A hydraulic automobile lift is designed to lift vehicles of mass $$5000 \mathrm{~kg}$$. The area of cross section of the cylinder carrying the load is $$250 \mathrm{~cm}^{2}$$. The maximum pressure the smaller piston would have to bear is $$\left[\right.$$ Assume $$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right]$$

An emf of $$0.08 \mathrm{~V}$$ is induced in a metal rod of length $$10 \mathrm{~cm}$$ held normal to a uniform magnetic field of $$0.4 \mathrm{~T}$$, when moves with a velocity of:

For particle P revolving round the centre O with radius of circular path $$\mathrm{r}$$ and angular velocity $$\omega$$, as shown in below figure, the projection of OP on the $$x$$-axis at time $$t$$ is

In photo electric effect

A. The photocurrent is proportional to the intensity of the incident radiation

B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.

C. Max. K.E with which photoelectrons are emitted depends on the frequency of incident light.

D. The emission of photoelectrons require a minimum threshold intensity of incident radiation.

E. Max. K.E of the photoelectrons is independent of the frequency of the incident light.

Choose the correct answer from the options given below:

A bullet of mass $$0.1 \mathrm{~kg}$$ moving horizontally with speed $$400 \mathrm{~ms}^{-1}$$ hits a wooden block of mass $$3.9 \mathrm{~kg}$$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $$20 \mathrm{~m}$$ before coming to rest. The coefficient of friction between the block and the surface is __________.

(Given $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

Given below are two statements

Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time.

Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time.

In the light of given statements, choose the correct answer from the options given below.

The acceleration due to gravity at height $$h$$ above the earth if $$h << \mathrm{R}$$ (Radius of earth) is given by

The equivalent resistance between A and B as shown in figure is:

The waves emitted when a metal target is bombarded with high energy electrons are

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A : Electromagnets are made of soft iron.

Reason R : Soft iron has high permeability and low retentivity.

In the light of above, statements, choose the most appropriate answer from the options given below.

Electric potential at a point '$$\mathrm{P}$$' due to a point charge of $$5 \times 10^{-9} \mathrm{C}$$ is $$50 \mathrm{~V}$$. The distance of '$$\mathrm{P}$$' from the point charge is:

(Assume, $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{+9} ~\mathrm{Nm}^{2} \mathrm{C}^{-2}$$ )

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be -

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $$27^{\circ} \mathrm{C}$$ is

The trajectory of projectile, projected from the ground is given by $$y=x-\frac{x^{2}}{20}$$. Where $$x$$ and $$y$$ are measured in meter. The maximum height attained by the projectile will be.

The width of fringe is $$2 \mathrm{~mm}$$ on the screen in a double slits experiment for the light of wavelength of $$400 \mathrm{~nm}$$. The width of the fringe for the light of wavelength 600 $$\mathrm{nm}$$ will be:

Match List I with List II

	LIST I		LIST II
A.	Torque	I.	$$\mathrm{ML^{-2}T^{-2}}$$
B.	Stress	II.	$$\mathrm{ML^2T^{-2}}$$
C.	Pressure gradient	III.	$$\mathrm{ML^{-1}T^{-1}}$$
D.	Coefficient of viscosity	IV.	$$\mathrm{ML^{-1}T^{-2}}$$

Choose the correct answer from the options given below:

The number density of free electrons in copper is nearly $$8 \times 10^{28} \mathrm{~m}^{-3}$$. A copper wire has its area of cross section $$=2 \times 10^{-6} \mathrm{~m}^{2}$$ and is carrying a current of $$3.2 \mathrm{~A}$$. The drift speed of the electrons is ___________ $$\times 10^{-6} \mathrm{ms}^{-1}$$

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $$30 \mathrm{~cm}$$. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of $$15 \mathrm{~cm}$$ from the pole of the surface. The distance of image from the pole of the surface is ____________ $$\mathrm{cm}$$.

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A body of mass $$5 \mathrm{~kg}$$ is moving with a momentum of $$10 \mathrm{~kg} \mathrm{~ms}^{-1}$$. Now a force of $$2 \mathrm{~N}$$ acts on the body in the direction of its motion for $$5 \mathrm{~s}$$. The increase in the Kinetic energy of the body is ___________ $$\mathrm{J}$$.

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _________.

A steel rod of length $$1 \mathrm{~m}$$ and cross sectional area $$10^{-4} \mathrm{~m}^{2}$$ is heated from $$0^{\circ} \mathrm{C}$$ to $$200^{\circ} \mathrm{C}$$ without being allowed to extend or bend. The compressive tension produced in the rod is ___________ $$\times 10^{4} \mathrm{~N}$$. (Given Young's modulus of steel $$=2 \times 10^{11} \mathrm{Nm}^{-2}$$, coefficient of linear expansion $$=10^{-5} \mathrm{~K}^{-1}$$ )

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $$3 \mathrm{~m} / \mathrm{s}$$ (as shown in figure). Maximum height with respect to the initial position covered by it will be __________ cm.

The ratio of magnetic field at the centre of a current carrying coil of radius $$r$$ to the magnetic field at distance $$r$$ from the centre of coil on its axis is $$\sqrt{x}: 1$$. The value of $$x$$ is __________

A $$600 ~\mathrm{pF}$$ capacitor is charged by $$200 \mathrm{~V}$$ supply. It is then disconnected from the supply and is connected to another uncharged $$600 ~\mathrm{pF}$$ capacitor. Electrostatic energy lost in the process is ____________ $$\mu \mathrm{J}$$