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A body started with a velocity of $20m{s}^{-1}$ and moving with an acceleration of $2m{s}^{-2}$. The distance (in $\text{m})$ travelled by the body in the $8^{th}$ second is

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t = 0. At this instant of time, the horizontal component of its velocity is v. A bead Q of the same mass as P is ejected from A at t = 0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let tp and tq be the respective times taken by P and Q to reach the point B. Then

Time taken by p is

a) less than Q

b) greater than Q

c)equal to Q

A solenoid having inductance 4.0 V battery at t = 0. Find (a) The times constant, (b) the times elapsed before the current reaches 0.63 of its steady state value, (c) the power deleered by the battery at this instant and (d) the power dissipated in joule heating at this instant.

What is the maximum current that can be drawn from a cell of emf E and internal resistance r connected to an external resistance R?

Three resistors having resistances, $r_1,r_2$ and $r_3$ are connected as shown in the given circuit. The ratio $\frac{i_3}{i_1}$ of currents in terms of resistances used in the circuit is -

Find potential difference between the point $\text{A}$ and $\text{B}$ (in volts)

The shown graph is the curve between magnetic field $\left(B\right)$ and time $\left(t\right)$. The magnetic field exists throughout the plane of a conducting loop, perpendicular to the plane of the loop. The induced emf in the loop is maximum during which of the following time interval?

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r=\frac{{\lambda }_1}{{\lambda }_2}$ is given by

A beam of plane polarized light falls normally on a polarizer (cross-sectional area $3\times {10}^{-4}{\text{m}}^2$) which rotates about the axis of the ray with an angular velocity of $31.4\text{rad/s}$. Find the energy of light $E$ passing through the polarizer per revolution and the intensity $I_{avg}$ of the emergent beam if the flux of energy of the incident ray is ${10}^{-3}\text{W}$.

1. 416.5

Which of the following represents an impossible situation?

A rotating machine is maintained at a uniform angular speed of 150 rad s^-1, with a torque of 100 Nm. The power is

A horizontal copper disc of diameter $20\text{cm}$, makes $10\text{revolution/s}$ about a vertical axis passing through its center. A uniform magnetic field of $100\text{G}$ acts perpendicular to the plane of the disc. Calculate the potential difference across its center and rim.



Take $1\text{G}={10}^{-4}\text{T}$

It is 260 from Patna to Ranchi by air and 320 km by road. An Aeroplane takes 30 minutes to go from Patna to Ranchi Whereas a delux bus takes 8 hours.

(a) Find the average speed of the plane.

(b) Find the average speed of the bus.

(c) Find the average velocity of the plane.

(d) Find the average velocity of the bus.

Multiple constant forces $F_1,......F_i$ are acting on an object of mass 'm' and produce a displacement S, with an acceleration a. Which of the following statements is true.

Which of the following substances are strongly attracted by magnetic field?

A block of weight $10N$ is fastened to one end of a wire of cross-sectional area $3m{m}^2$ and is rotated in a vertical circle of radius $20cm$. The speed of the block at the bottom of the circle is $2m/s$. Find the elongation of the wire when the block is at the bottom of the circle. Young’s modulus of the material of the wire $=2.0\times {10}^{11}N/m^2$.

A monkey of mass $12\text{kg}$ climbs up a light rope as shown in figure. The rope passes over a light and frictionless pulley and it is attached to a bunch of bananas having mass $16\text{kg}$. What will be maximum acceleration of monkey without lifting the bunch of bananas? (Take $g=10{\text{m/s}}^2$)

If work done by the heat engine is $600\text{J}$ and heat absorbed by the working substance is $800\text{J}$, the efficiency of the heat engine is

Each of the pictures shows four objects tied together with rubber bands being pulled to the right across a horizontal frictionless surface by a force $F$. All the objects have the same mass. All the rubber bands obey Hooke’s law and have the same equilibrium length and the same force constant. Which of the pictures is drawn most correctly?

Two spheres carrying charges $+6\mu Cand+9\mu C$, separated by a distance d, experiences a force of repulsion F. When a charge of $-3\mu C$ is given to both the sphere and kept at the same distance as before, the new force of repulsion is

A rod of length $10\text{m}$ is inclined on the wall at an angle ${37}^{\circ }$ with horizontal.


Find out position of centre of mass of the rod assuming the wall to be along $y-$ axis and foot of the wall as the origin.

In the circuit shown in figure three ideal sources have $\text{EMF}$, $E_1=1\text{V}$ and $E_2=2.5\text{V}$ and the resistances have the values $R_1=10\Omega$ and $R_2=20\Omega$. Find the potential differences $V_A-V_B$ between the plates $\text{A}$ and $\text{B}$ of the capacitor $\text{C}$ in steady state.

A bifocal lens is used for the correction of ____. The upper part of the bifocal lens is a ____ lens and the lower part is ____.

1. 8

Find out the value of resistance $R$ in figure.

Two balls of identical masses undergo perfectly elastic oblique collsion. One of the balls (Ball 1) is initially at rest while the other (Ball 2) is moving with velocity $u$. After the collisions, what angle will the final velocities of the balls make with each other?

A rod $\text{PQ}$ of mass of mass $M$ and length $L$ is hinged at end $\text{P}.$ The rod is kept horizontal by a massless string tied to point $\text{Q}$ as shown in figure. When string is cut, the initial angular acceleration of the rod is-

An AC generator is connected to an electrical appliance. In $10$ revolutions of the armature, the current in the appliance changes direction:

What is meant by mileage of a vehicle

For a given material, the energy $\left(E\right)$ and wavelength $\left(\lambda \right)$ of characteristic $\text{X}$-rays satisfies