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Define conductors and insulators. Give two examples for each.

Two elements $\text{A}$ and $\text{B}$ with atomic numbers $Z_A$ and $Z_B$ are used to produce characteristic $\text{X}$-rays with frequencies ${\nu }_A$ and ${\nu }_B$ respectively. If $Z_A:Z_B=1:2$, then ${\nu }_A:{\nu }_B$ will be

A vertical cylinder of height 100 cm contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to 75 cm of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston.

A truck of mass $3000\text{kg}$ is travelling on a road with a velocity of $90\text{km/h}$. The road has a pit which is concave upward. The approximate radius of curvature of the pit is $40\text{m}$. What is the force ($\text{kN}$) experienced by the truck while crossing through the pit? Take $g=10{\text{m/s}}^2$.

If potential (in volts) in a region is expressed as $V(x,y,z)=6xy-y+2yz$, the electric field $\left(\frac{N}{C}\right)$ at point $(1,1,0)$ is

Two point charges each $50\mu C$ are fixed on the y-axis. Another charged particle having charge Q1 and a mass 20 gm moving with a speed of $20m{s}^{-1}$. Find the speed of charged particle when it reaches the origin? Also, find the distance of particle when Kinetic energy is 0.

A planet of mass $M$ and a star of mass $2M$ are revolving around their common $\text{COM}$ under influence of mutual gravitational pull. Distance between them is $r$. Find the total mechanical energy of the system.

In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $h$ is proportional to

(ignore viscosity of air)

cot x log sin x

The masses and radii of earth and moon are $M_1,R_1\text{and}{M}_2,R_2$ respectively. Their centers are distance $d$ apart. The minimum velocity with which a particle of mass $m$ should be projected from a point midway between their centre so that it escapes to infinity is:-

A stone is dropped from the top of a tower of $500\text{m}$ height, into a pond of water at the base of the tower. When is the splash heard at the top?

$(\text{Given}g=10{\text{ms}}^{-2}$ and speed of sound $=340{\text{ms}}^{-1})$

A uniform electric field of magnitude $250\text{V/m}$ is directed in the positive $\text{x-}$direction. A $+12\mu \text{C}$ charge moves from the origin to the point $(x,y)=(20.0\text{cm},$$5.0\text{cm})$. What is the total work done required in moving the charge particle to the new position?

1. 16.2

Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to 5000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = $320\frac{m}{s}$.

An electron is projected with Velocity $V_0$ in a uniform electric field $E$ perpendicular to the field. Again it is projected with velocity $V_0$ perpendicular to a uniform magnetic field $B$. If $r_1$ is initial radius of curvature jsut after entering in the electric feld and $r_2$ is initial radius of curvature jsut after entering in magnetic field then the ratio $\frac{r_1}{r_2}$ is equal to

Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the figure. The magnitude of force P is:

A fun drive in an amusement park runs between two spots that are 2.0 km apart. For safety reasons the acceleration of the drive is limited to ± 4.0 m/$s^2$, and the jerk, or rate of change of acceleration, is limited to ± 1.0 m/$s^2$. The drive has a maximum speed to 144 km/h. Find the shortest time taken by the driver to travel between the spots?

A person pushes a box kept on a horizontal surface with a force of $100N$. In unit vector notation, the force can be expressed as

The elevator shown in the figure is descending with an acceleration of $2{\text{ms}}^{-2}$. The mass of the block $A=0.5\text{kg}$. The force exerted by the block $A$ on the block $B$ is $(g=10{\text{ms}}^{-2})$

A parallel plate capacitor is made of two square plates of side $a$, separated by a distance $d(d<<a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$, as shown in the figure. The capacitance of this capacitor is:

If $0<x<1$, then $\frac{3}{2}{x}^2+\frac{5}{3}{x}^3+\frac{7}{4}{x}^4+...,$ is equal to

If $n_1,n_2$ and $n_3$ are the fundamental frequencies of three segments of a string of length $l$, then the original fundamental frequency $n$ of the string is given by

In the figure shown, the tension at the mid – point of the rope of mass $3\text{kg}$ (point $B$) is $13\text{N}$. Find the tension in the rope at point $C$.

Nitrogen laser produces a radiation at a wavelength of 337.1 nm. If the number of photons emitted is 5.6 × 10²⁴, calculate the power of this laser.

Calculate
the temperature of 4.0 mol of a gas occupying 5 dm³
at 3.32 bar.

(R
= 0.083 bar dm³
K^–1
mol^–1).

A cord is used to lower vertically a block of mass $M$ for a distance $d$ at a constant downward acceleration $g/6$. Then the work done by the cord on the block is

The figure shows two charges of equal magnitude $q$ separated by a distance $2a$. As we move away from the charge situated at $x=0$ towards the charge situated at $x=2a$, which of the following graphs shows the correct behaviour of electric field?

At time $t=0$ magnetic field of $1000\text{G}$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500\text{G}$, in the next $5\text{s}$, then induced $EMF$ in the loop is:

The transfer characteristic curve of a transistor, having input and output resistances $100\Omega$ and $100\text{k}\Omega$ respectively, is shown in the figure. The voltage gain is