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NCERT Exemplar Class 12 Maths Solutions - Chapter Wise Problems with Solutions

NCERT Exemplar Class 12 Maths Solutions - Chapter Wise Problems with Solutions

Updated on Apr 03, 2025 09:10 PM IST | #CBSE Class 12th

NCERT Exemplar is a great tool for students to assist them in their pursuit of higher-level exams like JEE Mains, JEE Advanced, as well as giving better conceptual understanding and in-hand practice of all the chapters. NCERT Exemplar for Class 12 Maths covers some advanced and relatively new topics like matrices, determinants, linear programming, and integrals. Students can use as many quality materials as they get in hand to practice these topics thoroughly to have a grasp on them and perform well in the exam.

This Story also Contains
  1. Some of The Important Topics of NCERT Exemplar Class 12 Maths Solutions:
  2. NCERT Exemplar subject-wise
  3. Importance of solving NCERT Exemplar Class 12 Maths Solutions:
  4. NCERT solutions subject-wise
  5. NCERT Notes Subject wise
  6. NCERT Books and NCERT Syllabus

These NCERT 12 Maths solutions adhere to the 2025-26 CBSE syllabus and prepare students for CBSE Board Examinations in Class 12. Our experienced Careers360 experts have diligently made these solutions, keeping in mind their importance for the students. They explained every step of the solutions and provided all the necessary formulae to help students. A strategically made study plan with structured guidance and these solutions will give students the much-needed confidence to face the exam.

Background wave

NCERT Exemplar Class 12 Maths Solutions Chapter
NCERT Exemplar Class 12 Mathematics Chapter 1: Relations and Functions
NCERT Exemplar Class 12 Mathematics Chapter 2: Inverse Trigonometric Functions
NCERT Exemplar Class 12 Mathematics Chapter 3: Matrices
NCERT Exemplar Class 12 Mathematics Chapter 4: Determinants
NCERT Exemplar Class 12 Mathematics Chapter 5: Continuity and Differentiability
NCERT Exemplar Class 12 Mathematics Chapter 6: Applications of derivatives
NCERT Exemplar Class 12 Mathematics Chapter 7: Integrals
NCERT Exemplar Class 12 Mathematics Chapter 8: Applications of Integrals
NCERT Exemplar Class 12 Mathematics Chapter 9: Differential equations
NCERT Exemplar Class 12 Mathematics Chapter 10: Vector Algebra
NCERT Exemplar Class 12 Mathematics Chapter 11: Three-Dimensional Geometry
NCERT Exemplar Class 12 Mathematics Chapter 12: Linear Programming
NCERT Exemplar Class 12 Mathematics Chapter 13: Probability

Some of The Important Topics of NCERT Exemplar Class 12 Maths Solutions:

1. Calculus:

Calculus in NCERT Class 12 Maths is an important unit not only from an exam point of view but also in understanding other subjects and chapters. This unit contains chapters like Application of Derivatives, Integrals, Continuity and Differentiability, Applications of the Integrals, and Differential Equations. These units will help to make a foundation to learn Modeling, Parametric forms, Curve tracing, etc. The students are required to go through this unit thoroughly and should not skip any chapter from the same as it is allocated the highest weightage.

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2. Vectors and Three-Dimensional Geometry:

This unit consists of chapters like Vectors and Three-Dimensional Geometry, which play a vital role in understanding the directions in physics, Vector space, and Linear Algebra. It will also help in understanding projectile motion and its general equations. The important topics included in chapter Vectors are Scalar Products of Vectors, Projections of Vectors on a Line, Vector Products of Vectors, etc.

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3. Algebra:

Algebra in NCERT Exemplar Class 12 Maths Solutions comprises chapters like Matrices and Determinants. The important topics that the student must cover are the multiplication of matrices, properties of symmetric and skew matrices, and finding the inverse of matrices using elementary transformation. The important topics in the chapter are properties of determinants, matrix inverses and adjoint of matrices, and systems of linear equations solutions. It is also important because it gives the idea of computer programming.

NCERT Exemplar subject-wise

Students can use the following links to check the NCERT exemplar solutions of other subjects.

Importance of solving NCERT Exemplar Class 12 Maths Solutions:

Experts also formulate solutions which help the students to refer to them and be aware of the steps which must be followed and the format which should be maintained while answering a problem. For every chapter, there is a solution set which can be referred to by the students for their board examinations. The NCERT exemplar solutions for Class 12 Maths can also be used for the preparation of various competitive exams.

NCERT solutions subject-wise

After completing the math exercises, students can check the solved exercises of other subjects from these links.

NCERT Notes Subject wise

For clarity of concepts and a quick revision, students can check the following notes prepared by experienced experts at Careers360.

NCERT Books and NCERT Syllabus

Having a clear idea about the latest NCERT syllabus is a necessity. The following links give students access to the 2025-26 syllabus, as well as some important reference books.

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Questions related to CBSE Class 12th

Have a question related to CBSE Class 12th ?
Can I change my board from CBSE to CHSE Odisha in Class 12th?

Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.

Read Complete Answer
Manasvini Gupta 30 January,2025
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:

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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
View All

Popular CBSE Class 12th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

 Option 2)

0.16\; J
Option 3)

1.00\; J

 Option 4)

0.67\; J
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A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

 Option 2)

 6.45×10−3 kg
Option 3)

 9.89×10−3 kg

 Option 4)

12.89×10−3 kg

 
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An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

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200 \, \, J - 500 \, \, J
Option 3)

2\times 10^{5}J-3\times 10^{5}J

 Option 4)

20,000 \, \, J - 50,000 \, \, J
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A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

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\; K\;
Option 3)

zero\;

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K/4
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In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

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

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67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
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How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

 Option 2)

3.125 × 10-2
Option 3)

1.25 × 10-2

 Option 4)

2.5 × 10-2
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If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

 Option 2)

increase two fold
Option 3)

remain unchanged

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be a function of the molecular mass of the substance.
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With increase of temperature, which of these changes?

Option 1)

Molality

 Option 2)

Weight fraction of solute
Option 3)

Fraction of solute present in water

 Option 4)

Mole fraction.
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Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

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
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A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

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
Read More

Colleges After 12th

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