The graph which shows the variation of the de Broglie wavelength $(\lambda)$ of a particle and its associated momentum $(p)$ is?

When light propagates through a material medium of relative permittivity $\varepsilon_r$ and relative permeability $\mu_r,$ the velocity of light, $v$ is given by (where $c$ is the velocity of light in vacuum):

A long solenoid of radius $1$ mm has $100$ turns per mm. If $1$ A current flows in the solenoid, the magnetic field strength at the center of the solenoid is:

The peak voltage of the AC source is equal to:

An electric lift with a maximum load of $2000$ kg (lift + passengers) is moving up with a constant speed of $1.5$ m/s. The frictional force opposing the motion is $3000$ N. The minimum power delivered by the motor to the lift in watts is: ($g = 10$ m/s$^2$)

In a Young's double slit experiment, a student observes $8$ fringes in a certain segment of screen when a monochromatic light of $600$ nm wavelength is used. If the wavelength of light is changed to $400$ nm, then the number of fringes he would observe in the same region of the screen is:

A copper wire of length $10$ m and radius $\left( \frac{10}{\pi} \right)$ mm has electrical resistance of $10 \Omega.$ The current density in the wire for an electric field strength of $10$ V/m is:

The dimensions $[MLT^{-2}A^{-2}]$ belong to:

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

In half-wave rectification, if the input frequency is $60$ Hz, then the output frequency would be:

The displacement-time graphs of two moving particles make angles of $30^\circ$ and $45^\circ$ with the x-axis. The ratio of their respective velocity is:

As the temperature increases, the electrical resistance:

A square loop of side $1$ m and resistance $1 \Omega$ is placed in a magnetic field of $0.5$ T. If the plane of the loop is perpendicular to the direction of the magnetic field, the magnetic flux through the loop is:

The energy that will be ideally radiated by a $100$ kW transmitter in $1$ hour is:

A body of mass $60$ g experiences a gravitational force of $3.0$ N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is:

Match List - I with List - II regarding electromagnetic waves and their wavelengths:

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2 : 2: 1.$ If the fragments having equal mass fly off along mutually perpendicular directions with speed $v,$ the speed of the third (lighter) fragment is:

A biconvex lens has radii of curvature, $20$ cm each. If the refractive index of the material of the lens is $1.5,$ the power of the lens is:

Given below are two statements regarding Biot-Savart's law:$\newline$Statement I: Biot-Savart's law gives an expression for the magnetic field strength of an infinitesimal current element $(Idl)$ of a current carrying conductor only.$\newline$Statement II: Biot-Savart’s law is analogous to Coulomb's inverse square law of charge $q,$ with the former being related to the field produced by a scalar source, $Idl$ while the latter being produced by a vector source, $q. \newline$Choose the most appropriate answer:

In the given nuclear reaction, the element X is:$\newline$ $^{22}_{11} Na \rightarrow X + e^{+} + {v}$

Plane angle and solid angle have:

The angle between the electric lines of force and the equipotential surface is:

Let $T_1$ and $T_2$ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr’s model of an atom; the ratio $T_1 : T_2$ is:

A light ray falls on a glass surface of refractive index $\sqrt{3},$ at an angle $60^\circ.$ The angle between the refracted and reflected rays would be:

In the given circuits (a), (b), and (c), the potential drop across the two p-n junctions are equal in:

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $(v)$ as a function of time $(t)$ is:

Two resistors of resistances, $100 \Omega$ and $200 \Omega$ are connected in parallel in an electrical circuit. The ratio of thermal energy developed in $100 \Omega$ to that in $200 \Omega$ in a given time is:

When two monochromatic light of frequency $\nu$ and $\frac{\nu}{2}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_s}{2}$ and $V_s$ respectively. The threshold frequency for this metal is:

If a soap bubble expands, the pressure inside the bubble:

Two point charges $-q$ and $+q$ are placed at a distance of $L,$ as shown in the figure. The magnitude of electric field intensity at a distance $R$ ($R >> L$) varies as:

The area of a rectangular field (in $m^2$) of length $55.3$ m and breadth $25$ m after rounding off the value for correct significant digits is:

The truth table for the given logic circuit is:

Given below are two statements:$\newline$Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring.$\newline$Reason (R): A coil spring of copper has more tensile strength than a steel spring of the same dimensions.$\newline$Choose the most appropriate answer:

Two objects of mass $10$ kg and $20$ kg respectively are connected to the two ends of a rigid rod of length $10$ m with negligible mass. The distance of the center of mass of the system from the $10$ kg mass is:

From Ampere’s circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is:

A series LCR circuit with inductance $10H,$ capacitance $10 \mu F,$ resistance $50 \Omega$ is connected to an AC source of voltage, $V = 200 \sin(100t)$ volt. If the resonant frequency of the LCR circuit is $v_0$ and the frequency of the AC source is $v,$ then:

Match List - I with List - II regarding gravitational terms:

Two pendulums of length $121 cm$ and $100 cm$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:

A big circular coil of 1000 turns and average radius $10m$ is rotating about its horizontal diameter at $2 rad/s.$ If the vertical component of Earth’s magnetic field at that place is $2 \times 10^{-5} T$ and electrical resistance of the coil is $12.56 \Omega,$ then the maximum induced current in the coil will be:

A capacitor of capacitance $C = 900 pF$ is charged fully by a $100V$ battery. Then the battery is disconnected, and the capacitor is connected to another uncharged capacitor of capacitance $C = 900 pF.$ The electrostatic energy stored by the system is:

A nucleus of mass number $189$ splits into two nuclei having mass number $125$ and $64.$ The ratio of the radius of the two daughter nuclei is:

A Wheatstone bridge is used to determine the value of an unknown resistance $X$ by adjusting the variable resistance $Y$ as shown in the figure. For the most precise measurement of $X,$ the resistances $P$ and$Q$:

The volume occupied by the molecules contained in $4.5$ kg water at STP, if the intermolecular forces vanish away, is:

A ball is projected with a velocity, $10$ m/s, at an angle of $60^\circ$ with the vertical direction. Its speed at the highest point of its trajectory will be:

The ratio of the distance travelled by a freely falling body in the $1^{st}, 2^{nd}, 3^{rd}$ and $4^{th}$ second is:

Two transparent media, A and B, are separated by a plane boundary. The speed of light in those media are $1.5 \times 10^8$ m/s and $2.0 \times 10^8$ m/s, respectively. The critical angle for a ray of light for these two media is:

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:

The angular speed of a flywheel moving with uniform angular acceleration changes from $1200$ rpm to $3120$ rpm in $16$ seconds. The angular acceleration in rad/s$^2$ is:

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric, and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is:

Two hollow conducting spheres of radii $R_1$ and $R_2$ ($R_1 >> R_2$) have equal charges. The potential would be: