Physics Delhi Set 1 2024-2025 Science (English Medium) Class 12 Question Paper Solution

Figure shows variation of Coulomb force (F) acting between two point charges with `1/r^2`, r being the separation between the two charges (q₁, q₂) and (q₂, q₃). If q₂ is positive and least in magnitude, then the magnitudes of q₁, q₂ and q₃ are such that:

q₂ < q₃ < q₁

q₃ < q₁ < q₂

q₁ < q₂ < q₃

q₂ < q₁ < q₃

Two wires P and Q are made of the same material. The wire Q has twice the diameter and half the length as that of wire P. If the resistance of wire P is R, the resistance of the wire Q will be:

R

`R/2`

`R/8`

2R

A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field `vec B = (0.4 mT) hat j + (0.6 mT) hat k` is switched on, in the region. The force acting on the segment is ______.

`(2 hat j + 3 hat k)` mN

`(-3 hat j + 2 hat k)` μN

`(6 hat j + 4 hat k)` mN

`(-4 hat j + 6 hat k)` μN

A coil has 100 turns, each of area 0.05 m² and total resistance 1.5 Ω. It is inserted at an instant in a magnetic field of 90 mT, with its axis parallel to the field. The charge induced in the coil at that instant is ______.

3.0 mC

0.30 C

0.45 C

1.5 C

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be ______.

2592

2866

2976

3140

A voltage v = v₀ sin ωt applied to a circuit drives a current i = i₀ sin (ωt + Φ) in the circuit. The average power consumed in the circuit over a cycle is ______.

Zero

i₀ v₀ cos Φ

`(i_0 v_0)/2`

`(i_0 v_0)/2` cos Φ

The given diagram exhibits the relationship between the wavelength of the electromagnetic waves and the energy of photon associated with them. The three points P, Q and R marked on the diagram may correspond respectively to ______.

X-rays, microwaves, UV radiation

X-rays, UV radiation, microwaves

UV radiation, microwaves, X-rays

Microwaves, UV radiation, X-rays

A beaker is filled with water (refractive index `4/3`) upto a height H. A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be ______.

`H/4`

`(3 H)/4`

H

`(4 H)/3`

The stopping potential V₀ measured in a photoelectric experiment for a metal surface is plotted against frequency v of the incident radiation. Let m be the slope of the straight line so obtained. Then the value of charge of an electron is given by: (h is the Planck’s constant.)

mh

`m/h`

`h/m`

`1/(mh)`

Let λ_e, λ_p and λ_d be the wavelengths associated with an electron, a proton and a deuteron, all moving with the same speed. Then the correct relation between them is ______.

λ_d > λ_p > λ_e

λ_e > λ_p > λ_d

λ_p > λ_e > λ_d

λ_e = λ_p = λ_d

Which of the following figures correctly represent the shape of curve of binding energy per nucleon as a function of mass number?

When a p-n junction diode is forward biased ______.

the barrier height and the depletion layer width both increase.

the barrier height increases and the depletion layer width decreases.

the barrier height and the depletion layer width both decrease.

the barrier height decreases and the depletion layer width increases.

Assertion (A): It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.

Reason (R): The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.

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

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

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

Assertion (A) is false and Reason (R) is also false.

Assertion (A): The deflection in a galvanometer is directly proportional to the current passing through it.

Reason (R): The coil of a galvanometer is suspended in a uniform radial magnetic field.

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

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

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

Assertion (A) is false and Reason (R) is also false.

Assertion (A): We cannot form a p-n junction diode by taking a slab of a p-type semiconductor and physically joining it to another slab of a n-type semiconductor.

Reason (R): In a p-type semiconductor η_e  >> η_h while in a n-type semiconductor η_h >> η_e.

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

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

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

Assertion (A) is false and Reason (R) is also false.

Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.

Reason (R): The total energy of a charged particle is always positive.

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

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

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

Assertion (A) is false and Reason (R) is also false.

A battery of emf E and internal resistance r is connected to a rheostat. When a current of 2 A is drawn from the battery, the potential difference across the rheostat is 5 V. The potential difference becomes 4 V when a current of 4 A is drawn from the battery. Calculate the value of E and r.

In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm. The first minimum of the pattern falls at θ = 30°. Calculate the width of the slit.

In a Young’s double-slit experiment, two light waves, each of intensity I₀, interfere at a point, having a path difference `lambda/8` on the screen. Find the intensity at this point.

A transparent solid cylindrical rod (refractive index `2/sqrt 3`) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle θ.

Prove that, in Bohr model of hydrogen atom, the time period of revolution of an electron in n^th orbit is proportional to n³.

A p-type Si semiconductor is made by doping an average of one dopant atom per 5 × 10⁷ silicon atoms. If the number density of silicon atoms in the specimen is 5 × 10²⁸ atoms m⁻³, find the number of holes created per cubic centimetre in the specimen due to doping. Also give one example of such dopants.

Two batteries of emfs 3 V & 6 V and internal resistances 0.2 Ω & 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find:

1. the equivalent emf of the combination
2. the equivalent internal resistance of the combination
3. the current drawn from the combination

A conductor of length l is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to 2l by gradually stretching it. If R and R' are initial and final values of resistance and v_d and `v_d^'` are initial and final values of drift velocity, find the relation between

1. R' and R and
2. `v_d^'` and v_d.

When electrons drift in a conductor from lower to higher potential, does it mean that all the ‘free electrons’ of the conductor are moving in the same direction?

Using Biot-Savart law, derive expression for the magnetic field `(vecB)` due to a circular current carrying loop at a point on its axis and hence at its centre.

