NCERT Solutions Class 11 Physics
NCERT Solutions for Class 11 Physics are provided here to make learners understand the complex ways of learning. We have covered the entire syllabus of class 11 physics. These NCERT Solutions will help the students a lot. The NCERT solutions for Physics are structured as per the latest CBSE board guidelines. These NCERT Solutions for Physics will give you the best guidance for exam preparation as well as for future studies.
Do you know about the branches of physics?
The main branches of physics are mechanics, thermodynamics, vibration and wave phenomena, optics, electromagnetism, relativity, and quantum mechanics. Some of these you will study in class 11 and others in class 12. Physics is the most interesting subject of science. Physics is a natural science that studies matter, its motion, behavior through space and time, and related entities of energy and force. Here, at Study tutee, we have provided easily downloadable and most accurate solutions for the learners.
These NCERT Solutions for Physics will help students prepare for competitive exams like JEE (Mains and Advanced), VITEEE, and other state-level exams. NCERT Solutions for Class 11 Physics are designed by our subject experts in such a way that it is easy for the students to understand the concepts of Physics. Here, we have explained the solutions in detail so that students can solve numerical easily. If you have trouble understanding a topic, you can confirm your answer to the question at the end of the topic. Download a free pdf of NCERT Solutions Class 11 Physics from this page.
Class 11 Physics NCERT Solutions List of Chapters Available in Free PDF
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1) NCERT Solutions Class 11 Physics Chapter 1 Physical World
The physical world is the only world that is real. Traditionally, materialism was only a thesis about objects. The only things that exist are material. There is nothing in the world other than physical entities.
Download NCERT Solutions for Class 11 Physics Chapter 1 Physical World in free pdf. These solutions are provided here to help the students in their board exams. The list of subjects of the chapter ‘Physical world’ is given below: –
- What Is Physics
- Scope And Excitement Of Physics
- Physics, Technology And Society
- Fundamental Forces In Nature
- Gravitational Force
- Electromagnetic Force
- Nature Of Physical Laws
Some important points of the chapter ‘Physical World’ are as follows-
- Physics is concerned with the study of phenomena indifferent to the basic laws of nature and their manifestation. The basic laws of physics are universal and apply widely in a variety of contexts and situations.
- The scope of physics is broad, covering a wide range of magnitudes of physical quantities.
- Physics and technology are related to each other. Sometimes technology gives rise to new physics; Other times physics generates new technology. Both have a direct impact on society.
- Conservation laws are closely related to the symmetry of nature. The symmetry of space and time and other forms of symmetry plays a central role in modern theories of fundamental forces in nature.
2) NCERT Solutions Class 11 Physics Chapter 2 Units and Measurements
There are two types of measurement – standard units and non-standard units. A standard unit of measurement is to measure a specific object such as the length, weight, or capacity of an object. Nonstandard units are units of measurement that are not commonly used such as the pencil, hand, toothpick, or shoe.
Download NCERT Solutions for Class 11 Physics Chapter 2 Units and Measurements Free PDF. These solutions are provided here in detail for the students to upgrade their knowledge and prepare well for the exam. The list of topics in the chapter ‘Units and Measurements’ is given below: –
- The International System Of Units
- Measurement Of Length
- Measurement Of Mass
- Measurement Of Time
- Accuracy, Precision Of Instruments and Errors In Measurement
- Significant Figures
- Dimensions Of Physical Quantities
- Dimensional Formulae And dimensional Equations
- Dimensional Analysis And Its applications
Some important points of the chapter ‘Units and Measurements’ are as follows-
- Physics is a quantitative science based on the measurement of physical quantities. Some physical quantities have been chosen as fundamental or base quantities such as length, mass, time, electric current, thermodynamic temperature, amount of matter, and luminous intensity.
- The International System of Units (SI), based on seven base units, is currently the internationally accepted unit system and is widely used around the world.
- Physical measurements are usually expressed in scientific notation with powers of 10 for small and large quantities. Scientific notation and prefixes are used to simplify measurement notation and numerical calculations that indicate the correctness of numbers.
- Direct and indirect methods can be used to measure physical quantities. In the quantities measured, the accuracy and precision of the measuring instruments, as well as measurement errors, must be taken into account when expressing the result.
