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In amplitude modulation, the message signal $V_m\left(t\right)=1\sin (2\pi \times {10}^{5}t)$ volts and carrier signal $V_C\left(t\right)=20\sin (2\pi \times {10}^{7}t)$ volts. The modulated signal now contains the message signal with lower side band and upper side band frequency. Therefore the bandwidth of modulated signal is $\alpha \text{kHz}$. The value of $\alpha$ is :

A ray of light travelling in glass medium $({\mu }_g=\frac{3}{2})$ is incident on a horizontal glass-air interface at the critical angle ${\theta }_c$. If a thin layer of water $({\mu }_w=\frac{4}{3})$ is now poured on the glass-air interface , then the angle at which the ray of light emerges into water at glass-water surface will be

The distance between the plates of a circular parallel plate capacitor (PPC) of diameter $40\text{mm}$, whose capacity is equal to that of an isolated metallic sphere of radius $1\text{m}$ will be

1. 120

The resistance values of the bridge circuit shown in figure are $R_1=R_2=R_3=R\text{and}{R}_4=R+\Delta R.$ The bridge is balanced by introducing a small voltage v. The value of $\Delta R$ is

According to De Broglie 2$\pi$r=n$\lambda$ where n is the quantum number of an orbit, in visual representation of an electron as a wave, n stands for:

1. 50

1. 12

The true value of angle of dip at a place is ${60}^{\circ }$. The apparent dip, in a plane inclined at an angle of ${30}^{\circ }$ with the magnetic meridian is:

Each atom of an iron bar $(5cm\times 1cm\times 1cm)$ has a magnetic moment $1.8\times {10}^{-23}A{m}^2$. Knowing that the density of iron is $7.78\times {10}^{3}k{g}^{-3}m$, atomic weight is 56 and Avogadro's number is $6.02\times {10}^{23}$ the magnetic moment of bar in the state of magnetic saturation will be

The velocity of the centre of mass of a system changes from $\overrightarrow{v_1}=4\hat{i}\text{m/s}$ to $\overrightarrow{v_2}=3\hat{j}\text{m/s}$ during time $\Delta t=2\text{s}$. If the mass of the system is $m=10\text{kg}$, the magnitude of constant force acting on the system is

The peak voltage in a $220\text{V}$ AC source is -



Take $\sqrt{2}=1.414$

An electron jumps from $4^{\text{th}}$ orbit to the $2^{\text{nd}}$ orbit of a hydrogen atom. If Rydberg's constant $R={10}^5{\text{cm}}^{-1}$, the frequency (in $Hz$) of the emitted radiation will be,

The lowest pressure (the best vaccum) that can be created in laboratory at ${20}^{\circ }\text{C}$ is ${10}^{-10}\text{mm}$ of $\text{Hg}$. At this pressure, the number of ideal gas molecules per ${\text{cm}}^3$ will be

If the projections of the line segment $AB$ on the coordinate axes are $2,k,4$ such that $k\in R^{+}$ and $AB=\frac{7}{\sqrt{2}},$ then $2k^2-\sqrt{2}k+1$ is equal to :

Three resistors of resistance R of each are combined is various ways. Which of the following cannot be obtained?

A positive charge q is projected in magnetic field of width $\frac{mv}{\sqrt{2}qB}$ with velocity v as shown in figure. Then time taken by charged particle to emerge from the magnetic field is :

Force acting on a particle varies with $x$ as shown in figure. Calculate the work done by the force as the particle moves from $x=0$ to $x=6.0\text{m}$.

If two discs of moments of inertia $I_1$ and $I_2$, rotating about a collinear axis passing through their centres of mass and perpendicular to their planes with angular speeds ${\omega }_1$ and ${\omega }_2$ respectively in opposite directions are made to rotate combinedly along the same axis, then the magnitude of new angular velocity of the system is

A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is ${6.0}^{\circ }$, what would be the refracting angle of the crown prism ?

The displacement of the particle (in $m$) is given by

$y=2t+t^2-2t^3$

What is the velocity (in $m/s$) of the particle at the instant when its acceleration is zero?

A hanging spring stretches by $35.0\text{cm}$ when an object of mass $450\text{g}$ is hung on it at rest. In this situation, we define its position as $x=0$. The object is pulled down an additional $18.0\text{cm}$ and released from rest to oscillate. Find the position of the vibrating object from $x=0$ after $84.4\text{s}$ $($Neglect friction due to air$)$

If $\overrightarrow{A}=5\hat{i}-10\hat{j}$ and $\overrightarrow{B}=-2\hat{i}+6\hat{j}$, the magnitude and direction of $\overrightarrow{A}+\overrightarrow{B}$ is

You
are riding in an automobile of mass 3000 kg. Assuming that you are
examining the oscillation characteristics of its suspension system.
The suspension sags 15 cm when the entire automobile is placed on it.
Also, the amplitude of oscillation decreases by 50% during one
complete oscillation. Estimate the values of (a) the spring constant
k and
(b) the damping constant b for
the spring and shock absorber system of one wheel, assuming that each
wheel supports 750 kg.

A cube of sponge rubber with edge length $5\text{cm}$ has a force of $2\text{N}$ applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of $1\text{mm}$, find the shear modulus for the sponge rubber.

Concept of image charge makes it possible to find electric interaction in some cases where large conducting plates are kept infront of charge. For this we consider potential of conducting plate to zero and find another (image) charge which along with given charge can make potential of conducting plate zero. In this way we can find electrostatic force between charge and conducting plate by replacing conducting plate with image charge.

A charge q is kept infront of large conducting plate at a distance l. Work done to remove this charge slowly from l to infinity is