CBSE 2025, Set 1 Solutions
CBSE Physics (2025)

The electric field at a point in a region is given by $\vec{E} = \alpha\dfrac{\vec{r}}{|\vec{r}|^3}$, where $\alpha$ is a constant and $r$ is the distance of the point from the origin. The magnitude of potential of the point is :

A charged particle gains a speed of $10^6$ ms$^{-1}$, when accelerated from rest through a potential difference 10 kV. It enters a region of magnetic field of 0·4 T such that $\vec{v} \perp \vec{B}$. The radius of circular path described by it is :

Which of the following rays coming from the Sun plays an important role in maintaining the Earth's warmth ?

The dimensions of $(\mu\varepsilon)^{-1}$, where $\varepsilon$ is permittivity and $\mu$ is permeability of a medium, are :

Which of the following electromagnetic waves has photons of largest momentum ?

Two coherent light waves, each having amplitude $a$, superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between :

The kinetic energy of an alpha particle is four times the kinetic energy of a proton. The ratio of de Broglie wavelengths $\left(\dfrac{\lambda_\alpha}{\lambda_p}\right)$ associated with them will be :

Assertion (A): During formation of a nucleus, the mass defect produced is the source of the binding energy of the nucleus.

Reason (R): For all nuclei, the value of binding energy per nucleon increases with mass number.

Assertion (A): The Balmer series in hydrogen atom spectrum is formed when the electron jumps from higher energy state to the ground state.

Reason (R): In Bohr's model of hydrogen atom, the electron can jump between successive orbits only.

Assertion (A): In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering $\pi$ led him to the discovery of nucleus.

Reason (R): The size of nucleus is approximately $10^{-5}$ times the size of an atom and therefore only few alpha particles are rebounded.

The threshold frequency for a given metal is $3\cdot6 \times 10^{14}$ Hz. If monochromatic radiations of frequency $6\cdot8 \times 10^{14}$ Hz are incident on this metal, find the cut-off potential for the photoelectrons.

A point object is placed in air at a distance $R/3$ in front of a convex surface of radius of curvature $R$, separating air from a medium of refractive index $n$ ($< 4$). Find the nature and position of the image formed.

In Young's double slit experimental set-up, the intensity of the central maximum is $I_0$. Calculate the intensity at a point where the path difference between two interfering waves is $\lambda/3$.

A voltmeter of resistance 1000 $\Omega$ can measure up to 25 V. How will you convert it so that it can read up to 250 V ?

When a neutron collides with ${}^{235}_{92}\text{U}$, the nucleus gives ${}^{140}_{54}\text{Xe}$ and ${}^{94}_{38}\text{Sr}$ as fission products and two neutrons are ejected. Calculate the mass defect and the energy released (in MeV) in the process.

Given: $m\!\left({}^{235}_{92}\text{U}\right) = 235\cdot04393 \text{ u}, \quad m\!\left({}^{140}_{54}\text{Xe}\right) = 139\cdot92164 \text{ u}$ $m\!\left({}^{94}_{38}\text{Sr}\right) = 93\cdot91536 \text{ u}, \quad m\!\left({}^{1}_{0}\text{n}\right) = 1\cdot00866 \text{ u}$ $1 \text{ u} = 931 \text{ MeV}/c^2$

The resistance of a wire at 25°C is 10·0 $\Omega$. When heated to 125°C, its resistance becomes 10·5 $\Omega$. Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at $T = 0$ K. How is an electron-hole pair formed in a semiconductor at room temperature ?

(b) Carbon and silicon both are members of Group IV of the periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.

In Young's double slit experiment, the separation between the two slits is 1·0 mm and the screen is 1·0 m away from the slits. A beam of light consisting of two wavelengths 500 nm and 600 nm is used to obtain interference fringes. Calculate :

(a) the distance between the first maxima for the two wavelengths.

(b) the least distance from the central maximum, where the bright fringes due to both the wavelengths coincide.

Differentiate between half-wave and full-wave rectification. With the help of a circuit diagram, explain the working of a full-wave rectifier.

A rectangular glass slab ABCD (refractive index 1·5) is surrounded by a transparent liquid (refractive index 1·25) as shown in the figure. A ray of light is incident on face AB at an angle $i$ such that it is refracted out grazing the face AD. Find the value of angle $i$.

Two small solid metal balls A and B of radii $R$ and $2R$ having charge densities $2\sigma$ and $3\sigma$ respectively are kept far apart. Find the charge densities on A and B after they are connected by a conducting wire.

(a) (i) Draw a ray diagram of a reflecting telescope (Cassegrain) and explain the formation of image. State two important advantages that a reflecting telescope has over a refracting telescope.

(ii) In a refracting telescope, the focal length of the objective is 50 times the focal length of the eyepiece. When the final image is formed at infinity, the length of the tube is 102 cm. Find the focal lengths of the two lenses.

(a) (i) Three batteries $E_1$, $E_2$ and $E_3$ of emfs and internal resistances $(4\text{ V}, 2\text{ }\Omega)$, $(2\text{ V}, 4\text{ }\Omega)$ and $(6\text{ V}, 2\text{ }\Omega)$ respectively are connected as shown in the figure. Find the values of the currents passing through batteries $E_1$, $E_2$ and $E_3$.

(ii) The ends of six wires, each of resistance $R$ $(= 10\text{ }\Omega)$ are joined as shown in the figure. The points A and B of the arrangement are connected in a circuit. Find the value of the effective resistance offered by it to the circuit.