3) NCERT Solutions Class 11 Physics Chapter 3 Motion in a Straight Line
If a body moves in a straight line and covers the same distance in equal time intervals then it is said to be in uniform motion. In simple words, if the rate of change of velocity of a body remains constant, then it is said to have uniform acceleration.
Download NCERT Solutions for Class 11 Physics Chapter 3 Motion in a Straight Line in PDF for free. These solutions are provided here to help the students in their board exams. The list of topics of the chapter ‘Motion in a straight line’ is given below: –
- Position, Path Length And Displacement
- Average Velocity And Average speed
- Instantaneous Velocity And Speed
- Kinematic Equations For uniformly Accelerated Motion
- Relative Velocity
Some important points of the chapter ‘Motion in a straight line’ are as follows-
- The equation of motion in a straight line are-
- v = u + at
- S = ut + 1/2 at2
- v2 = u2 + 2as
[Where v = final velocity of the particle, u = initial velocity of the particle, s = displacement of the particle, a = acceleration of the particle, t = time interval in which the particle is in motion]
- When we say the motion of body A relative to B, we mean the motion of A, as seen from B’s frame of reference. Mathematically, it is called as shown VBA = VB – VA.
[Where VBA = Velocity of B as observed from A, VB = Velocity of B from the earth as a reference frame, VA = Velocity of A from the earth as reference frame]
4) NCERT Solutions Class 11 Physics Chapter 4 Motion in a Plane
One of the most common examples of motion in a plane is projectile motion. In a projectile motion, the only acceleration acting in the vertical direction is the acceleration due to gravity (g). Therefore, the equations of motion can be applied to the x-axis and y-axis separately to find the unknown parameter.
Download NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane Free PDF. These solutions are provided here in detail for the students to upgrade their knowledge and prepare well for the exam. The list of topics of the chapter ‘Motion in a plane’ is given below: –
- Scalars And Vectors
- Multiplication Of Vectors By Real numbers
- Addition And Subtraction Of vectors — Graphical Method
- Resolution Of Vectors
- Vector Addition – Analytical method
- Motion In A Plane
- Motion In A Plane With Constant acceleration
- Relative Velocity In Two dimensions
- Projectile Motion
- Uniform Circular Motion
Some important points of the chapter ‘Motion in a Plane’ are as follows-
- The velocity of an object is the rate of change of its position concerning a frame of reference and is a function of time.
- Velocity = (final position – initial position) / time
- The distance covered in unit time is called average speed
- Average speed = Total distance covered / total time taken
- Average velocity is the displacement divided by the time interval in which the displacement occurs.
- Average velocity = Total displacement / Total time taken
- The rate at which there is a change in velocity is called acceleration.
- Acceleration = Change in velocity / Time taken
5) NCERT Solutions Class 11 Physics Chapter 5 Laws of Motion
Newton’s laws of motion relate the motion of an object to the forces acting on it. Newton’s laws are used a lot in physics. Students can solve around 60% of physics with the help of these rules. Here, at Study tutee, we have provided the most accurate solutions for Physics.
Download NCERT Solutions for Class 11 Physics Chapter 5 Laws of Motion in PDF for free. In exams as well as in competitive exams, students will get more help from these solutions. The list of topics in the chapter ‘Laws of Motion’ is given below: –
- Aristotle’s Fallacy
- The Law Of Inertia
- Newton’s First Law Of Motion
- Newton’s Second Law Of motion
- Newton’s Third Law Of Motion
- Conservation Of Momentum
- Equilibrium Of A Particle
- Common Forces In Mechanics
- Circular Motion
- Solving Problems In mechanics
Some important points from the chapter ‘Laws of Motion’ are as follows-
- The first law of motion states that every object moves in a straight line unless a force is applied to it.
- The second law of motion states that the acceleration of an object is proportional to the total force acting on it and inversely proportional to the mass of the object.
- The third law of motion states that for every action there is an equal and opposite reaction.
- The weight of a body is the force with which the earth attracts a body towards its center. If M is the mass of the body and g is the acceleration due to gravity, then the mass of the body is ‘Mg’ in a vertically downward direction.
- If two bodies are in contact, a contact force is produced. If the surface is smooth then the direction of force is normal to the plane of contact. We call this force the normal force.
