Physics 55/4/1 2025-2026 Science (English Medium) Class 12 Question Paper Solution

Two wires of same length and same area of cross-section but made of different material of resistivities ρ₁ and ρ₂ are connected in series. The equivalent resistivity of the combination is ______.

`1/2 (rho_1 + rho_2)`

ρ₁ + ρ₂

`sqrt(rho_1 rho_2)`

2(ρ₁ + ρ₂)

Two particles of masses m₁ and m₂ having charges q₁ and q₂ respectively are projected with the same velocity in a region of uniform magnetic field `vec B` pointing vertically upward. If they describe circular paths as shown in the figure, one may conclude that:

`m_1/m_2 > q_1/q_2`

`m_1/m_2 > q_2/q_1`

`m_1/m_2 < q_1/q_2`

`m_1/m_2 < q_2/q_1`

An electron moves around the nucleus in a circular orbit of radius r and makes n revolutions per second. The value of equivalent current in the orbit is ______.

`e/n`

ne

`(n e)/r`

`e/(n r)`

The dimensions of the rate of change of magnetic flux are ______.

[M L T⁻³ A]

[M L² T⁻³ A⁻¹]

[M L² T⁻² A⁻¹]

[M L² T⁻³ A⁻²]

Two identical conductors 1 and 2 are placed on two frictionless conducting rails R and S in a uniform magnetic field directed vertically downward into the plane of the page. If conductor 1 is moved with a constant velocity in the direction as shown in figure, the force on conductor 2 will be along:

`- hat i`

`- hat j`

`hat k`

`hat i`

An ac voltage is given as v = 14 sin(314 t) V. The average and the effective value of the voltage (in V) over a cycle are respectively ______.

14 and 7

10 and 14

0 and 10

10 and 0

The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass (n = 1.5) is ______.

3 × 10⁸ ms⁻¹

2 × 10⁸ ms⁻¹

3.3 × 10⁻⁹ ms⁻¹

5 × 10⁻⁹ ms⁻¹

While studying photoelectric emission from a given surface, the wavelength of the incident radiation is changed from 600 nm to 400 nm, keeping the intensity of radiation the same. Then ______.

cut-off potential will decrease.

cut-off potential will increase.

saturation current will decrease.

saturation current will increase.

Radiation of wavelength 331 nm irradiates the following metals:

Which of the following statements is correct?

Only Na and K show photoelectric emission.

Only Mo will not show photoelectric emission.

All of the given metals show photoelectric emission.

None of them show photoelectric emission.

The kinetic energy of a charged particle is increased to four times of its initial value. The de Broglie wavelength associated with the particle will ______.

increase by 100% of its initial value.

increase by 50% of its initial value.

decrease by 25% of its initial value.

decrease by 50% of its initial value.

Paschen series in spectrum of hydrogen atom lies in ______.

infrared region

ultraviolet region

visible region

partly in ultraviolet region and partly in visible region

In a reversed-biased p-n junction diode, the applied voltage mostly drops across ______.

p-region only

n-region only

depletion region

the diode

Assertion (A): The work done, in taking a unit charge around a closed loop of an electric circuit involving cells and resistors in the loop, is zero.

Reason (R): The potential at a point depends on the location of the point in the loop. After completing one round, the charge comes back to the point of start.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Assertion (A) is true, but Reason (R) is false.

Both Assertion (A) and Reason (R) are false.

Assertion (A): When a ferromagnetic substance is heated to high temperature it becomes paramagnetic in nature.

Reason (R): The disappearance of magnetisation of a ferromagnet is abrupt and not gradual.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Assertion (A) is true, but Reason (R) is false.

Both Assertion (A) and Reason (R) are false.

Assertion (A): When a convex lens made of glass is immersed in water, its converging power increases.

Reason (R): The focal length of a lens depends only on the radii of curvature of its two faces.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Assertion (A) is true, but Reason (R) is false.

Both Assertion (A) and Reason (R) are false.

Assertion (A): The conductivity of an n-type semiconductor is higher than that of a p-type semiconductor at a given temperature.

