If mass is written as $$m = kc^{P}G^{-1/2}h^{1/2}$$, then the value of $$P$$ will be : (Constants have their usual meaning with $$k$$ a dimensionless constant)
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If mass is written as $$m = kc^{P}G^{-1/2}h^{1/2}$$, then the value of $$P$$ will be : (Constants have their usual meaning with $$k$$ a dimensionless constant)
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Projectiles $$A$$ and $$B$$ are thrown at angles of $$45°$$ and $$60°$$ with vertical respectively from top of a 400 m high tower. If their times of flight are same, the ratio of their speeds of projection $$v_A : v_B$$ is:
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Three blocks $$A$$, $$B$$ and $$C$$ are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tensions $$T_1$$ and $$T_2$$ in the string are respectively:
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A block of mass $$m$$ is placed on a surface having vertical cross section given by $$y = \frac{x^2}{4}$$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:
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A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $$60°$$ by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is : $$g = 10$$ m s$$^{-2}$$
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Escape velocity of a body from earth is 11.2 km s$$^{-1}$$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is:
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A block of ice at $$-10°C$$ is slowly heated and converted to steam at $$100°C$$. Which of the following curves represent the phenomenon qualitatively:
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Choose the correct statement for processes $$A$$ & $$B$$ shown in figure.
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If three moles of monoatomic gas $$\left(\gamma = \frac{5}{3}\right)$$ is mixed with two moles of a diatomic gas $$\left(\gamma = \frac{7}{5}\right)$$, the value of adiabatic exponent $$\gamma$$ for the mixture is:
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A particle of charge $$-q$$ and mass $$m$$ moves in a circle of radius $$r$$ around an infinitely long line charge of linear density $$+\lambda$$. Then time period will be given as: (Consider $$k$$ as Coulomb's constant)
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When a potential difference $$V$$ is applied across a wire of resistance $$R$$, it dissipates energy at a rate $$W$$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:
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An alternating voltage $$V(t) = 220\sin 100\pi t$$ volt is applied to a purely resistive load of $$50 \Omega$$. The time taken for the current to rise from half of the peak value to the peak value is:
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Match List I with List II
Choose the correct answer from the options given below:
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A beam of unpolarised light of intensity $$I_0$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $$45°$$ relative to that of $$A$$. The intensity of emergent light is:
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If the total energy transferred to a surface in time $$t$$ is $$6.48 \times 10^5$$ J, then the magnitude of the total momentum delivered to this surface for complete absorption will be:
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For the photoelectric effect, the maximum kinetic energy $$E_k$$ of the photoelectrons is plotted against the frequency $$(\nu)$$ of the incident photons as shown in figure. The slope of the graph give
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An electron revolving in $$n^{th}$$ Bohr orbit has magnetic moment $$\mu_n$$. If $$\mu_n \propto n^x$$, the value of $$x$$ is:
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In a nuclear fission reaction of an isotope of mass $$M$$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $$\Delta M$$ will be:
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In the given circuit, the voltage across load resistance $$(R_L)$$ is:
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If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:
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A vector has magnitude same as that of $$\vec{A} = 3\hat{i} + 4\hat{j}$$ and is parallel to $$\vec{B} = 4\hat{i} + 3\hat{j}$$. The $$x$$ and $$y$$ components of this vector in first quadrant are $$x$$ and 3 respectively where $$x$$ = ____.
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Two discs of moment of inertia $$I_1 = 4$$ kg m$$^2$$ and $$I_2 = 2$$ kg m$$^2$$ about their central axes & normal to their planes, rotating with angular speeds 10 rad s$$^{-1}$$ & 4 rad s$$^{-1}$$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is _________ J.
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A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, the $$E_1 : E_2$$ is $$x : 1$$, where $$x$$ = ________.
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A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be _________ s. [take $$g = \pi^2$$ m s$$^{-2}$$]
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A point source is emitting sound waves of intensity $$16 \times 10^{-8}$$ W m$$^{-2}$$ at the origin. The difference in intensity (magnitude only) at two points located at distances of 2 m and 4 m from the origin respectively will be ________ $$\times 10^{-8}$$ W m$$^{-2}$$.
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Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of $$37°$$ with each other. When suspended in a liquid of density $$0.7$$ g cm$$^{-3}$$, the angle remains same. If density of material of the sphere is $$1.4$$ g cm$$^{-3}$$, the dielectric constant of the liquid is _____ ($$\tan 37° = \frac{3}{4}$$)
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Two resistance of $$100\Omega$$ and $$200\Omega$$ are connected in series with a battery of 4 V and negligible internal resistance. A voltmeter is used to measure voltage across $$100\Omega$$ resistance, which gives reading as 1 V. The resistance of voltmeter must be _______ $$\Omega$$.
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The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is $$X\sqrt{2} \times 10^{-7}$$ T. The value of X is _________.
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A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A and its efficiency is 90%. The winding of transformer is made of copper. The output current of transformer is ____ A.
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In an experiment to measure the focal length $$(f)$$ of a convex lens, the magnitude of object distance $$(x)$$ and the image distance $$(y)$$ are measured with reference to the focal point of the lens. The $$y - x$$ plot is shown in figure. The focal length of the lens is ____ cm.
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