6) NCERT Solutions Class 11 Physics Chapter 6 Work, Energy and Power
The measure of energy transfer that occurs when an object is moved away by an external force, at least part of which is applied in the direction of the displacement, is called work.
Download NCERT Solutions for Class 11 Physics Chapter 6 Work, Energy, and Power Free PDF. Chapter 6 NCERT Solutions are provided here to help the students in better learning and problem-solving. Below is a list of topics from the chapter ‘Work, Energy and Power’: –
- Notions Of Work And Kinetic Energy : The Work-Energy Theorem
- Kinetic Energy
- Work Done By A Variable Force
- The Work-Energy Theorem For A Variable Force
- The Concept Of Potential Energy
- The Conservation Of Mechanical Energy
- The Potential Energy Of A Spring
- Various Forms Of Energy : The Law Of Conservation Of Energy
Some important points of the chapter ‘Work, Energy and Power’ are as follows-
- According to work-energy theorem, the work done by a force on a body is equal to the change in kinetic energy of the body.
W = Change in kinetic energy of a body
- Energy and momentum are related by E = p2 / 2m (where m is mass).
- The total energy of an isolated system does not change. Energy can be converted from one form to another but the total energy of an isolated system remains constant. This is called the ‘law of conservation of energy’.
- If we draw a graph between the applied force and the displacement, then the work done can be obtained by finding the area under the F-s graph.
- If a spring is pulled or compressed by a small distance from its incompressible configuration, the force on the block given by the spring will be
F = -kx, where x is the compression or elongation in the spring, k is a constant called the ‘spring constant’, whose value depends inversely on the length of the spring without stretching and the nature of the material of the spring.
- The negative sign indicates that the direction of the spring force is opposite to the displacement x of the free-end.
7) NCERT Solutions Class 11 Physics Chapter 7 System of particles and Rotational Motion
A group of related particles is called a system of particles. The motion of an object around a circular path in a fixed orbit is known as rotational motion.
Download NCERT Solutions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion Free PDF. The NCERT Solutions for Chapter 7 are provided herein a simple and understandable pattern for the students to gain more proficiency. The list of topics from the chapter ‘System of Particles and Rotational Motion’ is given below: –
- Centre of mass
- Motion of centre of mass
- Linear momentum of a system of particles
- Vector product of two vectors
- Angular velocity and its relation with linear velocity
- Torque and angular momentum
- Equilibrium of a rigid body
- Moment of inertia
- Theorems of perpendicular and parallel axes
- Kinematics of rotational motion about a fixed axis
- Dynamics of rotational motion about a fixed axis
- Angular momentum in case of rotation about a fixed axis
- Rolling motion
Some important points of the chapter ‘System of Particles and Rotational Motion’ are as follows-
- The center of mass of a body or system is its equilibirum point. The center of mass of a two-particle system is always on the line joining the two particles and is somewhere in between the particles.
- The ratio of change in angular velocity to change in a time interval is called angular acceleration.
- According to this theorem, the moment of inertia I of a body about any axis is equal to its moment of inertia of a body about a parallel axis through its center of mass, Icm plus Ma2 where M is the mass of the body, and V is the vertical distance between of the axes,
i.e. I = Icm + Ma2
- Angular acceleration = change in angular velocity / the time interval
- The rotational inertia of a rigid body is known as the moment of inertia.
8) NCERT Solutions Class 11 Physics Chapter 8 Gravitation
The force of universal attraction acting between all matter is called gravity. Download NCERT Book for Class 11 Physics Chapter 8 Gravitation Solutions Free PDF. The NCERT Solutions for Chapter 8 Gravitation are structured here for the students to score high in the exam. Below is a list of topics from the chapter ‘Gravitation’: –
- Kepler’s laws
- Universal law of gravitation
- The gravitational constant, G
- Acceleration due to gravity of the earth
- Acceleration due to gravity below and above the surface of earth
- Gravitational potential energy
- Escape speed
- Earth satellites
- Energy of an orbiting satellite
- Geostationary and polar satellites
Some important points of the chapter ‘Gravitation’ are as follows-
- The universal constant G of gravitation is numerically equal to the force of attraction between two particles of unit mass, each separated by unit distance.
