CBSE Class 12 Physics Set 3 - (55/1/3) Question Paper 2026 with Solution PDF

Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

• (A) (i) and (iii) only
  
• (B) (iii) and (iv) only
  
• (C) (i), (iii) and (iv) only
  
• (D) All of them

An electromagnetic wave passes from vacuum into a dielectric medium with relative electrical permittivity \(\dfrac{3}{2}\) and relative magnetic permeability \(\dfrac{8}{3}\). Then, its

• (A) wavelength is doubled and frequency remains unchanged.
  
• (B) wavelength is doubled and frequency is halved.
  
• (C) wavelength is halved and frequency remains unchanged.
  
• (D) wavelength and frequency both will remain unchanged.

In an unbiased p-n junction, at equilibrium, which of the following statements is true ?

• (A) Diffusion current is zero but drift current exists.
  
• (B) Diffusion current exists but drift current is zero.
  
• (C) Diffusion and drift currents are equal and opposite.
  
• (D) Both the diffusion and drift currents exist but are unequal.

A conducting wire connects two charged metallic spheres \(A\) and \(B\) of radii \(r_1\) and \(r_2\) respectively. The distance between the spheres is very large compared to their radii. The ratio of electric fields, \((E_A/E_B)\), at the surfaces of spheres \(A\) and \(B\) will be

• (A) \(\dfrac{r_1}{r_2}\)
  
• (B) \(\dfrac{r_2}{r_1}\)
  
• (C) \(\dfrac{r_1^2}{r_2^2}\)
  
• (D) \(\dfrac{r_2^2}{r_1^2}\)

The electric potential for various points in \(x\)-\(y\) plane is given by \(V = 1.0 x^2 - 2.0 y^2\), where \(V\) is in volts and \(x\), \(y\) are in metres. The angle that the electric field at point \((2.0\) m\(, 1.0\) m\()\) makes with the positive \(x\)-axis is:

• (A) \(45^\circ\)
• (B) \(90^\circ\)
• (C) \(135^\circ\)
• (D) \(315^\circ\)

A current of 1.5 A is maintained in a copper wire of length 1 m with area of cross-section \(1.7 \times 10^{-7}\) m\(^2\). The magnitude of electric field in the wire is \([\rho_{Cu} = 1.7 \times 10^{-8}\,\Omega\,\text{m}]\):

• (A) 0.15 V/m
• (B) 0.30 V/m
• (C) 1.5 V/m
• (D) 3.0 V/m

Light from a small object in air falls on a spherical glass surface \((n = 1.5)\) of radius of curvature \(R\). A real image of the object will be formed if the object distance \(u\) is related to \(R\) as:

• (A) \(u < \dfrac{R}{2}\)
• (B) \(\dfrac{R}{2} < u < R\)
• (C) \(R < u < 2R\)
• (D) \(u > 2R\)

The ratio of the potential energy to the kinetic energy of an electron in \(n^{\text{th}}\) orbit of Bohr model of hydrogen atom is:

• (A) \(-\dfrac{1}{2}\)
• (B) \(\dfrac{1}{2}\)
• (C) \(2\)
• (D) \(-2\)

Welders wear special glass goggles or face masks with glass windows to protect their eyes from:

• (A) Infrared rays
• (B) Ultraviolet rays
• (C) X-rays
• (D) Microwaves

• (A) \(2\pi I\), along \(+X\)-axis
• (B) \(2\pi I\), along \(-X\)-axis
• (C) \(\pi I\), along \(+X\)-axis
• (D) \(\pi I\), along \(-X\)-axis

The phenomenon of interference is shown by:

• (A) longitudinal mechanical wave only
• (B) transverse mechanical wave only
• (C) electromagnetic waves only
• (D) all these waves

A series LCR circuit with \(R = 3\,\Omega\), \(X_C = 4\,\Omega\) and \(X_L = 8\,\Omega\) is connected to a 220 V, 50 Hz ac source. The power factor for the circuit is:

• (A) 0.30
• (B) 0.45
• (C) 0.50
• (D) 0.60

Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  
• (C) Assertion (A) is true, but Reason (R) is false.
  
