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The radius of a well is 7 m. water init is at a depth of 20m and depth of water column is 10 m.work done in pumping out water completely from the well is,(g=10m/s²)?

A machine gun fires A bullet of mass 40 gram with the velocity of 1200m/s. The gun can exert a maximum force of 144N on the bullet. How many bullets can it fire per second at the most?

The light from a torch is normally incident on the surface at intensity of illumination $I_1$. If the surface is tilted to ${45}^{\circ }$ from initial position, then what will be intensity of illumination $I_2$ on the surface in terms of $I_1$ ?

A long solenoid of $50\text{cm}$ length having $100$ turns carries a current of $2.5\text{A}.$ The magnetic induction at the center of the solenoid is $[{\mu }_0=4\pi \times {10}^{-7}{\text{T Am}}^{-1}]$

Find $x$ if $\text{P}$ is a null point.

Standing waves are produced by the superposition of two waves, $y_1=0.05\sin (3\pi t-2x)$ and $y_2=0.05\sin (3\pi t+2x)$, where $x$ and $y$ are expressed in metres and $t$ is in seconds. What is the amplitude of a particle at $x=0.5\text{m}$? Given $\cos {57.3}^{\circ }=0.54$.

The graph of $y=\ln (x^2+1)$ is

The magnitude of electric field intensity $E$ is such that an electron placed in it would experience an electrical force equal to its weight is given by

(Mass of $e^{–}=m$)

If an electron and a proton having same momentum enter perpendicular to a magnetic field, then

The figure shows a square loop of side $5\text{cm}$ being moved towards the right at a constant speed of $v=1\text{cm/s}$. The front edge just enters the $20\text{cm}$ wide magnetic field at $t=0$. Find the induced emf in the loop at $t=2\text{s}$.

A TV transmission tower has a height of $140\text{m}$ and the height of the receiving antenna is $40\text{m}$. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth $=6.4\times {10}^6\text{m}$).

A chain is placed on a frictionless table with one fourth of it hanging over the edge. If the length of the chain is 2m and its mass is 4kg, the energy need to be spent to pull it back to the table is

A continuous time signal x(t) is obtained at the output of an ideal low pass filter with cut off frequency ${\omega }_c=1000\pi$. If instantaneous sampling is performed on x(t). Which of the following sampling periods will guarantee that x(t) can be recovered properly from its sampled version using an appropriate low-pass filters?

Half life of a radioactive element is $5\text{min. and}10\text{sec}$. The time taken for $90\%$ of it to disintegrate is nearly,

(Given: ${\log }_{10}2=0.301$)

A square plate of $1\text{m}$ side moves parallel to a second plate with velocity $4\text{m/s}$. A thin layer of water exist between plates. If the viscous force is $2\text{N}$ and the coefficient of viscosity is $0.01\text{Poise}$, then find the distance between the plates.

A compound microscope consists of an objective of focal length 1 cm and an eyepiece of focal length 5 cm. An object is placed at a distance of 0.5 cm from the objective. What should be the separation between the lenses so that the microscope projects an inverted real image of the object on a screen 30 cm behind the eyepiece?

In YDSE experiment a glass plate of refractive index 1.5 is placed infront of one of the slits. Minimum thickness 't' of this glass plate so that intensity of light at position of central maxima [before glass plate] remains unchanged is

A car is moving on a straight road. The velocity of the car varies with time as shown in the figure. Initially (at $t=0$), the car was at $x=0$, where, $x$ is the position of the car at any time ‘$t$’.

The maximum displacement from the starting position will be

Two pendulums have time period $T$ and $5T/4$. They start $\text{SHM}$ at the same time from the mean position. What will be the phase difference between them at the moment, when bigger pendulum completes one oscillation?

The change in potential energy when a body of mass $m$ is raised to height $nR$ from the earth's surface is ($R$ is radius of earth)

What is the work done by electric force in taking a charged particle of charge 1C by 10 cm along the equator of a dipole?

A plane electromagnetic wave, has frequency of $2.0\times {10}^{10}\text{Hz}$ and its energy density is $1.02\times {10}^{–8}{\text{Jm}}^{-3}$ in vacuum.

The amplitude of the magnetic field of the wave is close to:

$(\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9\frac{{\text{Nm}}^2}{C^2})\text{and speed of light}c=3\times {10}^8{\text{ms}}^{-1}$

The amplitude of a wave disturbance propagating in the positive x-direction is given by $y=\frac{1}{1+x^2}$ at t = 0 and $y=\frac{1}{[1+(x-1{)}^2]}$ at t = 2s. the wave speed is

In below figure two blocks are placed on fixed inclined plane and friction coefficient between the blocks and inclined plane are ${\mu }_1$ and ${\mu }_2$ respectively as shown in figure. Value of ${\mu }_1$ and ${\mu }_2$ are given in column 1 and value of $a_1$ and $a_2$ are given in column 2 and column 3 respectively.

$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2}& & \text{Column 3}\\ \left(i\right)& {\mu }_1=0.8& \left(i\right)& a_1=2m/s^2& \left(P\right)& a_2=2m/s^2\\ & {\mu }_2=0.8& & & & \\ \left(ii\right)& {\mu }_1=0.5& \left(ii\right)& a_1=0.8m/s^2& \left(Q\right)& a_2=0.8m/s^2\\ & {\mu }_2=0.5& & & & \\ \left(iii\right)& {\mu }_1=0.5& \left(ii\right)& a_1=4.4m/s^2& \left(R\right)& a_2=4.4m/s^2\\ & {\mu }_2=0.2& & & & \\ \left(iv\right)& {\mu }_1=0.5& \left(iv\right)& a_1=0& \left(S\right)& a_2=0\\ & {\mu }_2=0.8& & & & \end{array}$

In which of the following combination both blocks will move together and normal between them is zero?

A prism having an apex angle $4^{\circ }$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror?

The magnetic field $\left(B\right)$ due to revolving electron at the center is proportional to $\frac{Z^3}{n^x}$. The value of $x$ is -

A uniform solid sphere of radius $R$ has a cavity of radius $1\text{m}$ cut from it. If the centre of mass of the system lies at the periphery of the cavity, then:

A molecule with dipole moment $p$ is placed in an electric field of strength $E$. Initially the dipole is aligned parallel to the field . If the dipole is to be rotated to be anti-parallel to the field , the work required to be done by an external agency is

A circular disc of mass 300 gm and radius 20 cm can rotate freely about a vertical axis passing through is center O. A small insect of mass 100 gm is initially at a point A on the rim. The insect initially stationary starts walking from rest along the rim of disc with such a time varying relative velocity that the disc rotates in the opposite direction with a constant angular acceleration = $2\pi rad/s^2$. After some time T, the insect is back at the point A

. What is the time taken by insect to reach the original position?

A student is standing at a distance of 50 metres from the bus. As soon as the bus starts its motion with an acceleration of $1{\text{m/s}}^2$ , the student starts running towards the bus with an uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is