The problem is from atomic physics.

In hydrogen atom,there is only one electron and one proton. Electron is revolving around the nucleus. When excited by radiation of proper frequency,it makes a transition to higher state which gives rise to excitation spectra. Initially, the levels are largely separated but later on they merge together and forms a continuum.

In the problem, Balmer series of hydrogen is observed when electron makes a transition from or to level 2. In series limit of Balmer series, electron makes a transition from infinity(continuum) to level 2. In the same way, Paschen series is observed when the electron makes a transition from/to level 3. 

When ever an electron makes a transition or comes back to Ground state after excitation, it emits a photo of frequency equal to the energy difference between two levels.

Using this concept, the problem can be solved.

The question from diffraction.

Diffraction is a phenomenon that demonstrates the wave nature of light. When light encounters an obstacle of dimension comparable to its wavelength, it bends around the obstacle.There are two types of diffraction pattern. Fresnel's and fraunhofer's. The difference between the two lies in the distance between the source and screen.

In fraunhoffer diffraction, incoming wavefront is parallel to the slit,these sources are in phase. At the central point on the screen, path difference between the incoming waves is zero, so we get a principal maximum. But at the other points, waves reach at different phase, depending on the phase difference, secondary maxima/minima is observed. Using geometry, we can find the condition of maximum/minimum.

Now, on both sides of principal maxima, secondary maxima and minima are observed. 

This problem is from alternating current chapter.

In the given problem, an inductor,resistor and capacitor are connected in series with an alternating voltage supply. When they are connected in series, same current passes through each of them.

Now, rate of dissipation of energy in an electric circuit is  called Power. It is equal to the product of voltage and current. But, in alternating current circuit, power also depends upon the phase difference between the voltage current.

Phasor diagram is necessary to solve the problem. Remember, voltage across inductor leads the current y 90 degree whereas in capacitor it lags behind by 90 degree and in resistor ,it is in same phase. Using the information, the problem can be solved.

The problem is from capacitor chapter.

When a dielectric material is inserted with capacitor, its capacitance increases. When a dielectric material is placed in an electric field,its properties are modified.When it is placed in side the capacitor,slab becomes electrically polarised, its molecules become oriented along the direction of electric field.

One thing that must be kept in mind is, when the capacitor remains connected to the battery and slab is introduced then electric field and potential do not change but its charge increases hence its capacitance increases.

This problem is from interference.

when two light waves equal intensity superimpose together, the resultant intensity is enhanced/reduced depending on the phase difference between the two light waves. Resultant of the two waves is found out using vector addition law.

The resultant intensity is enhanced if the two light waves interfere constructively and the intensity is reduced if they  interfere destructively. The intensity is maximum if the initial intensity of two waves is same(interfere constructively) and minimum intensity is zero if two waves with equal intensity interfere destructively.

The problem is from transistor chapter.

Transistor is a semiconductor device that is operated in three different configurations. Common emitter,common base and common collector. common emitter configuration is commonly used due to its high voltage gain and high input resistance.

In the question given, Beta is the current gain for common emitter config. likewise, Alpha is the current gain for common base configuration.

Here, in the question , one is required to establish between the two different current gains. 

The problem is from radioactivity chapter.

Using the famous Rutherford and Soddy law for radioactive decay, the answer can be found out.

In the question, initial no. of atoms  undergoing radioactive decay is given to be 10,000. Then after 4 minutes, the no. of atoms left is given to be 2500 and radioactive decay constant is asked. Every element is associated with a decay constant that says how rapidly the elements decay with time. Higher the decay constant,more rapidly is the decay.

The question is from photoelectric effect.

When an electron revolves around the nucleus, we know it does not radiate energy. However, when it makes a transition from higher to lower state, it emits a photo with frequency equal to the difference between the two energy levels.

When light of proper frequency is incident on a material, it emits photo electrons with kinetic energy equal to the difference between the photon energy and threshold value of the given  material. The kinetic energy of the emitted photo electron is directly proportional to the stopping potential for the material. using the relation, value can be found out.

The question is from atomic physics.

When an electric moves around the nucleus , it constitutes a current loop. A current loop is always associated with a magnetic moment. Let us consider an electron , say electron in an hydrogen atom. When it is orbiting in its 1st Bohr's orbit, it has  angular momentum that is called orbital angular momentum.

Along with angular momentum, there is also magnetic moment . The ration of magnetic moment to its angular momentum is termed as Gyromagnetic ratio which is again proportional to its charge/mass. Now, we know from Bohr's model, angular momentum is quantised, it depends on principal quantum number(n).

Using this, answer can be found out.

This question is from rotational dynamics.

Here in the problem, a wheel is rotating about its axis perpendicular to its plane with a certain angular velocity. Due to friction, it continuously loses its energy and finally comes back to rest at t=5mins i.e it stops rotating.

During this interval, an angular acceleration is produced due to change in velocity. This angular accelaration is constant (independent of time). So, newton's equations of motions are applicable in this problem.

In the problem, one is asked to find the angular momentum 3 minutes before it stops rotating that is 2 minutes  after it begins its motion. our task would be to find out the angular acceleration and final angular velocity after 2 minutes. This will lead us to the answer.

