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Which of the following electric field configurations describes the lines of force in an electric field between two parallel plates of opposite charge?

An uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $\left(\frac{L}{n}\right)$ th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

In an experiment, the percentage of error occured in the measurement of physical quantities $A,B,C$ and $D$ are $1\%,2\%,3\%$and $4\%$ respectively. Then, the maximum percentage of error in the measurement of $X$, where $X=\frac{A^2{B}^{1/2}}{C^{1/3}{D}^3},$ will be

When a potential difference of 2V is applied across a resistor, you observed a current I. When the length of the resistor is doubled without changing the thickness, what is the current observed when 2V is applied across it.

If $\theta$ is angle that vector $\overrightarrow{A}=2\hat{i}+3\hat{j}+5\hat{k}$ makes with x-z plane then

A metal ball of mass $2\text{kg}$ moving with speed of $36\text{kmph}$ is having a collision with a stationary ball of mass $2\text{kg}$. If after collision, both the balls move together, the loss in kinetic energy due to collision is:

When a spring is stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2 cm, the stored energy will be increased by

A particle of mass $1\text{kg}$ is projected with a velocity $20\sqrt{2}\text{m/s}$ from the origin of an $x-y$ co- ordinate axis system at an angle ${45}^{\circ }$ with $x$ axis (horizontal). The angular momentum [in ${\text{kg m}}^2\text{/s}$] of the ball about the point of projection after $1\text{second}$ of projection is [Take $g=10{\text{m/s}}^2$ and $y$ - axis is taken as vertical]

In the circuit shown, A and B represent two inputs and C represents the output. The circuit represents

At the top of the trajectory of a projectile, the directions of its velocity and acceleration are

Energy levels A,B,C of an atom are shown below





If $E_A<E_B<E_C$, the wavelength emitted due to transistion from C to A is ${\lambda }_3$then correct statements of the following is

The wattage rating of a light bulb indicates the power dissipated by the bulb if it is connected across $110\text{V}$ DC potential difference. If a $50\text{W}$ and $100\text{W}$ bulb are connected in series to a $110\text{V}$ DC source, how much power will be dissipated in the $50\text{W}$ bulb?

When an ideal monoatomic gas is heated at constant pressure, the fraction of heat energy supplied which increases the internal energy of gas is

The flux passing through the surface $S_5$ will be

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s=t^3+5$, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t = 2 s is nearly

A body is projected with initial velocity of $(8\hat{i}+6\hat{j})\text{m/s}$ from origin, find angular velocity of body wrt to an axis passing through origin and perpendicular to the x -y plane when it lands. (Here $\hat{i},\hat{j}$ are unit vectors corresponding to X, Y axis respectively)

Take $g=10{\text{m/s}}^2$

Find the integral of the given function w.r.t x

$y=cos(8x+6)+cose{c}^2(7x+5)+6secxtanx$

A piece of wire is bent in the shape of a parabola $y=k{x}^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowestpoint of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

The mass of liquid flowing per second per unit area of cross section of the tube is proportional to $P^x$ and $v^y$, where $P$ is the pressure difference and $v$ is the velocity, then the relation between $x$ and $y$ is

A small bob hangs at one end of a massless string of length $l$ and the other end of the string is fixed. The bob is given a sharp hit to impart it a horizontal speed of $\sqrt{3gl}$. Find the angle $\left(\theta \right)$ made by the string with the vertical when the string becomes slack.

A simple pendulum has a time period $T$ in vaccum. Its time period when it is completely immersed in a liquid of density one-eight of the density of material of the bob is

A bullet is fired with a velocity of $196{\text{ms}}^{-1}$ at an angle ${30}^{\circ }$ with the horizontal. Calculate the maximum height attained by the bullet. (Take $g=9.8{\text{m/s}}^2$)

Find the moment of inertia of an equilateral triangular lamina of mass $1\text{kg}$ and having sides $3\text{m}$ about the axis passing through its centre of mass and perpendicular to the plane of triangular lamina.

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{\text{th}}\text{second}$ after its fall, to the next droplet, is $34.3\text{m}.$ At what rate the droplets are coming from the tap ? (Take $g=9.8{\text{m/s}}^2$)

A block is resting on a piston which is moving vertically with SHM of period 1 s. What is the minimum amplitude to be given to it so that the block and piston can separate?

As shown in figure, a ring of radius $R$ is rolling without slipping. What will be the magnitude of velocity of point $A$ on the ring ?