Reason (R): The electrons being in the conduction band in n-type semiconductor are more mobile than the holes in the valence band in p-type semiconductor.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Assertion (A) is true, but Reason (R) is false.

Both Assertion (A) and Reason (R) are false.

An electric dipole consists of two point charges +1 µC and −1 µC, held 10 cm apart. It is subjected to a uniform electric field of 100 N/C. Calculate the amount of work done in turning the dipole from its position of stable equilibrium to the position of unstable equilibrium, in the field.

State Huygen’s principle.

How did Huygens justify the absence of the backwave on a spherical wavefront?

In a single-slit diffraction experiment, light of wavelength λ illuminates the slit of width ‘a’. The diffraction pattern is observed on a screen kept at a distance D from the slits.

1. Depict variation of intensity in the fringe pattern with the angular position of the fringes.
2. How is the linear width of central maximum affected when separation between the slit and the screen is decreased?

A small bulb is placed at the bottom of a tank, containing a transparent liquid of refractive index `sqrt 2`, to a depth of 1 m. Calculate the area of the surface of the liquid through which light from the bulb emerges.

Draw the graph showing the variation of number of scattered alpha particles (N) detected with scattering angle (θ) in Geiger-Marsden experiment. Infer two conclusions from the graph.

The hole concentration in an intrinsic semiconductor is 5 × 10⁸ m⁻³ . When it is doped with certain impurity, the electron concentration becomes 4 × 10¹² m⁻³. Find the new value of the hole concentration. Also, identify the type of new semiconductor formed after doping.

State Kirchhoff’s rules. Using those rules, find the current flowing through branch FC in the given circuit.

The figure given below shows three straight long parallel conductors 1, 2 and 3 kept in x-y plane, carrying currents 2I, I and 3I respectively as shown in figure.

Find the magnitude and direction of:

1. net magnetic field at a point on conductor 1 and
2. net magnetic force acting on unit length of conductor 1, due to conductors 2 and 3.

A rectangular loop of sides l and b and resistance ‘R’ is kept in a region in which the magnetic field varies as B = B₀ sin ωt.

1. Derive expression for the emf induced in the loop.
2. Find the effective value of current that flows in the loop.

The figure given below shows a square-shaped loop MNOP of side 25 cm placed horizontally in a uniform magnetic field `vec B` directed vertically downward. The position of the loop at t = 0 s is as shown in figure. The loop is pulled with a constant velocity of 25 cm/s till it goes out of the field.

1. What will be the direction of the induced current in the loop as it goes out of the field? For how long would the current in the loop persist?
2. Plot graphs showing the variation of magnetic flux and the magnitude of induced emf as a function of time.

What are infrared waves?

Why are infrared waves referred to as ‘heat waves’?

Give any two uses of infrared waves.

Explain how the dual aspect of matter is evident in the de Broglie relation.

Radiation of wavelength λ is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.

In the nuclear reaction:

\[\ce{^2_1H + ^2_1H -> ^A_ZX + ^1_0n}\]

1. Find the value of A.
2. Calculate the amount of energy released in the reaction.

Given: \[\ce{m(^2_1H)}\] = 2.014102 u, \[\ce{m(^A_ZX)}\] = 3.016049 u, \[\ce{m(^1_0n)}\] = 1.008665 u, 1 u = 931.5 MeV/c²

1. If resistor X were made of manganin and readings for V and I are taken without switching off the circuit, the graph between V and I will be as:    (1)
   1. 
      
   2. 
      
   3. 
      
   4. 
      
2. Error in the value of X obtained from different sets of voltmeter and ammeter readings, is ______.    (1)
   1. due to error in voltmeter reading only.
   2. due to error in ammeter reading only.
   3. equal to the sum of error in voltmeter reading and error in ammeter reading.
   4. equal to error in voltmeter reading divided by the error in ammeter reading.
3. If the movable end of rheostat is moved towards P, then ______.    (1)
   1. reading in ammeter decreases and reading in voltmeter increases.
   2. readings in both voltmeter and ammeter increase.
   3. reading in ammeter increases and reading in voltmeter decreases.
   4. readings in both voltmeter and ammeter decrease.
4. 
   
