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Figure shows a cylindrical vessel of height 90 cm filled up to the brim. There are four holes in the vessel as shows in figure. The liquid falling at maximum horizontal distance from the vessel would come from

The density inside a solid sphere of radius a is given by $\rho$ =${\rho }_0$a/r where ${\rho }_0$ is the density at the surface and r denotes the distance from the centre. The gravitational field due to this sphere at a distance 2a form its centre is..

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F₁ on a particle placed at P, distance 2R from the centre O of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in figure. The sphere with cavity now applies a gravitational force F₂ on same particle placed at P. The ratio $\frac{F_2}{F_1}$ will be

Two trains each 50m long are travelling in opposite direction with velocity 10m/s and 15m/s. The time of crossing is..

According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is:

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to $R^{\frac{-5}{2}}$, then $T^2$ is proportional to

When a dielectric slab is introduced between the plates of an isolated charged capacitor, it

A photon of energy hv is absorbed by a free electron of a metal having work function $\varphi <hv$

Image formed on the retina is

A whistle sends out 256 waves in a second. If the whistle approaches the observer with velocity 1/3 of the velocity of sound in air, the number of waves per second the observer will receive

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample ? (b) What is its half-life ?

There are two objects of masses 1 kg and 2 kg located at (1, 2) and (-1, 3) respectively. The coordinates of the centre of mass are

Consider a block of mass $10\text{kg}$ collides with a spring of spring constant $10\text{N/m}$. The speed of block is $5\text{m/s}$, when the compression in spring is $2\text{m}$. Calculate the speed of the block, when compression is $5\text{m}$?

The coefficient of linear expansion of an inhomogeneous rod changes linearly from ${\alpha }_1$ to ${\alpha }_2$ from one end to the other end of the rod. The effective coefficient of linear expansion of the rod is

A box contains n molecules of a gas. How will the pressure of the gas be effected, if the number of molecules is made 2n

A square lamina of mass $m=4\text{kg}$ having sides of length $a=2\text{m}$. Find the moment of inertia of the lamina along one of its side.

Dimensional formula for megnatic flux is

One day Chetan's mother developed a severe stomach ache all of a sudden. She rushed to the doctor who suggested for an immediate endoscopy test and gave an estimate of expenditure for the same. Chetan immediately contacted his class teacher and shared the information with her. The class teacher arranged for the money and rushed to the hospital. On realizing that Chetan belonged to a below average income group family, even the doctor offered concession for the test fee. The test was conducted successfully.
Answer the following questions based on the above information :
(a) Which principle in optics is made use of in endoscopy ?
(b) Briefly explain the values reflected in the action taken by the teacher.
(c) In what way do you appreciate the response of the doctor on the given situation ?

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors and$\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$ then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $k$. If radius of the ball is $R$, then the fraction of total energy associated with its rotational energy will be

Figure shows a system consisting of a massless pulley, a spring of force constant k and a block of mass m. If the block is slightly displaced vertically down from its equilibrium position and released, find the period of its vertical oscillation.

A body of mass m hangs by an inextensible string that passes over a smooth massless pulley that is fitted with a light spring of stiffness k as shown in the figure, such that the spring is initially at natural length. If the body is released from rest and the spring is released, calculate the maximum elongation of the spring.

A U-tube containing a liquid is accelerated horizontally with a constant acceleration $a_0$. If the separation between the vertical limbs is l, find the difference in the heights of the liquid in the two arms.

The outer cylinders of two cylindrical capacitors of capacitance $2.2\mu F$ each, are kept in contact and the inner cylinders are connected through a wire. A battery of emf 10 V is connected as shown in figure (31-E5). Find the total charge supplied by the battery to the inner cylinders.

A ball falling down vertically collides with a smooth and fixed inclined plane of inclination $\theta$ . If it moves horizontally just after the impact, the coefficient of restitution is:

An object A is released from the top of a vertical building of height $H$. At an instant when it has descended $xm$ from the top, another object B is released from $ym$ below the top of that building. Right from this instant, both these objects take the same amount of time to reach the ground. Which of the following expressions in the given situation is correct ?

A light rod with uniform cross-section of ${10}^{-4}{m}^2$ is shown in the adjoining figure. The rod consists of three different materials whose lengths are 0.1 m, 0.2 m and 0.15 m respectively and whose Young's modulii are $2.5\times {10}^{10}\frac{N}{m^2},4\times {10}^{10}\frac{N}{m^2}$ and $1\times {10}^{10}\frac{N}{m^2}$ respectively.
The displacement of point B will be

Photons with energy $5eV$ are incident on a cathode $C$ in a photoelectric cell. The maximum energy of emitted photo electrons is $2eV$. When photons of energy $6eV$ are incident on $C$, no photoelectrons will reach the anode $A$. The stopping potential of $A$ relative to $C$ is

A student performs an experiment for determination of $g=\frac{4{\pi }^{2}l}{T^2}$ The error in length $l$ is $\Delta l$ and in time $T$ is $\Delta T$ and $n$ is number of times the reading is taken. The measurement of $g$ is most accurate for:

After arriving at saturation current further increase in anode potential does not change in magnitude of current why?

Find $\frac{dy}{dx}$, if $y=(x^3-2)x$.

The variation of acceleration due to gravity $g$ with distance $d$ from the center of the earth is best represented by ($R=$ Earth’s radius):

A string of length L fixed at both ends vibrates in its fundamental node at a frequency v and a maximum amplitude A. Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

A particle moves in a circular path with a continuously increasing speed. Its motion is

Astigmatism (for a human eye) can be removed by using

[CPMT 1972; MP PET/PMT 1988; CBSE PMT 1990]

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her walk up on the moving escalator will be

A boy is sitting on a swing at a maximum height of 5m above the ground. When the swing passes through the mean position which is 2m above the ground his velocity is approximately

The alphabet $\text{S}$ is placed in front of a plane mirror.


Which of the following options correctly represents the image in the mirror?

A prism having refractive index 1.414 and refracting angle ${30}^{\circ }$ has one of the refer A prism having refractive index 1.414 and refracting angle ${30}^{\circ }$ has one of the referacting surface silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is acting surface silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

A square loop of edge length $a$ is placed in the same plane as long straight wire carrying current $i$. The center of the loop is at distance $r$ from wire where $r$>>$a$. If loop is moved away from the wire at a constant velocity of $v$ induced emf in the loop is