The question is from travelling waves.

Whenever an equation of travelling wave is given, comparison should be made with the standard equation to get the required values. 

however, if equation of travelling wave is given in non linear sin/cos functions, they should be converted to linear sin/cos form before making any comparison. 

In the problem, one can easily draw comparison with the standard notation and get the answers.

The question is from black body radiation chapter.

Stefan's law is useful in solving the problem. According to the law, Power / energy emitted per second by a black body is proportional to the fourth power of its surface temperature and also its area.

Here, in the problem, the black body is assumed to be spherical in its shape. So, power emitted will be proportional to the square of the radius.

This is a problem of dynamics.

In the question given, a lift is accelerating in upward direction. To solve any problem of dynamics, it is always useful to draw its free body diagram. Since the lift in the question is ACCELERATING in the upward direction, the frame of lift is an example of accelarated frame. A pseudo force needs to be drawn in opposite direction to that of accelerating lift to solve the problem from lift frame.

Along with this pseudo force(acting downward) as the lift moves upward, there is gravitational force as well that acts downward.

Stress is the ratio of force to the cross sectional area of the rope. Force acting on it is gravity and pseudo force. Using the proper relation, result can be found out. 

The question is from rigid body dynamics.

Here,, in the problem, a sphere is rolling so it is associated with both transnational and rotational kinetic energy. Centre of Mass of the sphere is moving with a linear velocity. Condition of rolling is applied.

Now, with this energy, it strikes the rear end of the spring and produces compression. The maximum compression would be produced when the total energy of sphere is converted to the maximum potential energy of the spring. Equating both , you get your answer. 

The problem is from dynamics.

The flywheel, in the question is initially at rest, then it accelerates and reaches an angular velocity of magnitude 24 rad/s in 8s.  Since, angular acceleration is constant, Newton's laws of motion is applicable.

During this interval, it produces angular displacement and that is what we need to find out in the given question.Apply newton's equations of motion to get the answer.

This question is from vibrations of stretched strings/wires, often associated with stringed instruments.

When a wire is clamped at both ends and plucked in the middle, transverse progressive waves travel towards each end of the wire. These waves are then reflected from the other end .By superposition of incident and reflected waves, the transverse stationary waves are set up. Since the wire is clamped at both the ends, nodes are present at both the ends and anti node is  present in between.

Distance between the consecutive nodes is half the wavelength. By clamping at different positions, we get different frequencies produced by the wire. For first overtone, wire is clamped at the middle of the wire. In 2nd overtone, wire is clamped at the quarter of the length. Using the information above, problem can be solved.

The question is from surface tension chapter.

In the given question , a capillary is dipped in water. As a result of capillary action, water column rises inside of the tube. Due to surface tension of water, a force acts on the upward direction and this force is balanced by the weight of the water column. 

Surface tension is equal to the force per unit length . Here length will be the circumference of the inner capillary. Using the basic definition of Surface tension , answer can be found out.

This question is from thermodynamics.

In a diatomic molecules, there are 5 degrees of freedom, namely 3 transnational and 2 rotational. 

Now , we require to use the formula for C_p and C_v for ideal gas that has a relation with universal gas constant. There is another relation between C_p and C_v that is related to adiabatic coefficient. Using the two, we get our answer.

This question is from surface tension.

Here, a big water drop is formed by combination of n tiny water droplets. with equal radii. Although the big drop has a different radius than that of the smaller ones, the total mass before and after remains the same.

From mass conservation, relation between R and r can be found out. Surface energy follows superposition principle. it is added up for each of the tiny water droplets.

The question is from central force motion.

In this problem, ration of binding energy is asked. Binding energy is the total energy that binds any particle to the earth. It is always negative since the sign negative denotes the bound state.

When a satellite is at rest,It has only potential energy that contributes to the binding energy whereas when it is in motion, its KE also contributes to its total energy. Keep in mind that in central force motion, gravitational force of attraction between any two objects provide the necessary centripetal force.   

the question is from Simple harmonic Motion.

In SHM, the displacement of the particle is given by standard notation i.e either sin /cos form. Either of the two can be chosen depending on the initial conditions. Velocity is found by differentiating the displacement with time which on further differentiation yields accelaration.

Substituting the initial value conditions, answer can be found out. 

The question is from gravitational motion chapter.

the acceleration due to gravity is maximum at the surface, it decreases as we move up or go down. 

In the given problem, it is said that acceleration due to gravity at a particular depth is 1/n times the acceleration due to gravity on surface. using the relation that shows variation of g with d and the given information, answer can be found out.

This question is from vibration of air columns with one end closed.

There are musical instruments where sound is produced due to vibration of air columns. The simplest vibration occurs in cylindrical tube. Here, in the problem, one end is closed and the other end is opened. So when we blow the air at open end, it gets reflected from the other end . This incident and reflected waves constitute stationary longitudinal waves.

Hence, there is always a node at the closed end and an anti node at the open end. Using this logic, different modes of frequencies can be calculated.