^2+y^2=1$ and $\small x^2+y^2=1$ .

Answer:

1654758558749 Given curves are $\small (x-1)^2+y^2=1$ and $\small x^2+y^2=1$

Point of intersection of these two curves are

$A = \left ( \frac{1}{2},\frac{\sqrt3}{2} \right )$ and $B = \left ( \frac{1}{2},-\frac{\sqrt3}{2} \right )$

We can clearly see that the required area is symmetrical about the x-axis

Therefore,

Area of OBCAO = 2 $\times$ Area of OCAO

Now, join AB such that it intersects the x-axis at M and AM is perpendicular to OC

Coordinates of M = $\left ( \frac{1}{2},0 \right )$

Now,

Area OCAO = Area OMAO + Area CMAC

$=\left [ \int_{0}^{\frac{1}{2}}\sqrt{1-(x-1)^2}dx +\int_{\frac{1}{2}}^{1}\sqrt{1-x^2}dx \right ]$
$=\left [ \frac{x-1}{2}\sqrt{1-(x-1)^2}+\frac{1}{2}\sin^{-1}(x-1) \right ]_{0}^{\frac{1}{2}}+\left [ \frac{x}{2}+\frac{1}{2}\sin^{-1}x \right ]_{\frac{1}{2}}^{1}$

$=\left [- \frac{1}{4}\sqrt{1-(-\frac{1}{2})^2}+\frac{1}{2}\sin^{-1}(\frac{1}{2}-1)-0-\frac{1}{2}\sin^{-1}(-1) \right ]+\left [ 0+\frac{1}{2}\sin^{-1}(1)- \frac{1}{4}\sqrt{1-\left ( \frac{1}{2} \right )^2}-\frac{1}{2}\sin^{-1}\left ( \frac{1}{2} \right )\right ]$
$=\left [ -\frac{\sqrt3}{8}+\frac{1}{2}\left ( -\frac{\pi}{6} \right )-\frac{1}{2}\left ( -\frac{\pi}{2} \right ) \right ]+\left [ \frac{1}{2}\left ( \frac{\pi}{2} \right ) -\frac{\sqrt3}{8}-\frac{1}{2}\left ( \frac{\pi}{6} \right )\right ]$
$= \left [ -\frac{\sqrt3}{8}+\frac{\pi}{6} \right ]+\left [ \frac{\pi}{6}-\frac{\sqrt3}{8} \right ]$
$=2 \left [ -\frac{\sqrt3}{8}+\frac{\pi}{6} \right ]$
Now,
Area of OBCAO = 2 $\times$ Area of OCAO

$=2\times 2 \left [ -\frac{\sqrt3}{8}+\frac{\pi}{6} \right ]$
$=\frac{2\pi}{3}-\frac{\sqrt3}{2}$

Therefore, the answer is $\frac{2\pi}{3}-\frac{\sqrt3}{2}$

Question: 3 Find the area of the region bounded by the curves $\small y=x^2+2,y=x,x=0$ and $\small x=3$ .

Answer:

The area of the region bounded by the curves,

$\small y=x^2+2,y=x,x=0$ and $\small x=3$ is represented by the shaded area OCBAO as

1654758611010

Then, Area OCBAO will be = Area of ODBAO - Area of ODCO

which is equal to

$\int_0^3(x^2+2)dx - \int_0^3x dx$

$= \left ( \frac{x^3}{3}+2x \right )_0^3 -\left ( \frac{x^3}{2} \right )_0^3$

$= \left [ 9+6 \right ] - \left [ \frac{9}{2} \right ] = 15-\frac{9}{2} = \frac{21}{2}units.$

Question: 4 Using integration find the area of region bounded by the triangle whose vertices are $\small (-1,0),(1,3)$ and $\small (3,2)$ .

Answer:

So, we draw BL and CM perpendicular to x-axis.

