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A particle of mass m is moving along a trajectory given by x = x_{0} + a cosω_{1}t. y = y_{0} + b sinω_{2}t The torque,acting on the particle about the origin, at t=0 is :
A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz ad 530Hz. Their respective speeds are,in ms^{1 }(given speed of sound =300 m/s)
n moles of an ideal gas with constant volume heat capacity C_{v} undergo an isobraric expansion by certain volume . The ratio of the work done in the process, to the heat supplied is :
One Planoconvex and one plane ofconcave lens of same radius of Curvature ‘R’ but of different materials are joined side by side as shown in the figure . If refractive index of the material of 1 is µ_{1} and that of 2 is µ_{2} ,then the focal length of the combination is
n a photoelectric effect experiment the threshold wavelength of the is 380nm. If the wavelength of indent is 260nm, the maximum kinetic energy of emitted electrons will be: given E{in ev}= 1237/λ (innm)
The electric field of a plane electromagnetic wave is given by The corresponding magnetic field is then given by :
A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2kw. if the current in the secondary coil is 10A, then the input voltage and current in the primary Coil are:
A cylinder with fixed capacity of 67.2lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20^{0}C is : [Given that R=8.31J mol^{ 1}k ^{1 }]
Two radioactive materials A and B have decay constants 10λ and λ,respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time
In the given circuit,an ideal voltmeter connected across the 10 Ω resistance reads 2V. The internal resistance r, of each cell is
A ray of light AO in vacuum is incident on a glass slab at angle 60^{0} and refracted at angle 30^{0} along OB as shown in the figure.The optical path length of light ray from A to B is:
A current of 5A passes through a copper conductor (resistivity= 1.7 ´10^{8} Ωm) radius of cross section 5mm.Find the mobility of the charges if their drift velocity is 1.1x10^{3} m/s.
Figure shows charge (q) versus voltage (v) graph for series and parallel combination of two given capacitors . The capacitances are :
The value of acceleration due to gravity at Earth‘s surface is 9.8ms^{2} . The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms^{2}, is close to (Radius of earth = 6.4 x10^{6} m. )
Two wires A&B are carrying currents I_{1} & I_{2} as shown in the figure . the separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is Zero . The possible values of x are:
In a meter bridge experiment the circuit diagram and the corresponding observation table are shown in figure.
Q. Which of the readings is inconsistent ?
An npn transistor operates as a common emitter amplifier , with a power gain of 60dB. The input circuit resistance is 100 Ω and the output load resitance is 10K Ω .The common emitter current gain β is :
A massage signal of frequency 100MHz and peak voltage 100V is used to execute amplitude modulation on a carrier wave of frequency 300GHz and peak voltage 400 V . The modulation index and difference between the two side band frequencies are
A uniformly charged ring of radius 3a and total charge q is placed in xyplane centred at orign. A point charge q is moving towards the ring along the zaxis and has speed v at z = 4a The minimum value of v such that it crosses the origin is:
A proton,an electron, and a Helium nucleus, have the same energy. they are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let r_{p} , r_{e} and r_{He} be their respective radii, then,
The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135^{0} and 0^{0} respectively. it is observed that mercury gets depressed by an amount h in a capillary tube of radius r_{1} , while water rises by the same amount h in a capillary tube of radius r_{2} ,the ratio, (r_{1}/ r_{2}) is then close to:
a moving Coil galvanometer allows a full scale current 10^{4} A.A series resistance of2M Ω is required to convert the above galvanometer into a voltmeter of range 05V.Therefore the value of shunt resistance required to convert the above galvanometer in to ammeter of range 010mA is :
A ball is thrown upward with an initial velocity V_{0} from the surface of the earth. the motion of the ball is affected by a drag force equal to myV ^{2} ( where m is mass of the ball v is its instaneous velocity and g is a constant) . Time taken by the ball to rise to its zenith is :
A thin disc of mass M and radius R has mass per unit area σ (r ) =kr^{2} where r is the distance from its center . Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :
Given below in the left column are different modes of communication using the kinds of waves given in the right column .
From the options given below , find the most appropriate match between entries in the left and the right column.
In an experiment , the resistance of a material is plotted as a function of temperature ( in some range) .As shown in the figure , It is a straight line
A 25 x10^{3} m^{3 }volume cylinder is field with 1 mol O_{2 }gas room temperature (300k) The molicular diameter of O2,and its root mean square speed , are found to be 0.3 nm and 200m/s, respectively.what is the average collision rate (per second) for an O_{2} Molecule?
Two Coaxial discs , having moments of inertia I_{1}and I_{1}/2 are rotating with respective angular velocity ω_{1} and ω_{1}/2, about their common axis.They are brought in contact with each other and thereafter they rotate with a common angular velocity . If E_{f} and E_{i} `, are the final and initial total energies,then ( E_{f}  E_{i} ) is
Two Particles , of masses M and 2M moving , as shown,with speeds of 10m/s and 5m/s , collied elastically at the origin. After the collision , they move along the indicated directions with speeds v_{1} and v_{2} ,respectively , The value of v_{1} and v_{2} are nearly:
The displacement of a damped harmonic oscillator is given by x (t) = e^{0.1t} cos (10πt + φ) Here t it is in seconds.The time taken for its amplitude of vibration to drop to half of its initial value is close to:
The major product of the following reaction is
Major products of the following reaction are
Which of the following is a condensation polymer?
Ethylamine ( C_{2} H_{5} NH_{2} ) can be obtained from Nethylphthalimide on treatment with
1 videos356 docs217 tests

1 videos356 docs217 tests