- General formula of Gravitational Force, F = GMm / r2
- Orbital velocity of satellite, V0 = (GM/R)1/2
- Escape velocity, Ve = (2GM/R)1/2
- The acceleration produced in a body on due to the force of gravity is known as the acceleration due to gravity. It is usually denoted by ‘g’. It is always towards the center of the Earth.
- The value of acceleration due to gravity varies with height, depth, shape of the earth, and the rotation of the earth about its its axis.
- The space around a body within which the gravitational force of attraction is experienced by other bodies is called the gravitational field.
9) NCERT Solutions Class 11 Physics Chapter 9 Mechanical Properties Of Solids
Examples of mechanical properties are elasticity, plasticity, strength, friction, hardness, ductility, brittleness, ductility, and toughness.
Download NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Solids in PDF for free. Here are the solutions for Chapter 9 in the most simple and understandable pattern for the students. Below is a list of topics from the chapter ‘Mechanical Properties of Solids’: –
- Elastic behaviour of solids
- Stress and strain
- Hooke’s law
- Stress-strain curve
- Elastic moduli
- Applications of elastic behaviour of materials
Some important points from the chapter ‘Mechanical Properties of Solids’ are as follows-
- The property of a body to regain its original configuration (length, volume, or shape) when the deforming forces are removed is called elasticity.
- The inability of a body to return to its original size and shape even after removing of deforming force is called plasticity and such a body is called a plastic body.
- Tension is defined as the ratio of the change in size or shape to the original size or shape. It has no dimensions and is just a number.
- Longitudinal strain = change in length / original length
- Volumetric strain = change in volume / original volume
- Hooke’s law states that, within the elastic limits, the stress-to-strain ratio remains constant. This constant is called the modulus of elasticity. Thus, Modulus of elasticity = stress / strain
10) NCERT Solutions Class 11 Physics Chapter 10 Mechanical Properties Of Fluids
Fluids are substances that can flow, for example- liquids and gases. It has no fixed size. Examples of mechanical properties are density, viscosity, temperature, pressure, specific volume, and weight.
Download NCERT Solutions for Class 11 Physics Chapter 10 Mechanical Properties of Fluids in PDF for free. Here are NCERT Solutions for Chapter 10 for the exceptional preparation of students for the exam. These solutions will help them to score high in the exam. Below is a list of topics from the chapter ‘Mechanical Properties of Fluids’: –
- Streamline flow
- Bernoulli’s principle
- Surface tension
Some important points of the chapter ‘Mechanical Properties of Fluids’ are as follows-
- According to Stokes’ law, the backward pulling force acting on a small spherical body of radius r moving with a velocity v through the viscous medium through the coefficient of viscosity ή is given by F =6πηrv
- Terminal velocity is the maximum constant velocity attained by a body while falling freely in a viscous medium. This is achieved when the apparent weight is compensated by the viscous force.
- Surface tension is the property of a fluid due to which the free surface area of the fluid is minimum and thus behaves as a stretchable elastic membrane.
- The force per unit length of a line drawn on a liquid surface and parallel to the surface acting normally on it is called surface tension.
- The SI unit of surface tension is Nm-1 and its dimensional formula is [MT-2].
- Reynold number (Re) is a dimensionless number whose value gives an approximate estimate of whether a fluid will flow smoothly or turbulently.
- The energy contained in the surface of a liquid is called surface energy.
- According to Torricelli’s Theorem, the velocity of flow i.e. the velocity with which the liquid exists the orifice (a narrow hole) is equal to the body that falls down a vertical distance equal to the depth of the orifice. Will be received in the fall. The free surface of the liquid.
The velocity is given by V = √2gh
11) NCERT Solutions Class 11 Physics Chapter 11 Thermal Properties of Matter
The matter is defined as any substance that has mass and occupies space. The temperature of a substance defines its state.
Download NCERT Solutions for Class 11 Physics Chapter 11 Thermal Properties of Matter in PDF for free. Chapter 11 solutions are structured here for the students to score high marks in the examination. The list of topics in the chapter ‘Thermal Properties of Matter’ is given below: –
- Temperature and heat
- Measurement of temperature
- Ideal-gas equation and absolute temperature
- Thermal expansion
- Specific heat capacity
- Change of state
- Heat transfer
- Newton’s law of cooling
Some important points of the chapter ‘Thermal Properties of Matter’ are as follows-
- The temperature of a substance is a physical quantity that measures the degree of heat or coolness of a substance. The SI unit of temperature is the Kelvin (K) and the degree Celsius is the commonly used unit of temperature.
