A car of $$800 \mathrm{~kg}$$ is taking turn on a banked road of radius $$300 \mathrm{~m}$$ and angle of banking $$30^{\circ}$$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $$(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73)$$

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $$t_1$$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $$t_2$$. Time required to reach the ground, if it is dropped from the top of the tower, is :

Given below are two statements:

Statement (I) : Dimensions of specific heat is $$[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}]$$.

Statement (II) : Dimensions of gas constant is $$[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}]$$.

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

A body of weight $$200 \mathrm{~N}$$ is suspended from a tree branch through a chain of mass $$10 \mathrm{~kg}$$. The branch pulls the chain by a force equal to (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$) :

The number of electrons flowing per second in the filament of a $$110 \mathrm{~W}$$ bulb operating at $$220 \mathrm{~V}$$ is : (Given $$\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$)

The acceptor level of a p-type semiconductor is $$6 \mathrm{~eV}$$. The maximum wavelength of light which can create a hole would be : Given $$\mathrm{hc}=1242 \mathrm{~eV} \mathrm{~nm}$$.

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $$4^{\text {th }}$$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $$0.04 \mathrm{~mm}$$ then how many main scale divisions are there in $$1 \mathrm{~cm}$$ ?

In a coil, the current changes from $$-2 \mathrm{~A}$$ to $$+2 \mathrm{~A}$$ in $$0.2 \mathrm{~s}$$ and induces an emf of $$0.1 \mathrm{~V}$$. The self inductance of the coil is :

Energy of 10 non rigid diatomic molecules at temperature $$\mathrm{T}$$ is :

When UV light of wavelength $$300 \mathrm{~nm}$$ is incident on the metal surface having work function $$2.13 \mathrm{~eV}$$, electron emission takes place. The stopping potential is :

(Given hc $$=1240 \mathrm{~eV} \mathrm{~nm}$$ )

Match List I with List II:

	LIST I (Y vs X)		LIST II (Shape of Graph)
A.	Y-magnetic susceptibility X = magnetising field	I.
B.	Y = magnetic field X = distance from centre of a current carrying wire for x < a (where a = radius of wire)	II.
C.	Y = magnetic field $$\mathrm{X}=$$ distance from centre of a current carrying wire for $$x>\mathrm{a}$$ (where $$\mathrm{a}=$$ radius of wire)	III.
D.	Y = magnetic field inside solenoid X = distance from centre	IV.

Choose the correct answer from the options given below :

For the thin convex lens, the radii of curvature are at $$15 \mathrm{~cm}$$ and $$30 \mathrm{~cm}$$ respectively. The focal length the lens is $$20 \mathrm{~cm}$$. The refractive index of the material is :

Two identical conducting spheres P and S with charge Q on each, repel each other with a force $$16 \mathrm{~N}$$. A third identical uncharged conducting sphere $$\mathrm{R}$$ is successively brought in contact with the two spheres. The new force of repulsion between $$\mathrm{P}$$ and $$\mathrm{S}$$ is :

The longest wavelength associated with Paschen series is : (Given $$\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$$ unit)

A total of $$48 \mathrm{~J}$$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $$2^{\circ} \mathrm{C}$$. The work done by the gas is: Given, $$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$.

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$\mathrm{R}=$$ Radius of bubble, $$\mathrm{S}=$$ Surface tension of bubble)

Assuming the earth to be a sphere of uniform mass density, a body weighed $$300 \mathrm{~N}$$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $$=49 \mathrm{~MSD} ; 20$$ divisions on main scale in each $$\mathrm{cm}$$

For mark on paper

$$\text { MSR }=8.45 \mathrm{~cm}, \mathrm{VC}=26$$

For mark on paper seen through slab

$$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$$

For powder particle on the top surface of the glass slab

$$\text { MSR }=4.05 \mathrm{~cm}, \mathrm{VC}=1$$

(MSR $$=$$ Main Scale Reading, VC = Vernier Coincidence)

Refractive index of the glass slab is :

In the given electromagnetic wave $$\mathrm{E}_{\mathrm{y}}=600 \sin (\omega t-\mathrm{kx}) \mathrm{Vm}^{-1}$$, intensity of the associated light beam is (in $$\mathrm{W} / \mathrm{m}^2$$ : (Given $$\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$$ )

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $$2.5 \mathrm{~nF}$$. If resistance of $$200 \Omega$$ and $$100 \mathrm{~mH}$$ inductor is being used in the given circuit. The frequency of ac source is _________ $$\times 10^3 \mathrm{~Hz}$$ (given $$\mathrm{a}^2=10$$)

Three balls of masses $$2 \mathrm{~kg}, 4 \mathrm{~kg}$$ and $$6 \mathrm{~kg}$$ respectively are arranged at centre of the edges of an equilateral triangle of side $$2 \mathrm{~m}$$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ $$\mathrm{kg} \mathrm{~m}^2$$.

In the given figure an ammeter A consists of a $$240 \Omega$$ coil connected in parallel to a $$10 \Omega$$ shunt. The reading of the ammeter is ________ $$\mathrm{mA}$$.

A coil having 100 turns, area of $$5 \times 10^{-3} \mathrm{~m}^2$$, carrying current of $$1 \mathrm{~mA}$$ is placed in uniform magnetic field of $$0.20 \mathrm{~T}$$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $$90^{\circ}$$ is _________ $$\mu \mathrm{J}$$.

A capacitor of $$10 \mu \mathrm{F}$$ capacitance whose plates are separated by $$10 \mathrm{~mm}$$ through air and each plate has area $$4 \mathrm{~cm}^2$$ is now filled equally with two dielectric media of $$K_1=2, K_2=3$$ respectively as shown in figure. If new force between the plates is $$8 \mathrm{~N}$$. The supply voltage is ________ V.

A particle moves in a straight line so that its displacement $$x$$ at any time $$t$$ is given by $$x^2=1+t^2$$. Its acceleration at any time $$\mathrm{t}$$ is $$x^{-\mathrm{n}}$$ where $$\mathrm{n}=$$ _________.

Two coherent monochromatic light beams of intensities I and $$4 \mathrm{~I}$$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $$x \mathrm{~I}$$. The value of $$x$$ is __________.

Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $$10.2 \mathrm{~V}$$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $$=1245 \mathrm{~eV} \mathrm{~nm}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$).

A wire of cross sectional area A, modulus of elasticity $$2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and length $$2 \mathrm{~m}$$ is stretched between two vertical rigid supports. When a mass of $$2 \mathrm{~kg}$$ is suspended at the middle it sags lower from its original position making angle $$\theta=\frac{1}{100}$$ radian on the points of support. The value of A is ________ $$\times 10^{-4} \mathrm{~m}^2$$ (consider $$x<<\mathrm{L}$$ ).

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