   1. Suppose the unknown resistance X is replaced by a wire made of the same metal. This wire consists of three parts, of the same length L but has radii r, r/3 and r/2 as shown in the figure.    (1)
      
      For a particular setting of the rheostat, let v1, v2 and v3 be the value of drift velocities in parts AC, CD and DB. Then:
      
      1. v₁ > v₂ > v₃
      2. v₂ > v₃ > v₁
      3. v₃ > v₂ > v₁
      4. v₁ = v₂ = v₃
         OR
   2. Consider the same wire, as shown in figure in question (iv)(a) connected in place of X. For a particular setting of rheostat, let E₁, E₂ and E₃ be the value of electric fields in part AC, CD and DB. Then:    (1)
      1. E₁ = E₂ = E₃
      2. E₃ > E₂ > E₁
      3. E₂ > E₃ > E₁
      4. E₁ > E₂ > E₃

1. The images formed by the objective lens and the eyepiece are respectively ______.    (1)
   1. virtual, real
   2. real, virtual
   3. virtual, virtual
   4. real, real
2. The magnification produced by the telescope does not depend upon the ______.    (1)
   1. colour of light.
   2. focal length of objective lens.
   3. focal length of eyepiece.
   4. apertures of objective lens and eyepiece.
3. Which of the following statements is not correct for this telescope?    (1)
   1. The focal length of objective lens (f_o) is larger than the focal length of eyepiece (f_e).
   2. Its magnifying power can be increased by increasing the focal length of objective lens (f_o).
   3. The distance between two lenses is more than (f_o + f_e).
   4. The magnifying power can be decreased by increasing the focal length of eyepiece.
4. 
   
   1. An astronomical telescope has objective lens and eyepiece of focal lengths 80 cm and 4 cm respectively. To view the image in normal adjustment, the lenses must be separated by a distance of ______.    (1)
      1. 84 cm
      2. 76 cm
      3. 20 cm
      4. 320 cm
         OR
   2. Consider the telescope described in question (iv)(a). Its magnifying power in normal adjustment will be:    (1)
      1. 320
      2. 84
      3. 76
      4. 20

Define refractive index in terms of speed of light.

Derive the relation for the refractive index (µ) of a prism in terms of angle of minimum derivation (δ_m) and angle of prism (A).

A ray of light QP is incident normally on the face BC of a triangular prism ABC of refractive index 1.5 kept in air, as shown in the figure. Trace the path of the ray as it passes through the prism and give relevant explanation.

Differentiate between a wavefront and a ray.

Depict refraction of a plane wave by a convex lens.

Define the term resonant frequency.

Define the term power factor of a series LCR circuit.

For what value of the power factor will the power dissipated in the circuit be maximum?

An inductor of `5/pi` H, a capacitor of `50/pi` µF and a resistor of 400 Ω are connected in series across an ac voltage v = 140 sin(100 πt) V. Calculate:

1. impedance of the circuit, and
2. rms value of current that flows in the circuit. (Take `sqrt 2` = 1.4).

Draw a labelled diagram to show the various components of a step-up transformer.

Obtain the ratio of secondary voltage to primary voltage in terms of number of turns in the two coils.

The number of turns in the primary and the secondary coil of an ideal transformer are 100 and 5000 respectively. If 3.3 kW power is supplied to the transformer at 220 V, find

1. current in the primary coil, and
2. output voltage.

Explain the following statements giving reason:

An equipotential surface through a point is normal to the electric field at that point.

Explain the following statements giving reason:

When a dielectric is placed in an external electric field, the electric field inside the dielectric is less than that outside it.

Explain the following statements giving reason:

The potential difference between the plates of a charged parallel plate capacitor decreases when its plates are brought closer.

Obtain an expression for the work done to dissociate the system of three charges q, −4q and 2q placed at the vertices A, B and C respectively of an equilateral triangle of side ‘a’.