If $$R$$, $$X_L$$ and $$X_C$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
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If $$R$$, $$X_L$$ and $$X_C$$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
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The initial speed of a projectile fired from ground is $$u$$. At the highest point during its motion, the speed of projectile is $$\dfrac{\sqrt{3}}{2}u$$. The time of flight of the projectile is:
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As shown in figure, a 70 kg garden roller is pushed with a force of $$\vec{F} = 200$$ N at an angle of 30° with horizontal. The normal reaction on the roller is (Given $$g = 10$$ m s$$^{-2}$$)
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100 balls each of mass $$m$$ moving with speed $$v$$ simultaneously strike a wall normally and reflected back with same speed, in time $$t$$ s. The total force exerted by the balls on the wall is
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At a certain depth $$d$$ below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $$3R$$ above earth surface. Where $$R$$ is Radius of earth (Take $$R = 6400$$ km). The depth $$d$$ is equal to
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Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}
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If 1000 droplets of water of surface tension 0.07 N m$$^{-1}$$, having same radius 1 mm each, combine to form a single drop. In the process the released surface energy is- (Take $$\pi = \dfrac{22}{7}$$)
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The pressure of a gas changes linearly with volume from $$A$$ to $$B$$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be
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The correct relation between $$\gamma = \dfrac{C_P}{C_V}$$ and temperature $$T$$ is:
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The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At $$\dfrac{A}{2}$$, the kinetic energy of the block is
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Which of the following correctly represents the variation of electric potential $$(V)$$ of a charged spherical conductor of radius $$(R)$$ with radial distance $$(r)$$ from the centre?
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The drift velocity of electrons for a conductor connected in an electrical circuit is $$V_d$$. The conductor is now replaced by another conductor with same material and same length but double the area of cross-section. The applied voltage remains same. The new drift velocity of electrons will be
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A bar magnet with a magnetic moment 5.0 A m$$^2$$ is placed in parallel position relative to a magnetic field of 0.4 T. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is ________.
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A rod with circular cross-section area 2 cm$$^2$$ and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside the windings is $$4\pi \times 10^{-6}$$ Wb. The relative permeability of the rod is
(Given: Permeability of vacuum $$\mu_0 = 4\pi \times 10^{-7}$$ N A$$^{-2}$$)
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Two polaroids $$A$$ and $$B$$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $$C$$ is placed between $$A$$ and $$B$$ bisecting angle between them. If intensity of unpolarised light is $$I_0$$ then intensity of transmitted light after passing through polaroid $$B$$ will be:
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Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The beam of electrons shows wave nature and exhibit interference and diffraction.
Reason R: Davisson Germer Experimentally verified the wave nature of electrons.
In the light of the above statements. Choose the most appropriate answer from the options given below:
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If a source of electromagnetic radiation having power 15 kW produces $$10^{16}$$ photons per second, the radiation belongs to a part of spectrum is:
(Take Planck constant $$h = 6 \times 10^{-34}$$ J s)
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A free neutron decays into a proton but a free proton does not decay into neutron. This is because
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The effect of increase in temperature on the number of electrons in conduction band $$(n_e)$$ and resistance of a semiconductor will be as:
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The amplitude of 15sin(1000$$\pi t$$) is modulated by 10sin(4$$\pi t$$) signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz
(B) 2 Hz
(C) 250 Hz
(D) 498 Hz
(E) 502 Hz
Choose the correct answer from the options given below:
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The speed of a swimmer is 4 km h$$^{-1}$$ in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km, he reaches a point 750 m down the stream on the opposite bank. The speed of the river water is ______ km h$$^{-1}$$.
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A lift of mass $$M = 500$$ kg is descending with speed of 2 m s$$^{-1}$$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2 m s$$^{-2}$$. The kinetic energy of the lift at the end of fall through to a distance of 6 m will be ______ kJ.
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A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10^{-3}$$ J. The speed of the centre of mass of the sphere is ______ cm s$$^{-1}$$.
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A thin rod having a length of 1 m and area of cross-section $$3 \times 10^{-6}$$ m$$^2$$ is suspended vertically from one end. The rod is cooled from 210°C to 160°C. After cooling, a mass $$M$$ is attached at the lower end of the rod such that the length of rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are $$2 \times 10^{11}$$ N m$$^{-2}$$ and $$2 \times 10^{-5}$$ K$$^{-1}$$, respectively. The value of $$M$$ is ______ kg. (Take $$g = 10$$ m s$$^{-2}$$)
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In the figure given below, a block of mass $$M = 490$$ g placed on a frictionless table is connected with two springs having same spring constant ($$K = 2$$ N m$$^{-1}$$). If the block is horizontally displaced through $$X$$ m then the number of complete oscillations it will make in $$14\pi$$ seconds will be ______.
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Expression for an electric field is given by $$\vec{E} = 4000 \; x^2 \; \hat{i}$$ V m$$^{-1}$$. The electric flux through the cube of side 20 cm when placed in electric field (as shown in the figure) is ______ V cm.
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Two identical cells, when connected either in parallel or in series gives same current in an external resistance 5 $$\Omega$$. The internal resistance of each cell will be ______ $$\Omega$$.
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An inductor of 0.5 mH, a capacitor of 20 $$\mu$$F and resistance of 20 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $$\sqrt{x}$$ A. The value of $$x$$ is-
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In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $$x$$:1. The value of $$x$$ is ______.
(Given speed of light in free space $$= 3 \times 10^8$$ m s$$^{-1}$$ and for the given medium $$\mu_r = 1$$)
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For hydrogen atom, $$\lambda_1$$ and $$\lambda_2$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $$\lambda_1$$ and $$\lambda_2$$ is $$\dfrac{x}{32}$$. The value of $$x$$ is ______.
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