Did you realise that electricity can actually be stored and discharged when needed, as a power bank does for your mobile? This is achievable due to a device referred to as a capacitor, which holds the electrostatic charge and releases it in a burst-like manner, e.g., in a camera flash or some radio circuits. The concept of the electrical energy stored is a very interesting concept, which is related to potential energy, which you learned about in Class 11 Physics.
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The NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance are all the answers to each and every in-text and exercise question, step-by-step, in full detail, and without any errors. These NCERT solutions are carefully formulated by subject experts and simplify the process of learning by deconstructing the hard derivations and numerical problems into simple explanations. The key concepts addressed in this chapter are the electric potential, equipotential surfaces, as well as potential energy of a system of charges, capacitance of conductors, combination of capacitors and energy stored in a capacitor, and the use of dielectrics. These are not only essential to pass the CBSE Class 12 board exams but also to have a solid foundation for other competitive exams such as the JEE and NEET. By practising these NCERT Solutions for Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance regularly, students can enhance their conceptualisation in electrostatics, develop self-confidence in the ability to solve theoretical and numerical problems and learn the problem-solving that they need to achieve at the advanced physics level. The NCERT solutions are deemed as one of the most effective study resources in Class 12 Physics, whether one wants to study it on his/her own, complete an assignment, revise, or prepare it at the last moment.
Students who are about to undertake exams usually require fast, dependable and systematically arranged study content. NCERT Solutions of Chapter 2 -Electrostatic Potential and Capacitance of Class 12 Physics Chapter of the physics textbook are available in a step-by-step format in the PDF. By downloading this free PDF, offline access is easy, revision is easy, and examination is easy any time and anywhere.
Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance question answers of Exercises are straightforward solutions with step-by-step answers to every question in the textbook. These solutions are developed by professionals to enable students to learn how to solve problems and be more accurate when passing exams. These well-designed solutions are important to practice with to be well-structured and perform better on board and competitive exams.
Answer:
Given two charge particles
The separation between two charged particles
Now, let's assume the point P between two charged particles where the electric potential is zero is x meter away from
So,
The potential at point P :
Hence the point between two charged particles where the electric potential is zero lies 10cm away from
Now, Let's assume a point Q which is outside the line segment joining two charges and having zero electric potential. Let the point Q lie r meter away from
So electric potential at point Q = 0
Hence the second point where the electric potential is zero is 24cm away from
Answer:
The electric potential at O due to one charge,
q = 5 × 10 -6 C
r = distance between charge and O = 10 cm = 0.1 m
Using the superposition principle, each charge at the corners contributes in the same direction to the total electric potential at point O.
Therefore, the required potential at the centre is
Answer:
Given 2 charges with charges
An equipotential plane is a plane where the electric potential is the same at every point on the plane. Here if we see the plane which is perpendicular to line AB and passes through the midpoint of the line segment joining A and B, we see that at every point the electric potential is zero because the distance of all the points from two charged particles is the same. Since the magnitude of charges is the same, they cancel out the electric potential between them.
Hence required plane is a plane perpendicular to the line AB and passing through the midpoint of AB which is 3cm away from both charges.
Answer:
The direction of the electric field on this surface is normal to the plane and in the direction of the line joining A and B. Since both charges have the same magnitude and different signs, they cancel out the component of the electric field which is parallel to the surface.
Answer:
Since the charge is uniformly distributed and it always remains on the surface of the conductor, the electric field inside the sphere will be zero.
Answer:
Given,
Charge on the conductor
The radius of a spherical conductor
Now,
The electric field outside the spherical conductor is given by:
Hence electric field just outside is
Answer:
Given,
charge on the conductor
The radius of the spherical conductor
Now,
The electric field at point 18cm away from the centre of the spherical conductor is given by:
Hence electric field at the point 18cm away from the centre of the sphere is
Answer:
As we know,
where A= area of the plate
d = distance between the plates.
Now, Given
The capacitance between plates initially
Now, capacitance when the distance is reduced by half and filled with the substance of dielectric 6
Hence new capacitance is 96pF.