Then it can be observed in the following figure that,

$Area(\triangle ACB) = Area (ALBA)+Area(BLMCB) - Area (AMCA)$

We have the graph as follows:

1654758688421

Equation of the line segment AB is:

$y-0 = \frac{3-0}{1+1}(x+1)$ or $y = \frac{3}{2}(x+1)$

Therefore we have Area of $ALBA$

$=\int_{-1}^1 \frac{3}{2}(x+1)dx =\frac{3}{2}\left [ \frac{x^2}{2}+x \right ]_{-1}^1$

$=\frac{3}{2}\left [ \frac{1}{2}+1-\frac{1}{2}+1 \right ] =3units.$

So, the equation of line segment BC is

$y-3 = \frac{2-3}{3-1}(x-1)$ or $y= \frac{1}{2}(-x+7)$

Therefore the area of BLMCB will be,

$=\int_1^3 \frac{1}{2}(-x+7)dx =\frac{1}{2}\left [ -\frac{x^2}{2}+7x \right ]_1^3$

$= \frac{1}{2}\left [ -\frac{9}{2}+21+\frac{1}{2}-7 \right ] =5units.$

Equation of the line segment AC is,

$y-0 = \frac{2-0}{3+1}(x+1)$ or $y = \frac{1}{2}(x+1)$

Therefore the area of AMCA will be,

$=\frac{1}{2}\int_{-1}^3 (x+1)dx =\frac{1}{2}\left [ \frac{x^2}{2}+x \right ]_{-1}^3$

$=\frac{1}{2}\left ( \frac{9}{2}+3-\frac{1}{2}+1 \right ) = 4units.$

Therefore, from equations (1), we get

The area of the triangle $\triangle ABC =3+5-4 =4units.$

Question:5 Using integration find the area of the triangular region whose sides have the equations $\small y=2x+1,y=3x+1$ and $\small x=4$ .

Answer:

The equations of sides of the triangle are $y=2x+1, y =3x+1,\ and\ x=4$ .

ON solving these equations, we will get the vertices of the triangle as $A(0,1),B(4,13),\ and\ C(4,9)$

1654758730701

Thus it can be seen that,

$Area (\triangle ACB) = Area (OLBAO) -Area (OLCAO)$

$= \int_0^4 (3x+1)dx -\int_0^4(2x+1)dx$

$= \left [ \frac{3x^2}{2}+x \right ]_0^4 - \left [ \frac{2x^2}{2}+x \right ]_0^4$

$=(24+4) - (16+4) = 28-20 =8units.$

Question:6 Choose the correct answer.

Smaller area enclosed by the circle $\small x^2+y^2=4$ and the line $\small x+y=2$ is

(A) $\small 2(\pi -2)$ (B) $\small \pi -2$ (C) $\small 2\pi -1$ (D) $\small 2(\pi +2)$

Answer:

So, the smaller area enclosed by the circle, $x^2+y^2 =4$ , and the line, $x+y =2$ , is represented by the shaded area ACBA as

1654758775744

Thus it can be observed that,

Area of ACBA = Area OACBO - Area of $(\triangle OAB)$

$=\int_0^2 \sqrt{4-x^2} dx -\int_0^2 (2-x)dx$

$= \left ( \frac{x}{2}\sqrt{4-x^2}+\frac{4}{2}\sin^{-1}{\frac{x}{2}} \right )_0^2 - \left ( 2x -\frac{x^2}{2} \right )_0^2$

$= \left [ 2.\frac{\pi}{2} \right ] -[4-2]$

$= (\pi -2) units.$

Thus, the correct answer is B.

Question:7 Choose the correct answer.

Area lying between the curves $\small y^2=4x$ and $\small y=2x$ is

(A) $\small \frac{2}{3}$ (B) $\small \frac{1}{3}$ (C) $\small \frac{1}{4}$ (D) $\small \frac{3}{4}$

Answer:

The area lying between the curve, $\small y^2=4x$ and $\small y=2x$ is represented by the shaded area OBAO as

1654758937961

The points of intersection of these curves are $O(0,0)$ and $A (1,2)$ .

So, we draw AC perpendicular to x-axis such that the coordinates of C are (1,0).

Therefore the Area OBAO = $Area(\triangle OCA) -Area (OCABO)$

$=2\left [ \frac{x^2}{2} \right ]_0^1 - 2\left [ \frac{x^{\frac{3}{2}}}{\frac{3}{2}} \right ]_0^1$

$=\left | 1-\frac{4}{3} \right | = \left | -\frac{1}{3} \right | = \frac{1}{3} units.$

Thus the correct answer is B.