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

For the arrangement of mirror and object shown in figure, the velocity of image w.r.t ground is:

A metallic sphere of mass $3\text{kg}$ is held by a string and is completely immersed in a liquid of relative density $0.8$. The relative density of the metallic sphere is $10$. What is the tension in the string? Take $g=10{\text{ms}}^{-2}$

Find the co-ordinates of the centre of mass of the lamina, shown in figure.

Two blocks of mass $3\text{kg}$ and $2\text{kg}$ are tied by a massless string. A force of $100\text{N}$ is applied on $3\text{kg}$ block as shown. Find the tension in the string. $(g=10{\text{m/s}}^2)$

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are placed at rest on a frictionless surface and connected by a spring. An external hit gives a velocity of $21\text{m/s}$ to the heavier block towards the lighter one. Velocities of both blocks (heavier and lighter one) in the centre of mass frame, just after the kick will be respectively:

(Consider direction of motion of heavier block as $+ve$ direction)

Two identical tuning forks vibrating at the same frequency 256 Hz are kept fixed at some distance apart. A listener runs between the forks at a speed of 3.0 m/s so that he approaches one tuning fork while receding from the other (figure). Find the beat frequency observed by the listener. Speed of sound in air = 332 m/s.

A thin rod of length $4l$, mass $4m$ is bent at the points shown in the figure. What is the moment of inertia of the rod about the axis passing point $\text{O}$ and perpendicular to the plane of the paper?

An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are $Q_1=5960\text{J},Q=-5585\text{J},Q_3=-2980\text{J}$ and $Q_4=3645\text{J}$ respectively. The corresponding quantities of work done by gas for each steps are $W_1=2200\text{J},W_2=-825\text{J},W_3=-1100\text{J}$ and $W_4=765\text{J}$ respectively. The efficiency of the cycle is

A particle starts from rest with a time-varying acceleration, $a=(2t-4)$. Here $t$ is in $s$ and $a$ in $m/s^2$. After what time (in $s$) particle comes to rest?

Find the radius of gyration of a thin uniform rod of mass ${}^{\prime }{m}^{\prime }$ and length $l=9\text{m}$ about an axis passing through one end and perpendicular to the rod as shown in figure.

In the system shown in figure, masses of the blocks are such that when system is released, acceleration of pulley $P_1$ is $a$ upwards and acceleration of block 1 is $a_1$ upwards, such that $a<a_1<2a$.

It is found that acceleration of block 3 is same as that of 1 both in magnitude and direction.



$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{a) Acceleration of}2& p)2a+a_1\\ \text{b) Acceleration of}4& q)2a-a_1\\ \text{c) Acceleration of}2\text{w.r.t.}3& \text{r) upwards}\\ \text{d) Acceleration of}2\text{w.r.t.}4& \text{s) downwards}\end{array}$

Figure shows four $P-V$ diagrams. Which of these curves represent isothermal and adiabatic process?

The angular position of a rotating disc is given as $\theta =6t^2+5t-4$ where $\theta$ is in radians, $t$ is in seconds. What is the average angular velocity for the first time interval from $t=0\text{(s)}$ to $t=4\text{(s)}$?

The simple pendulum bob is given a horizontal velocity $\sqrt{gl}$ at the bottom. The angle with the vertical through which the ball swings before its velocity becomes zero is

Figure shows two cylinders of radii $r_{1}and{r}_2$ having moments of inertia $I_{1}and{I}_2$ about their respective axes. Initially, the cylinders rotate about their axes with angular speeds ${\omega }_{1}and{\omega }_2$ as shown in the figure. The cylinders are moved closer to touch each other keeping the axes parallel. The cylinders first slip over each other at the contact but the slipping finally ceases due to the friction between them. Find the angular speeds of the cylinder 1 and 2 respectively after the slipping ceases.

If the coefficient of friction between $A$ and $B$ is $\mu$, the minimum horizontal acceleration of the wedge $A$ for which $B$ will remain at rest w.r.t. the wedge is

A geostationary satellite orbits around the earth in a circular orbit of radius 36,000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface (Re = 6400 km) will approximately​

be:

A copper rod of length $88cm$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is

(${\alpha }_{Cu}=1.7\times {10}^{-5}{K}^{-1}$and ${\alpha }_{Al}=2.2\times {10}^{-5}{K}^{-1}$)