Answer:
Given 3 capacitors of 9pF connected in series,
The equivalent capacitance when connected in series is given by
Hence total capacitance of the combination is 3pF
Answer:
Given,
Supply Voltage V = 120 V
The potential difference across each capacitor will be one-third of the total voltage
Hence potential difference across each capacitor is 40V.
Answer:
Given, 3 capacitors with
The equivalent capacitance when connected in parallel is given by
Hence, the equivalent capacitance is 9pF.
Answer:
Given, 3 capacitors connected in parallel with
Supply voltage
Since they are connected in parallel, the voltage across each capacitor is 100V.
So, charge on 2pf capacitor :
Charge on 3pF capacitor:
Charge on 4pF capacitor:
Hence charges on capacitors are 200pC,300pC and 400pC respectively
Answer:
Given,
Area of the capacitor plate
Distance between the plates
Now,
The capacitance of the parallel plate capacitor is
putting all known value we get,
Hence capacitance of the capacitor is 17.71pF.
Now,
Charge on the plate of the capacitor :
Hence charge on each plate of the capacitor is
Answer:
Given,
The dielectric constant of the inserted mica sheet = 6
The thickness of the sheet = 3mm
Supply voltage
Initial capacitance =
Final capacitance =
Final capacitance
Final capacitance
Final charge on the capacitor =
Hence on inserting the sheet charge on each plate changes to
Answer:
If a 3mm mica sheet is inserted between plates of the capacitor after disconnecting it from the power supply, the voltage across the capacitor will be changed. Since the charge on the capacitor can not go anywhere, if we change the capacitance (which we are doing by inserting mica sheet here), the voltage across the capacitor has to be adjusted accordingly.
As obtained from question number 8 charge on each plate of the capacitor is
Answer:
As we know,
the electrostatic energy stored in the capacitor is
Here,
So,
Hence energy stored in the capacitor is
Answer:
Given
Energy stored :
Now, when it is disconnected and connected to another capacitor of capacitance 600pF
New capacitance
New electrostatic energy
Hence loss in energy
Electrostatic Potential and Capacitance class 12 question answers - Additional Questions will provide the students with additional practice on top of the textbook questions. These questions help in the enhancement of problem-solving skills, learning of tricky principles and organising learners to take tests at higher levels such as JEE and NEET. Being a great revision and practice guide, they include step-by-step proven solutions.
Answer:
Given,
The initial distance between two charges
The final distance between two charges
Hence total work is done
The path of the charge does not matter; only the initial and final positions matters.
Answer:
As we know,
the distance between vertices and the centre of the cube
Where b is the side of the cube.
So potential at the centre of the cube:
Hence electric potential at the centre will be
The electric field will be zero at the centre due to symmetry i.e. every charge lying in the opposite vertices will cancel each other's field.
3. (a) Two tiny spheres carrying charges
Answer:
As we know
outside the sphere, we can assume it like a point charge. so,
the electric potential at midpoint of the two-sphere
where q1 and q2 are charges and d is the distance between them
So,
The electric field
3. (b) Two tiny spheres carrying charges
Answer:
The distance of the point from both the charges :
Hence,
Electric potential:
Electric field due to q1
Electric field due to q2
Now,
Resultant Electric field :
Where
Here,
Hence
4. (a) A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge Q.A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
Answer:
The charge placed on the centre is q, so -q will be the charge induced in the inner shell and + q will be induced in the outer shell
So,
charge density on the inner shell
charge Density on the outer shell
4. (b) A spherical conducting shell of inner radius r 1 and outer radius r 2 has a charge Q. Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
Answer:
Yes, the electric field inside the cavity is zero even when the shape is irregular and not the sphere. Suppose a Gaussian surface inside the cavity, now since there is no charge inside it, the electric flux through it will be zero according to the guess law. Also, all of the charges will reside on the surface of the conductor so, net charge inside is zero. hence electric field inside cavity is zero.