Benefits of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2

The Class 12th Maths chapter 8 exercise has 3 exercises in total maily dealing with the application of integrals.
These Class 12 Maths chapter 8 exercise 8.2 solutions are helpful in solving the questions in the upcoming exercise also.
NCERT solutions for Class 12 Maths chapter 8 exercise 8.2 provides mostly moderate to difficult level of questions.

50+ Entrance Exams for 10+2 Students Must Not Miss

Download this ebook to learn about 50+ entrance exams for 12th students to get admission to the best colleges for undergraduates.

Download EBook

Key Features Of NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8

Comprehensive Coverage: The solutions encompass all the topics covered in ex 8.2 class 12, ensuring a thorough understanding of the concepts.
Step-by-Step Solutions: In this class 12 maths ex 8.2, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
Accuracy and Clarity: Solutions for class 12 ex 8.2 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
Conceptual Clarity: In this 12th class maths exercise 8.2 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
Inclusive Approach: Solutions for ex 8.2 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
Relevance to Curriculum: The solutions for class 12 maths ex 8.2 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

Also see-

NCERT Solutions Subject Wise

Subject Wise NCERT Exemplar Solutions

Happy learning!!!

Frequently Asked Questions (FAQs)

1. How many questions are there in exercise 8.2 Class 12 Maths ?

Total of 7 questions are there in exercise 8.2 Class 12 Maths.

2. Which applications are mentioned in this exercise ?

Area under two curves are discussed in this chapter mainly.

3. Is this chapter very important for Board exams ?

Yes, this chapter holds good weightage so it is important to cover comprehensively.

4. What is the difficulty level of this exercise 8.2 ?

Moderate to difficult level of questions are asked from this exercise.

5. Mention some of the topics discussed in this chapter ?

Maily area and at higher level volume etc. are discussed in this.

6. How many exercises does this chapter include ?

3 exercises are there in this chapter including miscellaneous exercise.

Also Read

NCERT Class 12 Maths Notes - Download Chapter wise Free PDFs

NCERT Class 12 Physics Chapter 9 Notes Ray Optics and Optical Instruments - Download PDF

NCERT Class 12 Physics Chapter 8 Notes Electromagnetic Waves - Download PDF

NCERT Class 12 Physics Chapter 7 Notes Alternating Current - Download PDF

NCERT Class 12 Physics Chapter 6 Notes Electromagnetic Induction - Download PDF

NCERT Class 12 Physics Chapter 5 Notes Magnetism and Matter - Download PDF

NCERT Books for Class 12 - Download All Subjects PDFs Here

NCERT Solutions for Miscellaneous Exercise Chapter 7 Class 12 - Integrals

NCERT Solutions for Exercise 4.1 Class 11 Maths Chapter 4 - Principle of Mathematical Induction

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

NCERT Exemplar Class 12 Physics Solutions Chapter 8 Electromagnetic Waves

Articles

APOSS Inter Time Table 2025 - Check Andhra Pradesh Open School Exam Dates

Dec 19, 2024

CBSE Class 11 Date Sheet 2025 – Download Class 11th Exam Schedule for All Subjects

Dec 19, 2024

CBSE Class 12 Maths Syllabus 2024-25: Download PDF

Dec 19, 2024

UP Board Practical Exams 2025 - UPMSP High School and Inter Viva to Be Recorded to Ensure Transparency

Dec 19, 2024

JAC 12th Result 2024 Commerce OUT, Check Jharkhand 12th Commerce Result @jacresults.com