- The branch of science that deals with measuring the temperature of a substance are called thermometry. The instrument which is used to measure the temperature of a body is called a thermometer.
- If tc and tF are values of body temperature on the Celsius temperature scale and Fahrenheit temperature scale, respectively, then the relationship between Fahrenheit and Celsius temperature is given by (tc – 0) / 100 = (tF -32) / 180
- An ideal gas obeys the following law, that is PV = gRT, where P, V and T are pressure, volume, and temperature of the gas respectively & g is the number of moles in an ideal gas and R = 8.31 J mol-1K-1 which is known as the universal gas constant.
- The equation, PV = gRT is known as the ideal gas equation.
12) NCERT Solutions Class 11 Physics Chapter 12 Thermodynamics
Thermodynamics is the branch of physics that deals with the relationship between heat and other forms of energy. It describes how thermal energy is converted into other forms of energy and how thermodynamics affects matter.
Download NCERT Solutions for Class 11 Physics Chapter 12 Thermodynamics in free pdf. Here are the solutions for Chapter 12 to help the students learn and solve the problem better. The list of topics in the chapter ‘Thermodynamics’ is given below: –
- Thermal equilibrium
- Zeroth law of Thermodynamics
- Heat, internal energy and work
- First law of thermodynamics
- Specific heat capacity
- Thermodynamic state variables and equation of state
- Thermodynamic processes
- Heat engines
- Refrigerators and heat pumps
- Second law of thermodynamics
- Reversible and irreversible processes
- Carnot engine
Some important points of the chapter ‘Thermodynamics’ are as follows-
- The system refers to the part of the universe that is under observation.
- Everything else in the universe except the system is called the surroundings.
- The Universe = The System + The Surroundings.
- When the operation is performed at a constant temperature, the process is said to be isothermal. For the isothermal process, dT = 0 where dT is the temperature change.
- An adiabatic process is a process in which there is no transfer of heat between the system and the surroundings.
- When the process is done under constant pressure, it is called the isobaric process. i.e., dP = 0
- A process when carried out in constant quantity is known as an isochoric process in nature.
13) NCERT Solutions Class 11 Physics Chapter 13 Kinetic Theory
The kinetic energy of an object is the energy that dominates due to its motion. It is defined as the work required to accelerate a body of a given mass from rest to its stated velocity.
Download NCERT Solutions for Class 11 Physics Chapter 13 Kinetic Theory in free pdf. Here are the Chapter 13 solutions in easy ways for the learners to understand them better in their exams. The list of topics of the chapter ‘Kinetic Theory’ is given below: –
- Molecular nature of matter
- Behaviour of gases
- Kinetic theory of an ideal gas
- Law of equipartition of energy
- Specific heat capacity
- Mean free path
Some important points of the chapter ‘Kinetic Theory’ are as follows-
- In Boyle’s Law, the volume (V) of a given mass of gas is inversely proportional to the pressure (P) of the gas, provided the temperature of the gas is kept constant.
i.e. V ∝ 1 / P or PV = constant
- In Charle’s Law, the volume (V) of a given mass of gas is directly proportional to the
temperature of the gas, provided the gas pressure remains constant.
i.e. V ∝ T or V / T = constant or V1 / T1 = V2 / T2
- Gay Lussac’s Law (or Pressure Law) states that the pressure P of a given mass of gas is directly proportional to its absolute temperature T, provided the volume V of the gas remains constant.
i.e. P ∝ T or P/ T = constant or P1 / T1 = P2 / T2
- The relation between pressure P, volume V and absolute temperature T of a gas is called its equation of state. Equation of state of an ideal gas
PV = nRT
where n is the number of moles of the gas attached and R is the molar gas constant which is the same for all gases and its value is R = 8.315 JK-1mol-1
- According to Avogadro’s Law, S.T.P. the number of molecules is equal to 6.023 x 1023.
- Graham’s Law of expansion of Gases states that rate of expansion of a gas is inversely proportional to the square root of the density of the gas. i.e. r ∝ (1 / ρ)1/2
- The denser the gas, the slower the rate of diffusion.