5. (a) Show that the normal component of the electrostatic field has a discontinuity from one side of a charged surface to another given by
Answer:
The electric field on one side of the surface with charge density
The electric field on another side of the surface with charge density
Now, resultant of both surfaces:
As
There has to be a discontinuity at the sheet of the charge since both electric fields are in the opposite direction.
Now,
Since the electric field is zero inside the conductor,
the electric field just outside the conductor is
Answer:
Let's assume a rectangular loop of length l and small width b.
Now,
Line integral along the loop :
This implies
From here,
Since
Answer:
The charge density of the cylinder with length l and radius r =
The radius of another hollow cylinder with the same length = R
Now, let our gaussian surface be a cylinder with the same length and different radius r
the electric flux through Gaussian surface
Hence electric field ar a distance r from the axis of the cylinder is
7. (a) In a hydrogen atom, the electron and proton are bound at a distance of about
Answer:
As we know,
the distance between electron-proton of the hydrogen atom
The potential energy of the system = potential energy at infinity - potential energy at distance d
As we know,
Hence potential energy of the system is -27.2eV.
7. (b) In a hydrogen atom, the electron and proton are bound at a distance of about
Answer:
The potential energy of the system is -27.2eV. (from the previous question)
Kinetic energy is half of the potential energy in magnitude. so kinetic energy = 27/2 = 13.6eV
so,
total energy = 13.6 - 27.2 = -13.6eV
Hence the minimum work required to free the electron is 13.6eV
7. (c) In a hydrogen atom, the electron and proton are bound at a distance of about 0.53
Answer:
When potential energy is zero at
The potential energy of the system =potential energy at
Hence potential energy, in this case, would be -13.6eV
Answer:
Given,
Distance between proton 1 and 2
Distance between proton 1 and electron
Distance between proton 2 and electron
Now,
The potential energy of the system :
Substituting the values, we get
Answer:
Since both spheres are connected through the wire, their potential will be the same
Let the electric field at A and B be
Now,
also
Also
Therefore,
Therefore the ratio of the electric field is b/a.
10. (a) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively. What is the electrostatic potential at the points (0, 0, z) and (x, y, 0) ?
Answer:
1)electric potential at point (0,0,z)
distance from
distance from
Now,
Electric potential :
2) Since the point,(x,y,0) lies in the normal to the axis of the dipole, the electric potential at this point is zero.
10. (b) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively. Obtain the dependence of potential on the distance r of a point from the origin when
Answer:
Here, since distance r is much greater than half the distance between charges, the potential V at a distance r is inversely proportional to the square of the distance
10. (c) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a), respectively How much work is done in moving a small test charge from the point (5,0,0) to (–7,0,0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?
Answer:
Since point (5,0,0) is equidistant from both charges, they both will cancel out each other's potential and hence the potential at this point is zero.
Similarly, point (–7,0,0) is also equidistant from both charges. and hence potential at this point is zero.
Since the potential at both points is zero, the work done in moving a charge from one point to another is zero. Work done is independent of the path.
Answer:
Here, as we can see
The electrostatic potential caused by the system of three charges at point P is given by
Since
From here, we conclude that
Whereas we know that for a dipole,
And for a monopole,
Answer:
Let's assume n capacitors connected in series and m numbers of such rows,
Now,
As given
The total voltage of the circuit = 1000V
and the total voltage a capacitor can withstand = 400
From here the total number of the capacitors in series
Since the number of capacitors can never be a fraction, we take n = 3.
Now,
Total capacitance required =
Number of rows we need
Hence capacitors should be connected in 6 parallel rows, where each row contains 3 capacitors in series.
Answer:
Given,
The capacitance of the parallel plate capacitor
Separation between plated
Now, as we know
Hence, to get capacitance in farads, the area of the plate should be of the order of a kilometre, which is not good practice, and that is why ordinary capacitors are of the range
Answer:
Given.
Now,
Let's first calculate the equivalent capacitance of
Now let's calculate the equivalent of
Now let's calculate the equivalent of
Now,
The total charge on
So,
The voltage across
The charge on
The potential difference across
Hence Charge on
And Charge on
15. (a) The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply. How much electrostatic energy is stored by the capacitor?