Dec 19, 2024

CBSE Class 12 English 2025: Expected Article Writing Questions to Prepare

Dec 17, 2024

Score Above 90% in CBSE Class 12 Board Exam 2025: 2-month Preparation Plan

Dec 17, 2024

CBSE Exam Rules for Class 10 and 12: New Guidelines For CBSE Exams 2024-25

Dec 13, 2024

Upcoming School Exams

Bihar Open Board 10th Examination

Application Date:11 November,2024 - 10 January,2025

Admit Card

Result

Bihar Open Board 12th Examination

Application Date:11 November,2024 - 10 January,2025

Admit Card

Result

National Means Cum-Merit Scholarship

Admit Card Date:27 November,2024 - 22 December,2024

Eligibility Criteria

Application Process

Exam Pattern

Madhya Pradesh State Open School 12th Examination

Admit Card Date:13 December,2024 - 06 January,2025

Admit Card

Result

Gujarat Board Higher Secondary School Certificate

Late Fee Application Date:13 December,2024 - 22 December,2024

Exam Pattern

Result

Admit Card

View All School Exams

Certifications By Top Providers

My SQL Basics

Via Great Learning

Full-Stack Web Development

Via Masai School

Business Analytics Foundations

Via PW Skills

Digital Banking Business Model

Via State Bank of India

Full-Stack Android Development

Via Masai School

Machine Learning with Python a Practical Introduction

Via IBM

1115 courses

816 courses

394 courses

295 courses

Harvard University, Cambridge

98 courses

University of Michigan, Ann Arbor

83 courses

IT & Software

Teaching and Academics

Programming and Development

Health, Fitness and Medicine

Business and Management

Engineering and Architecture

General Management

Financial Management

Environmental Studies

History

Psychology

Artificial Intelligence

Explore Top Universities Across Globe

University of Essex, Colchester

Wivenhoe Park Colchester CO4 3SQ

University College London, London

Gower Street, London, WC1E 6BT

The University of Edinburgh, Edinburgh

Old College, South Bridge, Edinburgh, Post Code EH8 9YL

University of Bristol, Bristol

Beacon House, Queens Road, Bristol, BS8 1QU

University of Delaware, Newark

Newark, DE 19716

University of Nottingham, Nottingham

University Park, Nottingham NG7 2RD

Exams Required to Study in USA: GMAT, GRE, SAT, ACT, IELTS, PTE

9 min ⋆ Dec 19, 2024 06:12 AM IST

Countries Tightened Visa Rules for International Students in 2025

9 min ⋆ Dec 19, 2024 06:12 AM IST

PR in France for Indian and International Students 2025

11 min ⋆ Dec 19, 2024 05:12 AM IST

PR in USA for Indian Students in 2025

8 min ⋆ Dec 19, 2024 05:12 AM IST

Cheapest and Affordable Universities in France for International Students in 2025

12 min ⋆ Dec 19, 2024 05:12 AM IST

Study in Singapore for Indian Students in 2025

12 min ⋆ Dec 19, 2024 05:12 AM IST

Related E-books & Sample Papers

CBSE Class 12 Accountancy Question Papers 2024 (Code-PQ1RS/1) – All Sets (1, 2, 3)

35+ Downloads

CBSE Class 12 Maths Question Papers 2024 (Code-QSS4R/4) – All Sets (1, 2, 3)

40+ Downloads

CBSE Class 12 Maths Question Papers 2024 (Code-Q5QPS/5) – All Sets (1, 2, 3)

17+ Downloads

CBSE Class 12 Maths Question Papers 2024 (Code- PQ3RS/3) – All Sets (1, 2, 3)

6+ Downloads

CBSE Class 12 Maths Question Papers 2024 (Code-PQ2RS/2) – All Sets (1, 2, 3)

5+ Downloads

CBSE Class 12 Maths Question Papers 2024 (Code-PQ1RS/1) – All Sets (1, 2, 3)

6+ Downloads

Questions related to CBSE Class 12th

Have a question related to CBSE Class 12th ?

quartely question paper for mathematics cbse

Hello there! Thanks for reaching out to us at Careers360.

Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.

Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!

Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.

If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.

Let me know if you need any other tips for your math prep. Good luck with your studies!

Read Complete Answer

Jefferson 25 September,2024

i have taken admission in clg after my campartment exam in chemistry along with the neet 2025 preperation but unfortunately i again got campartment after doing all this preparation i got 15 marks only now I can't able to think what should I do next.

It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.