14) NCERT Solutions Class 11 Physics Chapter 14 Oscillations
Oscillation refers to any periodic motion that moves about a distance about the equilibrium position and repeats over and over for some time.
Download NCERT Solutions for Class 11 Physics Chapter 14 Oscillations Free PDF. Here are the solutions of Chapter 14 in the most simple and understandable pattern for the students to get more proficiency. Below is the list of topics from the chapter ‘Oscillations’: –
- Periodic and oscillatory motions
- Simple harmonic motion
- Simple harmonic motion and uniform circular motion
- Velocity and acceleration in simple harmonic motion
- Force law for simple harmonic motion
- Energy in simple harmonic motion
- Some systems executing simple harmonic motion
- Damped simple harmonic motion
- Forced oscillations and resonance
Some important points from the chapter ‘Oscillations’ are as follows-
- Motions, processes, or events that repeat themselves at regular intervals are called periods.
- The motion of a body is said to be oscillatory if it moves back and forth about a fixed point after regular intervals. The fixed point about which the body oscillates is called the mean position or equilibrium position.
- Displacement is a vector quantity which means “how far is an object from its position”, it is the overall change in position of the object. It is denoted by D.
- Acceleration is a vector quantity defined as the rate at which an object changes its velocity. It is represented by a.
- The unit of acceleration is expressed in meter/second2.
- The number of oscillations in one second is called frequency. It is expressed as f or n.
- Unit of frequency is expressed in sec-1 or Hertz.
- Frequency and time are independent of amplitude.
- Frequency = 1/Time period
- Time and frequency of particle acting S.H.M. can be expressed in the following way
- Total period, T = 2π x (displacement / acceleration)1/2
- Total frequency, f = (1/2π) x (acceleration / displacement)1/2
15) NCERT Solutions Class 11 Physics Chapter 15 Waves
There are two types of waves – longitudinal and transverse. Transverse waves are water waves and longitudinal waves are sound waves.
Download NCERT Solutions for Class 11 Physics Chapter 15 Waves in PDF for free. Here are Chapter 15 solutions for students to prepare exceptionally for the exam. These solutions will help them to score high in the exam. The list of topics of the chapter ‘Waves’ is given below: –
- Transverse and longitudinal waves
- Displacement relation in a progressive wave
- The speed of a travelling wave
- The principle of superposition of waves
- Reflection of waves
- Doppler effect
Some important points of the chapter ‘Waves’ are as follows-
- Mechanical waves can be produced or propagated only in a physical medium. These waves are governed by Newton’s laws of motion. For example, waves on the surface of the water, waves on stars, sound waves, etc.
- These are those waves that do not require any physical medium for their production and propagation, i.e. they can pass through vacuum and any other physical medium.
- Common examples of electromagnetic waves are visible light, ultraviolet light, radio waves, microwaves, etc.
- These waves are associated with moving particles of matter like electrons, protons, neutrons, etc.
- There are two types of mechanical waves:
(i) Transverse wave motion (ii) Longitudinal wave motion
- Wave velocity is the time rate of propagation of wave motion in the given medium. It is different from particle velocity. The wave velocity depends on the nature of the medium.
- Wave velocity (υ) = Frequency (v) x Wavelength (λ)
- The amplitude of the wave is the maximum displacement of the particles of the medium from their mean position.
- The number of vibrations made by a particle in one second is called frequency. It is denoted by v. Its unit is Hertz (Hz).
Benefits of Solving Class 11 Physics NCERT Solutions
- NCERT Solutions provides step by step explanation of every question given in the textbooks. It is one of the most valuable aids to the students in their homework and exams as well.
- Solving these NCERT solutions will help the students to clear all their doubts.
- These NCERT solutions are designed as per the syllabus of the subject concerned and thus, provide proper guidance along with the entire learning process.
- NCERT solutions help in clearing difficult concepts as these NCERT solutions are prepared using proper explanations.
- To score maximum marks in the exam, students need to practice these NCERT solutions as it consists of different types of questions for practice purpose. This will help the students to solve the wrong questions easily.
- While studying in CBSE board schools, students always get confused while selecting the right study material. Hence, the best option is NCERT Solutions as it covers the entire CBSE syllabus of Class 11 Physics.
- NCERT solutions give valuable education and also help students to upgrade their skills.
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