Answer:
Here
The capacitance of the parallel plate capacitor :
The electrostatic energy stored in the capacitor is given by :
Hence, the electrostatic energy stored by the capacitor is
15. (b) The plates of a parallel plate capacitor have an area of 90 cm2 each and are separated by 2.5 mm. The capacitor is charged by connecting it to a 400 V supply. View this energy as stored in the electrostatic field between the plates, and obtain the energy per unit volume u. Hence arrive at a relation between u and the magnitude of electric field E between the plates.
Answer:
The volume of the capacitor is:
Now,
Energy stored in the capacitor per unit volume :
Now, the relation between u and E.
Answer:
Here,
The charge on the capacitance initially
Total electrostatic energy initially
Now, when it is disconnected and connected to another capacitor
Total new capacitance =
Now, by conserving the charge on the capacitor:
Now,
New electrostatic energy :
Therefore,
Lost in electrostatic energy
Answer:
Let
The surface charge density of the capacitor =
Area of the plate =
Now,
As we know,
When the separation is increased by
work done by external force=
Now,
Increase in potential energy :
By the work-energy theorem,
putting the value of
The origin of 1/2 lies in the fact that the field is zero inside the conductor and field just outside is E, hence it is the average value of E/2 that contributes to the force.
Answer:
Given
The radius of the outer shell =
The radius of the inner shell =
charge on the Inner surface of the outer shell =
Induced charge on the outer surface of the inner shell =
Now,
The potential difference between the two shells
Now Capacitance is given by
Hence proved.
19. (a) A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5
Answer:
The capacitance of the capacitor is given by:
Here,
Hence Capacitance of the capacitor is
19. (b) A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5
Answer:
The potential of the inner sphere is given by
Hence, the potential of the inner sphere is
19. (c) A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed and the inner sphere is given a charge of 2.5
Answer:
The radius of the isolated sphere
Now, the Capacitance of a sphere:
On comparing it with the concentric sphere, it is evident that it has lesser capacitance. This is due to the fact that the concentric sphere is connected to the Earth.
Hence, the potential difference is less and the capacitance is more than the isolated sphere.
Answer:
The charge on the sphere is not exactly a point charge; we assume it when the distance between two bodies is large. When the two charged spheres are brought closer, the charge distribution on them will no longer remain uniform. Hence, it is not true that the electrostatic force between them is exactly given by
20. (b) If Coulomb’s law involved
Answer:
Since the solid angle is proportional to
The Gauss law, which is equivalent to Coulomb's law, will not hold true.
When a small test charge is released at rest at a point in an electrostatic field configuration, it travels along the field line passing through that point only if the field lines are straight, because electric field lines give the direction of acceleration, not the velocity
Answer:
The initial and final positions will be the same for any orbit, whether it is circular or elliptical. Hence, work done will always be zero.
Answer:
Since the electric potential is not a vector quantity, unlike the electric field, it can never be discontinuous.
20. (f) What meaning would you give to the capacitance of a single conductor?
Answer:
There is no meaning in the capacitor with a single plate, factually. but we give it meaning by assuming the second plate at infinity. Hence capacitance of a single conductor is the amount of charge required to raise the potential of the conductor by one unit.
Answer:
Water has a much greater dielectric constant than mica because it possesses a permanent dipole moment and has an unsymmetrical shape.
Answer:
Given
Length of cylinder
inner radius
outer radius
Charge on the inner cylinder
Now as we know,
The capacitance of this system is given by
Now
Since the outer cylinder is earthed, the potential at the inner cylinder is equal to the potential difference between the two cylinders.
So
Potential of inner cylinder:
Answer:
Given
Voltage rating in designing a capacitor
The dielectric constant of the material
Dielectric strength of material =
Safety Condition:
The capacitance of the plate
Now, as we know,
Now,
Hence the minimum required area is
23. (a) Describe schematically the equipotential surfaces corresponding to a constant electric field in the z-direction
Answer:
When the electric field is in the z-direction is constant, the potential in a direction perpendicular to z-axis remains constant. In other words, every plane parallel to the x-y plane is an equipotential plane.
