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A regular hexagon of
side 10 cm has a charge 5 µC at each of its vertices. Calculate
the potential at the centre of the hexagon.

A receiver and a source of sonic oscillations of frequency $2000\text{Hz}$ are located on the x-axis. The source swings harmonically along x-axis with circular frequency $\omega$ and amplitude $50\text{cm}$. At what approximate value of $\omega$ will the frequency bandwidth (difference of maximum and minimum frequency) registered by stationary receiver be equal to $200\text{Hz}$? (The velocity of sound in air is $340\text{m/s}$ and assume that the velocity of source is small compared to the velocity of sound)

The moment of inertia of a uniform circular disc of radius ${}^{\prime }{R}^{\prime }$ and mass ${}^{\prime }{M}^{\prime }$ about an axis passing from the edge of the disc and normal to the disc is

The radius of an air
bubble is increasing at the rate of

cm/s. At what rate is the volume of the bubble increasing when the
radius is 1 cm?

The equilibrium constant of the reaction:

$Cu\left(s\right)+2A{g}^{+}\left(aq\right)\to C{u}^{2+}\left(aq\right)+2Ag\left(s\right);E^{\circ }=0.46V$ at 298K is :

In LCR circuit, resonant frequency is $600\text{Hz}$ and half power points are at $650$ Hz and $550\text{Hz}$. The quality factor is

A gun fires a shell and recoils horizontally. If the shell travels with speed $\text{v}$ with respect to the barrel, the ratio of speed with which the gun recoils if (i) the barrel is horizontal (ii) inclined at an angle of ${30}^{\circ }$ with horizontal is

A source of sound emits sound waves in uniform medium. If energy density is E and maximum speed of
particles of the medium is $V_{max}$ then the graph between E and $V_{max}$ is best represented by

A capacitor $C$ is connected to the two equal resistances as shown in the figure. What is the ratio of time constant during charging and discharging of the capacitance ?

A coil of resistance $300\Omega$ and inductance $1.0\text{H}$ is connected across an alternating voltage of frequency $\frac{300}{2\pi }\text{Hz}$. Calculate the phase difference between the voltage and current in the circuit.

The variation of electric potential $\left(V\right)$ with distance $\left(r\right)$ from a fixed point is as shown in the figure. Electric field intensity $(\text{in V/m)}$ at $r=1\text{m},3\text{m}$ and $4.5\text{m}$ are respectively

Let $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}.$

Then the magnitude of $\overrightarrow{a}\times \overrightarrow{b}$ is



[2 marks]

Capacity of a spherical capacitor is C₁
when inner sphere is charged and outer sphere is earthed and C₂ when
inner sphere is earthed and outer sphere is charged. Thenis (a = radius of inner sphere, b = radius of outer sphere)

The variation of lengths of two metal rods $A$ and $B$ with change in temperature is shown in Fig. The coefficients of linear expansion ${\alpha }_A$ for the metal $A$ and the temperature $T$ will be (given ${\alpha }_B$ = 9$\times$${10}^{-6}$/ ${}^{\circ }C$)

From a solid sphere of mass $M$ and radius $R$, a cube of maximum possible volume is cut. Then, moment of inertia of the cube about an axis passing through its centre and perpendicular to one of its faces is:

A tunnel is dug along a chord of the earth at a perpendicular distance $\frac{R}{2}$ from the earth's centre. The wall of the tunnel may be assumed to be frictionless. The particle is released from the one end of the tunnel. The pressing force by the particle on the wall and the accelaration of the particle varies with $x$ (distance of the particle from the centre) according to

In a Young's double slit experiment the intensity at a point is $I$ , where the corresponding path difference is one sixth of the wavelength of light used. If $I_0$ denotes the maximum intensity, the ratio $\frac{I}{I_0}$ is equal to,

Consider an infinte ladder network shown in figure. A voltage $V$ is applied between the points $A$ and $B$. This applied value of voltage is halved after each section. Then:

The centre of mass of a system of three particles of masses $2\text{g},3\text{g}$ and $5\text{g}$ is taken as the origin of a co-ordinate system. The position vector of a fourth particle of mass $8\text{g}$, such that the centre of mass of the four particle system lies at the point $(3,4,7)\text{m}$, is $\lambda (3\hat{i}+4\hat{j}+7\hat{k})\text{m}$ where $\lambda$ is a constant. Find the value of $\lambda$.

A particle is moving with a velocity of $v=(3+6t+9t^2)\text{cm}/s$. Find out the displacement of the particle in the interval $t=5\text{s}$ to $t=8\text{s}$.

A copper rod of length $20\text{cm}$ and cross-sectional area $2{\text{mm}}^2$ is joined with a similar aluminium rod as shown below. Find the resistance of the combination between the ends. Resistivity of copper $=1.7\times {10}^{-8}\Omega \text{m}$ and that of aluminium $=2.6\times {10}^{-8}\Omega \text{m}$ .

Which of the following is the most precise device for measuring length : (a) a vernier callipers with 20 divisions on the sliding scale (b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale (c) an optical instrument that can measure length to within a wavelength of light?

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by

Where are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

From a point at some height one body is dropped, while a second body is thrown downward with an initial velocity of $1{\text{ms}}^{-1}$ simultaneously in the same vertical line. The separation between these is $1.8\text{m}$ after a time

If y=x lnx, then $\frac{dy}{dx}$=?

The angular width $\Delta \theta$ of the central maximum in the diffraction pattern of a slit illuminated by light of wavelength $500\text{nm}$ is measured. The angular width of the central maximum is found to increase by $25\text{\%}$, when the same slit is illuminated by another light of wavelength ${\lambda }^{\prime }$. Then wavelength ${\lambda }^{\prime }$ will be

A conducting rod of length $l$ and mass $m$ is moving down a smooth inclined plane of inclination $\theta$ with constant velocity $v$. A current $I$ is flowing in the conductor in a direction perpendicular to the paper inwards. A vertically upward magnetic field $\overrightarrow{B}$ exists in space. Then, magnitude of magnetic field $\overrightarrow{B}$ is

Two large conducting sheet are placed parallel to each other with a separation of $2\text{cm}$ between them. An electron starting from rest near one of the sheets reaches the other plate in $2\mu \text{s}$. The surface charge density on the inner surface is

[Assume both sheets have same charge density]

At what time instance t, the particle's displacement is positive but particle's velocity negative

A moving block having mass $m$ collides with another stationary block having mass $4m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution ($e$) will be

A block of mass $2.0\text{kg}$ is moving on a frictionless horizontal surface with a velocity of $1.0\text{m/s}$ as shown in figure, move towards another block of equal mass at rest. The spring constant of the spring fixed at one end is $100\text{N/m}$. Find maximum compression of the spring.