Show that the energy required to build up the current I in a coil of inductance L is `1/2 LI^2`.

Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field B is `B^2/(2mu_0)`.

1. A parallel plate capacitor is charged by an ac source. Show that the sum of conduction current (I_c) and the displacement current (I_d) has the same value at all points of the circuit.
2. In case (a) above, is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Answer the following giving reason:

1. All the photo electrons do not eject with the same kinetic energy when monochromatic light is incident on a metal surface.
2. The saturation current in case (a) is different for different intensity.

Answer the following giving reason:

If one goes on increasing the wavelength of light incident on a metal surface, keeping its intensity constant, emission of photo electrons stop at a certain wavelength for this metal.

Define the ‘Mass defect’ of a nucleus.

Define ‘Binding energy’ of a nucleus.

Describe the ‘Fission process’ on the basis of binding energy per nucleon.

A deuteron contains a proton and a neutron and has a mass of 2.013553 u. Calculate the mass defect for it in u and its energy equivalence in MeV.

(m_p = 1.007277 u, m_n = 1.008665 u, 1u = 931.5 MeV/c²)

1. Draw a circuit arrangement for studying the V-I characteristics of a p-n junction diode.
2. Show the shape of the characteristics of a diode.
3. Mention two information that you can get from these characteristics.

(i) The final charge on the capacitor, when key S₁ is closed and S₂ is open, is ______.

1. 5 μC
2. 5 mC
3. 25 mC
4. 0.1 C

(ii) For sufficient time the key S₁ is closed and S₂ is open. Now key S₂ is closed and S₁ is open. What is the final charge on the capacitor?

1. Zero
2. 5 mC
3. 2.5 mC
4. 5 μC

(iii) The dimensional formula for RC is ______.

1. [M L² T⁻³ A⁻²]
2. [M⁰ L⁰ T⁻¹ A⁰]
3. [M⁻¹ L⁻² T⁴ A²]
4. [M⁰ L⁰ T A⁰]

(iv) The key S₁ is closed and S₂ is open. The value of current in the resistor after 5 seconds, is ______.

1. `1/(2 sqrte)` mA
2. `sqrt e` mA
3. `1/sqrt e` mA
4. `1/(2e)` mA

OR

(iv) The key S₁ is closed and S₂ is open. The initial value of charging current in the resistor, is ______.

1. 5 mA
2. 0.5 mA
3. 2 mA
4. 1 mA

(i) 

Consider the arrangement shown in figure. A black vertical arrow and a horizontal thick line with a ball are painted on a glass plate. It serves as the object. When the plate is illuminated, its real image is formed on the screen.

Which of the following correctly represents the image formed on the screen?

(ii) Which of the following statements is incorrect?

1. For a convex mirror magnification is always negative.
2. For all virtual images formed by a mirror magnification is positive.
3. For a concave lens magnification is always positive.
4. For real and inverted images, magnification is always negative.

(iii) A convex lens of focal length ‘f’ is cut into two equal parts perpendicular to the principal axis. The focal length of each part will be ______.

1. f
2. 2 f
3. `f/2`
4. `f/4`

OR

(iii) If an object in case (i) above is 20 cm from the lens and the screen is 50 cm away from the object, the focal length of the lens used is ______.

1. 10 cm
2. 12 cm
3. 16 cm
4. 20 cm

(iv) The distance of an object from first focal point of a biconvex lens is X₁ and distance of the image from second focal point is X₂. The focal length of the lens is ______.

1. X₁X₂
2. `sqrt(X_1 + X_2)`
3. `sqrt(X_1 X_2)`
4. `sqrt(X_2/X_1)`

Two point charges 5 μC and −1 μC are placed at points (−3 cm, 0, 0) and (3 cm, 0, 0) respectively. An external electric field `vec E = A/r^2 hat r` where A = 3 × 10⁵ Vm is switched on in the region. Calculate the change in electrostatic energy of the system due to the electric field.

A system of two conductors is placed in air and they have net charge of +80 μC and −80 μC which causes a potential difference of 16 V between them.

1. Find the capacitance of the system.
2. If the air between the capacitor is replaced by a dielectric medium of dielectric constant 3, what will be the potential difference between the two conductors?
3. If the charges on two conductors are changed to +160 μC and −160 μC, will the capacitance of the system change? Give reason for your answer.

Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, −4q, and 14q respectively. Their inner metal balls are also given charges −2q, +8q and −10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres.

A charge −6 pC is placed at the centre B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge +5 μC is moved from point ‘C’ to point ‘A’ along the circumference. Calculate the work done on the charge.

A proton moving with velocity `vec V` in a non-uniform magnetic field traces a path as shown in the figure.

The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R? What can you say about relative magnitude of magnetic fields at these points?

A current carrying circular loop of area A produces a magnetic field B at its centre. Show that the magnetic moment of the loop ia `(2 BA)/mu_0 sqrt(A/pi)`.

Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.

A charged particle is moving in a circular path with velocity `vec V` in a uniform magnetic field `vec B`. It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will

1. the radius of its path
2. its time period of revolution change?

What are coherent sources of light? 

Why are coherent sources necessary to produce a sustained interference pattern?

Lights from two independent sources are not coherent. Explain.

Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits.

1. How far apart will adjacent bright interference fringes beon the screen?
2. Find the angular width (in degree) of the first bright fringe.

Define a wavefront.

An incident plane wave falls on a convex lens and gets refracted through it. Draw a diagram to show the incident and refracted wavefront.

A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.