A proton, a deuteron and an $$\alpha$$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F₁. Now a spherical cavity of radius $$\left( {{R \over 2}} \right)$$ is made in the sphere (as shown in figure) and the force becomes F₂. The value of F₁ : F₂ is

An $$\alpha$$ particle and a proton are accelerated from rest by a potential difference of 200V. After this, their de Broglie wavelengths are $$\lambda$$_$$\alpha$$ and $$\lambda$$_p respectively. The ratio $${{{{\lambda _p}} \over {{\lambda _\alpha }}}}$$ is :

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ________.

Match List - I with List - II :

	List I		List II
(a)	h (Planck's constant)	(i)	$$[ML{T^{ - 1}}]$$
(b)	E (kinetic energy)	(ii)	$$[M{L^2}{T^{ - 1}}]$$
(c)	V (electric potential)	(iii)	$$[M{L^2}{T^{ - 2}}]$$
(d)	P (linear momentum)	(iv)	$$[M{L^2}{I^{ - 1}}{T^{ - 3}}]$$

Choose the correct answer from the options given below :

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.

If T_A and T_B are the time periods of A and B respectively then the value of T_B $$-$$ T_A :


[Given : radius of earth = 6400 km, mass of earth = 6 $$\times$$ 10²⁴ kg]

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio $${{{I_{\max }} - {I_{\min }}} \over {{I_{\max }} + {I_{\min }}}}$$ will be :

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.

Reason R : On heating, the length of the rod increases.

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

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72^nd division on circular scale coincides with the reference line. The radius of the wire is :

If the time period of a two meter long simple pendulum is 2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :

A diatomic gas, having $${C_p} = {7 \over 2}R$$ and $${C_v} = {5 \over 2}R$$, is heated at constant pressure. The ratio dU : dQ : dW :

A 5V battery is connected across the points X and Y. Assume D₁ and D₂ to be normal silicon diodes. Find the current supplied by the battery if the +ve terminal of the battery is connected to point X.

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is :

In an octagon ABCDEFGH of equal side, what is the sum of

$$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF} + \overrightarrow {AG} + \overrightarrow {AH} $$,

if, $$\overrightarrow {AO} = 2\widehat i + 3\widehat j - 4\widehat k$$

The current (i) at time t = 0 and t = $$\infty $$ respectively for the given circuit is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass.

Reason R : The product of their mass and radius must be same. M₁R₁ = M₂R₂

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

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s²)

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is $${x \over {3R}}$$. Value of x is ___________.

The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is __________ cm.

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______J.

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as

$$U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3$$

where, $$\alpha$$ and $$\beta$$ are positive constants. The equilibrium distance between two atoms will be $${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$$, where a = ___________.

The electric field in a region is given by $$\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}$$. The ratio of flux of reported field through the rectangular surface of area 0.2 m² (parallel to y $$-$$ z plane) to that of the surface of area 0.3 m² (parallel to x $$-$$ z plane) is a : b, where a = __________ [Here $${\widehat i}$$, $${\widehat j}$$ and $${\widehat k}$$ are unit vectors along x, y and z-axes respectively.]

In a certain thermodynamical process, the pressure of a gas depends on its volume as kV³. The work done when the temperature changes from 100$$^\circ$$C to 300$$^\circ$$C will be ___________ nR, where n denotes number of moles of a gas.

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $$\mu$$F is used in the resonant circuit. The self inductance of coil necessary for resonance is __________ $$\times$$ 10^$$-$$8 H.