The de-Broglie wavelength associated with a particle of mass $$m$$ and energy $$E$$ is $$h/\sqrt{2mE}$$. The dimensional formula for Planck's constant is :
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The de-Broglie wavelength associated with a particle of mass $$m$$ and energy $$E$$ is $$h/\sqrt{2mE}$$. The dimensional formula for Planck's constant is :
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Two cars are travelling towards each other at speed of $$20 \text{ m s}^{-1}$$ each. When the cars are $$300 \text{ m}$$ apart, both the drivers apply brakes and the cars retard at the rate of $$2 \text{ m s}^{-2}$$. The distance between them when they come to rest is :
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A $$1 \text{ kg}$$ mass is suspended from the ceiling by a rope of length $$4 \text{ m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45°$$ with respect to the vertical axis as shown in figure.
The magnitude of $$F$$ is : (Assume that the system is in equilibrium and $$g = 10 \text{ m/s}^2$$)
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A satellite of $$10^3 \text{ kg}$$ mass is revolving in circular orbit of radius $$2R$$. If $$\frac{10^4 R}{6} \text{ J}$$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $$g = 10 \text{ m/s}^2$$, $$R$$ = radius of earth)
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The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:
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A spherical ball of radius $$1 \times 10^{-4} \text{ m}$$ and density $$10^5 \text{ kg/m}^3$$ falls freely under gravity through a distance $$h$$ before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of $$h$$ is approximately: (The coefficient of viscosity of water is $$9.8 \times 10^{-6} \text{ N s/m}^2$$)
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A real gas within a closed chamber at $$27°C$$ undergoes the cyclic process as shown in figure. The gas obeys $$PV^3 = RT$$ equation for the path $$A$$ to $$B$$. The net work done in the complete cycle is (assuming $$R = 8 \text{ J/molK}$$):
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The temperature of a gas is $$-78°C$$ and the average translational kinetic energy of its molecules is $$K$$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $$2K$$ is :
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Five charges $$+q, +5q, -2q, +3q$$ and $$-4q$$ are situated as shown in the figure.
The electric flux due to this configuration through the surface $$S$$ is :
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The effective resistance between $$A$$ and $$B$$, if resistance of each resistor is $$R$$, will be
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A proton and a deutron ($$q = +e, m = 2.0u$$) having same kinetic energies enter a region of uniform magnetic field $$\vec{B}$$, moving perpendicular to $$\vec{B}$$. The ratio of the radius of deutron path to the radius of the proton path is:
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A square loop of side $$15 \text{ cm}$$ being moved towards right at a constant speed of $$2 \text{ cm/s}$$ as shown in figure. The front edge enters the $$50 \text{ cm}$$ wide magnetic field at $$t = 0$$. The value of induced emf in the loop at $$t = 10 \text{ s}$$ will be :
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The magnetic field in a plane electromagnetic wave is $$B_y = (3.5 \times 10^{-7}) \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ T}$$. The corresponding electric field will be :
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The following figure represents two biconvex lenses $$L_1$$ and $$L_2$$ having focal length $$10 \text{ cm}$$ and $$15 \text{ cm}$$ respectively. The distance between $$L_1$$ & $$L_2$$ is
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UV light of $$4.13 \text{ eV}$$ is incident on a photosensitive metal surface having work function $$3.13 \text{ eV}$$. The maximum kinetic energy of ejected photoelectrons will be:
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A hydrogen atom in ground state is given an energy of $$10.2 \text{ eV}$$. How many spectral lines will be emitted due to transition of electrons?
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A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2 : 1$$. After disintegration they will move :
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The energy released in the fusion of $$2 \text{ kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released in the fission of $$2 \text{ kg}$$ of $$^{235}U$$ is $$E_U$$. The ratio $$\frac{E_H}{E_U}$$ is approximately: (Consider the fusion reaction as $$4 \mid H + 2e^- \to {}^4_2He + 2\nu + 6\gamma + 26.7 \text{ MeV}$$, energy released in the fission reaction of $$^{235}U$$ is $$200 \text{ MeV}$$ per fission nucleus and $$N_A = 6.023 \times 10^{23}$$)
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The $$I - V$$ characteristics of an electronic device shown in the figure. The device is:
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In the truth table of the above circuit the value of $$X$$ and $$Y$$ are :
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The resultant of two vectors $$\vec{A}$$ and $$\vec{B}$$ is perpendicular to $$\vec{A}$$ and its magnitude is half that of $$\vec{B}$$. The angle between vectors $$\vec{A}$$ and $$\vec{B}$$ is ______ °.
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A force $$(3x^2 + 2x - 5) \text{ N}$$ displaces a body from $$x = 2 \text{ m}$$ to $$x = 4 \text{ m}$$. Work done by this force is ______ J.
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A circular disc reaches from top to bottom of an inclined plane of length $$l$$. When it slips down the plane, it takes $$t$$ s. When it rolls down the plane then it takes $$\left(\frac{\alpha}{2}\right)^{1/2} t$$ s, where $$\alpha$$ is ______
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At room temperature $$(27°C)$$, the resistance of a heating element is $$50\Omega$$. The temperature coefficient of the material is $$2.4 \times 10^{-4} \text{ °C}^{-1}$$. The temperature of the element, when its resistance is $$62\Omega$$, is ______ °C.
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A particle of mass $$0.50 \text{ kg}$$ executes simple harmonic motion under force $$F = -50 \text{ (Nm}^{-1}\text{)}x$$. The time period of oscillation is $$\frac{\pi}{x}$$ s. The value of $$x$$ is ______ (Given $$\pi = \frac{22}{7}$$)
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An electric field $$\vec{E} = (2x\hat{i}) \text{ NC}^{-1}$$ exists in space. A cube of side $$2 \text{ m}$$ is placed in the space as per figure given below.
The electric flux through the cube is ______ $$\text{Nm}^2/\text{C}$$.
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To determine the resistance $$(R)$$ of a wire, a circuit is designed below. The $$V - I$$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $$R$$ is ______ $$\Omega$$.
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A straight magnetic strip has a magnetic moment of $$44 \text{ Am}^2$$. If the strip is bent in a semicircular shape, its magnetic moment will be ______ $$\text{Am}^2$$. (given $$\pi = \frac{22}{7}$$)
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A capacitor of reactance $$4\sqrt{3} \Omega$$ and a resistor of resistance $$4\Omega$$ are connected in series with an ac source of peak value $$8\sqrt{2} \text{ V}$$. The power dissipation in the circuit is ______ W.
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Monochromatic light of wavelength $$500 \text{ nm}$$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $$= 1.5$$), the central maximum is shifted to a position previously occupied by the $$4^{th}$$ bright fringe. The thickness of the glass-plate is ______ $$\mu m$$.
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