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A) : All atoms have a net magnetic moment. Reason (R) : A current loop does not always behave as a magnetic dipole.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  
• (C) Assertion (A) is true, but Reason (R) is false.
  
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A) : In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R) : In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  
• (C) Assertion (A) is true, but Reason (R) is false.
  
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A) : If accelerated electrons are passed through a narrow slit, a diffraction pattern is observed. Reason (R) : Electrons behave as both particles and waves.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  
• (C) Assertion (A) is true, but Reason (R) is false.
  
• (D) Both Assertion (A) and Reason (R) are false.

What is the order of magnitude of drift velocity of electrons in a conductor ? Deduce the relation between the current flowing through a conductor and drift velocity of electrons in it.

A wire of length \(L\) is bent round into (i) a square coil having \(N\) turns and (ii) a circular coil having \(N\) turns. The coil in both cases is free to turn about a vertical axis coinciding with the plane of the coil, in a uniform, horizontal magnetic field and carry the same currents. Find the ratio of the maximum value of the torque acting on the square coil to that on the circular coil.

A beam of light consisting of two wavelengths \(400\ \text{nm}\) and \(600\ \text{nm}\) is used to illuminate a single slit of width \(1\ \text{mm}\). Find the least distance of the point from the central maximum where the dark fringes due to both wavelengths coincide on the screen placed \(1.5\ \text{m}\) from the slit.

In a Young's double-slit experimental set-up with slit separation \(0.6\ \text{mm}\), a beam of light consisting of two wavelengths \(440\ \text{nm}\) and \(660\ \text{nm}\) is used to obtain an interference pattern on a screen kept \(1.5\ \text{m}\) in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.

In an electron microscope, accelerated electrons have wavelength of \(0.011\) nm. Calculate the voltage through which electrons were accelerated to attain this wavelength.

(Take \(e = 1.6 \times 10^{-19}\) C, \(m_e = 9 \times 10^{-31}\) kg, \(h = 6.6 \times 10^{-34}\) J.s)

Suppose a nucleus with mass number \(A = 240\) and B.E. per nucleon \(= 7.6\) MeV, breaks into two nuclei, each of mass number \(A = 120\) with B.E. per nucleon \(= 8.5\) MeV. Calculate the energy released in the process.

An ac voltage \(V_i = 12 sin (100 \pi t)V\) is applied between points A and B in a network of two ideal diodes and three resistors as shown in figure. During the positive half-cycle of the input voltage Vi supplied to the network.

Figure shows a narrow beam of electrons entering with a velocity of \(3\times10^7\ \text{m s}^{-1}\), symmetrically through the space between two parallel horizontal plates \(P_1P_1'\) and \(P_2P_2'\) kept \(2\ \text{cm}\) apart. If each plate is \(3\ \text{cm}\) long, calculate the potential difference \(V\) applied between the plates so that the beam just strikes the end \(P_2'\).

State the two conditions under which total internal reflection occurs.

Using Gauss's law, deduce an expression for electric field at a point due to a uniformly charged infinite plane thin sheet.

Two large thin plane sheets, each having surface charge density \(\sigma\), are held close and parallel to each other in air. What is the net electric field at a point (i) inside and (ii) outside the sheets ?

Find the net resistance of the network of resistors connected between \(A\) and \(B\), as shown in the figure.

Obtain the condition of balance of a Wheatstone bridge.

A parallel plate capacitor of capacitance \(C\) is charged to \(V\) volt by a battery. After sometime the battery is disconnected and the distance between the plates is doubled. A slab of dielectric constant \(k = 1.8\) is then introduced to completely fill the space between the plates. How will the following be affected?

(a) The capacitance of the capacitor.
(b) The electric field between the plates of the capacitor.
(c) The energy stored in the capacitor.

Justify your answer in each case.

(a) Draw the V-I characteristics of silicon diode.

(b) Explain the following terms:

(i) minority carrier injection in forward bias
(ii) breakdown voltage in reverse bias

(a) Why does one prefer to view the image formed at infinity than that formed at near point in microscope/telescope?