Possible steps:

Re-evaluate Your Study Strategies:
- Identify Weak Areas: Pinpoint the specific topics or concepts that caused difficulties.
- Seek Clarification: Reach out to teachers, tutors, or online resources for additional explanations.
- Practice Regularly: Consistent practice is key to mastering chemistry.
Consider Professional Help:
- Tutoring: A tutor can provide personalized guidance and support.
- Counseling: If you're feeling overwhelmed or unsure about your path, counseling can help.
Explore Alternative Options:
- Retake the Exam: If you're confident in your ability to improve, consider retaking the chemistry compartment exam.
- Change Course: If you're not interested in pursuing chemistry further, explore other academic options that align with your interests.
Focus on NEET 2025 Preparation:
- Stay Dedicated: Continue your NEET preparation with renewed determination.
- Utilize Resources: Make use of study materials, online courses, and mock tests.
Seek Support:
- Talk to Friends and Family: Sharing your feelings can provide comfort and encouragement.
- Join Study Groups: Collaborating with peers can create a supportive learning environment.

Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.

I hope this information helps you.

Read Complete Answer

Kanishka kaushikii 17 September,2024

i scored 84 percent in cbse 2 years ago.Am i eligible for medhavi scholarship if give 12th again after 2 drop years and will got 75+ in mpboard

Hi,

Qualifications:
Age: As of the last registration date, you must be between the ages of 16 and 40.
Qualification: You must have graduated from an accredited board or at least passed the tenth grade. Higher qualifications are also accepted, such as a diploma, postgraduate degree, graduation, or 11th or 12th grade.
How to Apply:
Get the Medhavi app by visiting the Google Play Store.
Register: In the app, create an account.
Examine Notification: Examine the comprehensive notification on the scholarship examination.
Sign up to Take the Test: Finish the app's registration process.
Examine: The Medhavi app allows you to take the exam from the comfort of your home.
Get Results: In just two days, the results are made public.
Verification of Documents: Provide the required paperwork and bank account information for validation.
Get Scholarship: Following a successful verification process, the scholarship will be given. You need to have at least passed the 10th grade/matriculation scholarship amount will be transferred directly to your bank account.

Scholarship Details:

Type A: For candidates scoring 60% or above in the exam.

Type B: For candidates scoring between 50% and 60%.

Type C: For candidates scoring between 40% and 50%.

Cash Scholarship:

Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).

Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.

Hope you find this useful!

Read Complete Answer

Yuvan 30 August,2024

i upload 12th board result screenshot in ncweb form from the cbse site so it is valid

hello mahima,

If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.

hope this helps.

Read Complete Answer

Ashvadha 12 July,2024

Kya mujhe class 12 ka important question milega jo exam mai per year puche jate hai

Hello Akash,

If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.

You can get the Previous Year Questions (PYQs) on the official website of the respective board.

I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.

Thank you and wishing you all the best for your bright future.

Read Complete Answer

kumardurgesh1802 10 July,2024

View All

Stay up-to date with CBSE Class 12th News

Download Careers360 App

All this at the convenience of your phone

Regular Exam Updates
Best College Recommendations
College & Rank predictors
Detailed Books and Sample Papers
Question and Answers

Scan and download the app

Central Board of Secondary Education Class 12th Examination

CBSE 12th Syllabus 2025

Applications Open

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8 - Application of Integrals

NCERT Solutions For Class 12 Maths Chapter 8 Exercise 8.2

Pearson | PTE

Access NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2

Application of Integrals Class 12 Chapter 8 Exercise: 8.2

More About NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2

Also Read| Application of Integrals Class 12 Notes

Benefits of NCERT Solutions for Class 12 Maths Chapter 8 Exercise 8.2

Key Features Of NCERT Solutions for Exercise 8.2 Class 12 Maths Chapter 8

Also see-

NCERT Solutions Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

Also Read

Articles

Upcoming School Exams

Certifications By Top Providers

Explore Top Universities Across Globe

Related E-books & Sample Papers

Questions related to CBSE Class 12th

Popular CBSE Class 12th Questions

Colleges After 12th

JEE Main Important Physics formulas

JEE Main Important Chemistry formulas

TOEFL ® Registrations 2024

Pearson | PTE

JEE Main high scoring chapters and topics

JEE Main Important Mathematics Formulas

Stay up-to date with CBSE Class 12th News

Explore on Careers360

NCERT Solutions

NCERT Exemplars

NCERT Books

NCERT Notes

CBSE

CBSE Class 10

CBSE Class 12th

CISCE Board 10th

IMO

IEO

NSO

NMMS

NVS

JNVST

Schools By Medium

By Ownership

By City

By State

Download Careers360 App

All this at the convenience of your phone

Scan and download the app