The dimension of mutual inductance is
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The dimension of mutual inductance is
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In the arrangement shown in figure $$a_1, a_2, a_3$$ and $$a_4$$ are the accelerations of masses $$m_1, m_2, m_3$$ and $$m_4$$ respectively. Which of the following relation is true for this arrangement?
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Arrange the four graphs in descending order of total work done; where $$W_1, W_2, W_3$$ and $$W_4$$ are the work done corresponding to figure a, b, c and d respectively.
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A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is
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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: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below
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If $$p$$ is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed $$v$$ in the pipe of diameter $$d$$, the correct formula for Reynolds number $$R_e$$ is
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A flask contains argon and oxygen in the ratio of $$3 : 2$$ in mass and the mixture is kept at $$27°$$C. The ratio of their average kinetic energy per molecule respectively
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For a specific wavelength $$670$$ nm of light coming from a galaxy moving with velocity $$v$$, the observed wavelength is $$670.7$$ nm. The value of $$v$$ is
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Sixty four conducting drops each of radius $$0.02$$ m and each carrying a charge of $$5$$ $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be
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The charge on capacitor of capacitance $$15\mu$$F in the figure given below is
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A parallel plate capacitor with plate area $$A$$ and plate separation $$d = 2$$ m has a capacitance of $$4$$ $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $$K = 3$$ (as shown in figure) will be
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Find the equivalent resistance between point A and B
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A bar magnet having a magnetic moment of $$2.0 \times 10^5$$ J T$$^{-1}$$, is placed along the direction of uniform magnetic field of magnitude $$B = 14 \times 10^{-5}$$ T. The work done in rotating the magnet slowly through $$60°$$ from the direction of field is
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A metal surface is illuminated by a radiation of wavelength $$4500$$ Å. The ejected photo-electron enters a constant magnetic field of $$2$$ mT making an angle of $$90°$$ with the magnetic field. If it starts revolving in a circular path of radius $$2$$ mm, the work function of the metal is approximately
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Two coils of self inductance $$L_1$$ and $$L_2$$ are connected in series combination having mutual inductance of the coils as $$M$$. The equivalent self inductance of the combination will be
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A metallic conductor of length $$1$$ m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity $$5$$ rad s$$^{-1}$$. If the horizontal component of earth's magnetic field is $$0.2 \times 10^{-4}$$ T, then emf induced between the two ends of the conductor is
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Which is the correct ascending order of wavelengths?
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A radioactive nucleus can decay by two different processes. Half-life for the first process is $$3.0$$ hours while it is $$4.5$$ hours for the second process. The effective halflife of the nucleus will be
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The positive feedback is required by an amplifier to act as an oscillator. The feedback here means
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A sinusoidal wave $$y(t) = 40\sin(10 \times 10^6 \pi t)$$ is amplitude modulated by another sinusoidal wave $$x(t) = 20\sin(1000\pi t)$$. The amplitude of minimum frequency component of modulated signal is
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A ball is projected vertically upward with an initial velocity of $$50$$ m s$$^{-1}$$ at $$t = 0$$ s. At $$t = 2$$ s, another ball is projected vertically upward with same velocity. At $$t =$$ ______ s, second ball will meet the first ball.
$$(g = 10$$ m s$$^{-2})$$
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A system to 10 balls each of mass $$2$$ kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $$7^{th}$$ and $$8^{th}$$ ball is ______ N when $$6^{th}$$ ball just leaves the table.
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A batsman hits back a ball of mass $$0.4$$ kg straight in the direction of the bowler without changing its initial speed of $$15$$ m s$$^{-1}$$. The impulse imparted to the ball is ______ N s.
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A geyser heats water flowing at a rate of $$2.0$$ kg per minute from $$30°$$C to $$70°$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$$^{-1}$$.
[Heat of combustion $$= 8 \times 10^3$$ J g$$^{-1}$$, Specific heat of water $$= 4.2$$ J g$$^{-1}$$ °C$$^{-1}$$]
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A heat engine operates with the cold reservoir at temperature $$324$$ K. The minimum temperature of the hot reservoir, if the heat engine takes $$300$$ J heat from the hot reservoir and delivers $$180$$ J heat to the cold reservoir per cycle, is ______ K.
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A set of $$20$$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $$4$$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.
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Two $$10$$ cm long, straight wires, each carrying a current of $$5$$ A are kept parallel to each other. If each wire experienced a force of $$10^{-5}$$ N, then separation between the wires is ______ cm.
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A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt{7}$$ m. The refractive index of water is $$\frac{4}{3}$$. The area of the surface of water through which light from the bulb can emerge out is $$x\pi$$ m$$^2$$. The value of $$x$$ is ______
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The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $$6630$$ Å is $$0.42$$ V. If the threshold frequency is $$x \times 10^{13}$$ s, where $$x$$ is (nearest integer): (Given, speed light $$= 3 \times 10^8$$ m s$$^{-1}$$, Planck's constant $$= 6.63 \times 10^{-34}$$ J s)
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A travelling microscope is used to determine the refractive index of a glass slab. If $$40$$ divisions are there in $$1$$ cm on main scale and $$50$$ Vernier scale divisions are equal to $$49$$ main scale divisions, then least count of the travelling microscope is ______ $$\times 10^{-6}$$ m.
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