(b) Consider lenses \(L_1\), \(L_2\) and \(L_3\) as specified in the following table. Which of them will you select as objective and eyepiece for constructing best possible (i) telescope (ii) compound microscope? Give reason for your answer.

Comprehension:

A galvanometer is used to detect or/and measure small currents in an electrical circuit. It essentially works on the fact that a current-carrying coil experiences a deflecting torque when placed in a magnetic field. This deflection in the coil can be measured and it is related to the current flowing

The torque on the coil remains constant irrespective of the coil's orientation during rotation due to:

The best way to increase current sensitivity of a galvanometer is by:

A moving coil galvanometer has a coil with area of cross-section \(4.0 \times 10^{-3}\) m\(^2\) and number of turns 50. The coil is rotating in a magnetic field of 0.25 T. The torque acting on the coil when a current of 5 A passes through it is:

A galvanometer coil has a resistance of 15 \(\Omega\) and the meter shows full scale deflection for a current of 3 mA. The value of resistance required to convert it into a voltmeter of range \((0\text{-}12\) V\()\) is:

A galvanometer with coil of resistance 20 \(\Omega\) shows full scale deflection for a current of 5 mA. To convert it into an ammeter of range \((0\text{-}10\) A\()\), a resistance of:

Comprehension:

A researcher performs an experiment on photoelectric effect using two metals A and B with unknown work functions. She illuminates the surfaces of A and B with monochromatic radiation of various frequencies and records the corresponding stopping potentials \((V_s)\). The graph shows the variation of stopping

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potential \((V_s)\) with the frequency of incident radiation \((\nu)\) for metals A and B.

Answer the following questions:

From the graph, the work functions of A and B are (\(h\) is Planck's constant and \(e\) value of charge on an electron):

For radiation of frequency \(\nu \gt \nu_2\) incident on the surfaces of A and B, the maximum kinetic energy of ejected electron is:

If the intensity of the incident radiation for both metals A and B, is doubled keeping its frequency constant, then:

The threshold frequency for a metal surface is \(\nu_0\). If the radiation of frequency \(3\nu_0\) illuminates the surface, the maximum kinetic energy (KE) of photoelectrons is \(E_1\). If the frequency were increased to \(6\nu_0\), the maximum KE of the photoelectrons becomes \(E_2\). Then \(\dfrac{E_1}{E_2}\) equals:

Let \(m\) be the slope of the graph line for metal B. If \(e\) is the value of electron charge, then Planck's constant '\(h\)' is given by:

Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula.

Three lenses \(L_1\), \(L_2\) and \(L_3\), each of focal length \(40\) cm, are placed coaxially. The distance between \(L_1\) and \(L_2\) and between \(L_2\) and \(L_3\) are \(120\) cm and \(20\) cm respectively. An object is kept at a distance of \(80\) cm to the left of lens \(L_1\). Find the distance of the final image formed from the object.

Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula.

A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.

Derive an expression for the self-inductance of an air-filled long solenoid of length \(l\) and cross-sectional area \(A\) having \(N\) turns.

A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod.

State Faraday’s law of electromagnetic induction.

Draw a labelled diagram of a step-up transformer. State the principle on which it works and obtain the ratio of secondary voltage to primary voltage in terms of number of turns and currents in the two coils.

The ratio of the number of turns in the primary to the secondary of an ideal transformer is \(1:5\). If \(5\) kW power at \(200\) V is supplied to the primary, find
(i) current in the primary, and
(ii) output voltage.

An electric dipole consists of two point charges \(+q\) and \(-q\) separated by a distance \(2a\). Derive an expression for the electric field \(\vec E\) due to this dipole at a point distant \(r\) from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. \(r \gg a\).

Two cells of emf \(E_1\) and \(E_2\) with internal resistances \(r_1\) and \(r_2\) respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination.

A parallel combination, as stated in (a) above, of two cells of emfs \(E\) and \(3E\) and internal resistances \(R\) each is connected across a resistance \(2R\). Find the current that flows through resistance \(2R\).