23. (b) Describe schematically the equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains in a constant (say, z) direction
Answer:
The potential in a direction perpendicular to the direction of the field is always gonna be same irrespective of the magnitude of the electric field. Hence equipotential surface will be the plane, normal of which is the direction of the field.
23. (c) Describe schematically the equipotential surfaces corresponding to a single positive charge at the origin.
Answer:
For a single positive charge, the equipotential surface will be the sphere with centre at the position of the charge, which is the origin in this case.
23. (d) Describe schematically the equipotential surfaces corresponding to a uniform grid consisting of long equally spaced parallel charged wires in a plane.
Answer:
The equipotential surface near the grid is periodically varying, and after a long distance, it becomes parallel to the grid.
Answer:
The potential difference between the inner sphere and shell;
So, the potential difference is independent of
Answer:
The surface of the earth and our body are both good conductors. So our body and the ground both have the same equipotential surface, as we are connected to the ground. When we move outside the house, the equipotential surfaces in the air change so that our body and the ground are kept at the same potential. Therefore we do not get an electric shock.
Answer:
Yes, the man will get an electric shock. The aluminium sheet is gradually charged up by discharging current from the atmosphere. Eventually, the voltage will increase up to a certain point depending on the capacitance of the capacitor formed by the aluminium sheet, the insulating slab and the ground. When the man touches that charged metal, he will get a shock.
Answer:
Thunderstorms and lightning across the globe keep the atmosphere charged by releasing light energy, heat energy, and sound energy in the atmosphere. In one way or another, the atmosphere is discharged through regions of ordinary weather. on an average, the two opposing currents are in equilibrium. Hence, the atmosphere perpetually remains charged.
Answer:
Electrical energy, of the atmosphere, is dissipated as light energy, which comes from lightning, heat energy and sound energ,y which comes from the thunderstorm.
The NCERT Class 12 Physics Chapter 2- HOTS (Higher Order Thinking Skills) questions are designed to enhance the analytical and logical thinking ability. These difficult problems extend beyond what can be applied directly, and these problems push the students to think critically and transfer concepts to new situations. Their practice gives them confidence in taking competitive exams such as JEE and NEET, and also confidence that they have learned the basics of Physics.
Q1. The stored energy of a capacitor charged to 100 V, is 1 J. The capacitance of the capacitor is -
Answer:
The energy stored in a capacitor,
Rearrange the formula to solve for capacitance
On Substituting the values
The capacitance of the capacitor is
Q.2 A capacitor is filled by two dielectric materials equally in two configurations as shown in the figure. The dielectric constants of materials are
Answer:
The first arrangement is a parallel combination.
and
The second arrangement is a series combination:
The approximate value of
Q.3 Two equal charges
Answer:
Potential energy -
Q.4 Twenty-seven drops of water of the same size are equally and similarly changed. They are then united to form a bigger drop. By what factor will the electrical potential change?
A) 9 times
B) 27 times
C) 6 times
D) 3 times
Answer:
Let
but
Hence, the answer is the option 1A
Q.5 Find the total charge (in
Answer:
The given circuit is a balanced bridge. Total capacitance
Hence, the answer is 10.
Solving Physics questions effectively requires a structured method that balances conceptual clarity with logical problem-solving. By breaking down each problem into smaller steps and applying the right formulas at the right stage, students can avoid confusion and errors. Developing a systematic approach ensures accuracy, saves time in exams, and builds confidence in tackling both numerical and theoretical problems.
Electric Potential:
Use Diagrams:
Understand Capacitors:
Combination of Capacitors:
Know Dielectrics:
Practice NCERT Questions:
In order to study well before taking exams, students should make emphasis on the important concepts that have maximum weightage. Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance, contains a number of basic principles, which provide the foundation of not only advanced physics, but also competitive examinations. The following is a list of the strategic aspects that the students will use to revise in a systematic way and enhance the preparation.