(b) (i) Current $I$ $(= 1$ A$)$ is passing through a copper rod ($n = 8\cdot5 \times 10^{28}$ m$^{-3}$) of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are $1\cdot0 \times 10^{-7}$ m$^2$ and $2\cdot0 \times 10^{-7}$ m$^2$ respectively.

Calculate: (I) the ratio of electric fields at points A and B. (II) the drift velocity of free electrons at point B.

(ii) Two point charges $q_1$ $(= 16\text{ }\mu\text{C})$ and $q_2$ $(= 1\text{ }\mu\text{C})$ are placed at points $\vec{r}_1 = (3\text{ m})\hat{i}$ and $\vec{r}_2 = (4\text{ m})\hat{j}$. Find the net electric field $\vec{E}$ at point $\vec{r} = (3\text{ m})\hat{i} + (4\text{ m})\hat{j}$.

(b) (i) Write any two advantages of a compound microscope over a simple microscope. Draw a ray diagram for the image formation at the near point by a compound microscope and explain it.

(ii) A thin planoconcave lens with its curved face of radius of curvature $R$ is made of glass of refractive index $n_1$. It is placed coaxially in contact with a thin equiconvex lens of same radius of curvature of refractive index $n_2$. Obtain the power of the combination lens.

Four resistors, each of resistance R and a key K are connected as shown in the figure. The equivalent resistance between points A and B when key K is open, will be :

A compound microscope has an objective and an eyepiece of focal lengths $f_o$ and $f_e$, respectively. To obtain a large magnification of a small object, the microscope should have :

Two infinitely long straight wires '1' and '2' are placed $d$ distance apart, parallel to each other, as shown in the figure. They are uniformly charged having charge densities $\lambda$ and $-\dfrac{\lambda}{2}$ respectively. Locate the position of the point from wire '1' at which the net electric field is zero and identify the region in which it lies.

The magnetic flux linked with a coil changes with time $t$ as $\phi = (8t^2 + 5t + 7)$, where $t$ is in seconds and $\phi$ is in Wb. The value of emf induced in the coil at $t = 4$ s is :

(a) (i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current $I$ in a coil of self-inductance $L$.

(ii) The currents passing through two inductors of self-inductances 10 mH and 20 mH increase with time at the same rate.

Draw graphs showing the variation of : (I) the magnitude of emf induced with the rate of change of current in each inductor. (II) the energy stored in each inductor with the current flowing through it.

(b) (i) Define the term mutual inductance. Deduce the expression for the mutual inductance of two long coaxial solenoids of the same length having different radii and different number of turns.

(ii) The current through an inductor is uniformly increased from zero to 2 A in 40 s. An emf of 5 mV is induced during this period. Find the flux linked with the inductor at $t = 10$ s.

A current of $\left(\dfrac{10}{\pi}\right)$ A is maintained in a circular loop of radius 14 cm. The value of dipole moment associated with the loop is :

An electron of mass $m$ and charge $-e$ is revolving anticlockwise around the nucleus of an atom.

(a) Obtain the expression for the magnetic dipole moment ($\mu$) of the atom.

(b) If $\vec{L}$ is the angular momentum of electron, show that $\vec{\mu} = -\left(\dfrac{e}{2m}\right)\vec{L}$.

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance :

A parallel plate capacitor has plate area $A$ and plate separation $d$. Half of the space between the plates is filled with a material of dielectric constant $K$ in two ways as shown in the figure.

(a) Dielectric fills half the gap vertically (side by side — parallel combination)
(b) Dielectric fills half the gap horizontally (one on top of other — series combination)

Find the values of the capacitance of the capacitors in the two cases.

Assertion (A): The impurities in p-type Si are not pentavalent atoms.

Reason (R): The hole density in valence band in p-type semiconductor is almost equal to the acceptor density.

The value of the current sensitivity of a galvanometer is given by :

Which of the following correctly describes the variation of photoelectric current $I$ with the intensity of incident light?

When the frequency of incident light is increased without changing its intensity, the saturation current :

A galvanometer of resistance $6\ \Omega$ shows full scale deflection for a current of $0.2\text{ A}$. The value of shunt to be used to convert it into an ammeter of range ($0 \text{ – } 5\text{ A}$) is :

Which of the following graphs can be used to obtain the value of Planck's constant?

A galvanometer of resistance $6\ \Omega$ shows full scale deflection for a current of $0.2\text{ A}$. It is converted into an ammeter of range ($0 \text{ – } 5\text{ A}$) using a shunt. The value of resistance of the resulting ammeter will be :

Red, yellow and blue light of the same intensity are incident successively on a metal surface. Let $K_R$, $K_Y$, and $K_B$ represent the maximum kinetic energy of the photoelectrons emitted under each respective illumination. Which of the following relationships is correct?

A galvanometer is converted into a voltmeter of range ($0 \text{ – } V$) by connecting a resistance $R_1$ in series. If $R_1$ is replaced by $R_2$, the range becomes ($0 \text{ – } 2V$). The resistance of the galvanometer is :

Which of the following metals exhibits the photoelectric effect with visible light?

A current of $5\text{ mA}$ flows through a galvanometer. Its coil has $100$ turns, each of area $18\text{ cm}^2$, and is suspended in a magnetic field of $0.20\text{ T}$. The deflecting torque acting on the coil will be :