Mastering the formulas of Class 12 Physics Chapter 2 - Electrostatic Potential and Capacitance is essential for solving numerical problems quickly and accurately in exams. These formulas not only simplify complex derivations but also help in applying concepts directly to JEE, NEET, and board-level questions. A quick revision of these key formulas ensures better problem-solving speed and boosts confidence during exam preparation.
1. Electrostatic Potential
2. Potential Due to a Point Charge:
3. Potential Due to a Dipole:
4. Relation Between Field and Potential:
5. Capacitance of a Capacitor:
6. Parallel Plate Capacitor:
7. Effect of Dielectric:
8. Combination of Capacitors:
Series:
Parallel:
Although NCERT offers the fundamental basis of the knowledge of Electrostatic Potential and Capacitance, competitive examinations such as JEE and NEET require in-depth problem-solving and conceptual implementation. To fill this gap, students need to read more complicated problem sets, mathematical applications with unusual twists, and different forms of theory. The table below indicates the disparity between the preparation in NCERT and the extra preparation needed in JEE/NEET.
The availability of the Chapter-by-Chapter solutions to Class 12 Physics in the NCERT makes the process of preparing the exams more efficient and formal. All in-text and exercise questions are answered step-by-step, in detail and on each link, allowing students to update on the essential concepts in a short time. The solutions are developed in line with the recent CBSE syllabus and are useful in board tests, competitive tests such as JEE and NEET and also in self study and practice of homework.
Frequently Asked Questions (FAQs)
Electric potential energy represents the stored energy due to the positions of charges in an electric field. It determines the work required to assemble a system of charges and plays a crucial role in electrostatic interactions.
Capacitors are widely used in electronic circuits for energy storage, power conditioning, signal filtering voltage regulation and in memory devices. They are essential components in devices like radios, televisions, electric motors, and even flash cameras.
The unit Electrostatics have the first two chapters of Class 12 Physics. A total of 6 to 8 marks questions can be expected from the chapter for CBSE board exam. A good score can be obtained in the CBSE board exam by following NCERT syllabus and problems. For extra questions related to the chapter refer NCERT exemplar questions and the CBSE previous year board papers.
The Class 12 NCERT chapter Electrostatic Potential and Capacitance is an important chapter for NEET exams. Combining the chapter 1 and 2 of class 12 NCERT Physics a total of 8 to 10% questions can be expected for NEET.
A total of 2 or 3 questions can be expected from the unit Electrostatics. From the chapter Electrostatic Potential and Capacitance 1 or 2 questions can be expected or the questions may be using the combinations of concepts in the Class 12 Physics chapter 1 and 2
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Yes, you can switch from Science in Karnataka State Board to Commerce in CBSE for 12th. You will need a Transfer Certificate from your current school and meet the CBSE school’s admission requirements. Since you haven’t studied Commerce subjects like Accountancy, Economics, and Business Studies, you may need to catch up before or during 12th. Not all CBSE schools accept direct admission to 12th from another board, so some may ask you to join Class 11 first. Make sure to check the school’s rules and plan your subject preparation.
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For the 12th CBSE Hindi Medium board exam, important questions usually come from core chapters like “Madhushala”, “Jhansi ki Rani”, and “Bharat ki Khoj”.
Questions often include essay writing, letter writing, and comprehension passages. Grammar topics like Tenses, Voice Change, and Direct-Indirect Speech are frequently asked.
Students should practice poetry questions on themes and meanings. Important questions also cover summary writing and translation from Hindi to English or vice versa.
Previous years’ question papers help identify commonly asked questions.
Focus on writing practice to improve handwriting and presentation. Time management during exams is key to answering all questions effectively.
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If you want to improve the Class 12 PCM results, you can appear in the improvement exam. This exam will help you to retake one or more subjects to achieve a better score. You should check the official website for details and the deadline of this exam.
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For the 2025-2026 academic session, the CBSE plans to conduct board exams from 17 February 2026 to 20 May 2026.
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