The dimensional formula of latent heat is :
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The dimensional formula of latent heat is :
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A particle moving in a straight line covers half the distance with speed $$6$$ m/s. The other half is covered in two equal time intervals with speeds $$9$$ m/s and $$15$$ m/s respectively. The average speed of the particle during the motion is :
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A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :
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A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $$v = \alpha\sqrt{x}$$, where $$\alpha$$ is a constant. The total work done by all the forces applied on the particle during its displacement from $$x = 0$$ to $$x = d$$, will be :
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A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :
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An astronaut takes a ball of mass $$m$$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $$318.5$$ km. From earth's surface to the orbit, the change in total mechanical energy of the ball is $$x\frac{GM_e m}{21R_e}$$. The value of $$x$$ is (take $$R_e = 6370$$ km) :
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A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac{D}{d}$$, if it just floats on water in a tank is :
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A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is $$\gamma = \frac{3}{2}$$, then the work done by the gas in the process is:
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The volume of an ideal gas $$(\gamma = 1.5)$$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is:
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A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:
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A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $$\frac{A}{3}$$ and the height is $$d$$, the capacitance of the arrangement is
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A galvanometer has a coil of resistance $$200\Omega$$ with a full scale deflection at $$20\mu A$$. The value of resistance to be added to use it as an ammeter of range $$(0 - 20)$$ mA is :
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The equivalent resistance between A and B is :
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Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :
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A plane EM wave is propagating along $$x$$ direction. It has a wavelength of $$4$$ mm. If electric field is in $$y$$ direction with the maximum magnitude of $$60$$ Vm$$^{-1}$$, the equation for magnetic field is :
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Given below are two statements :
Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.
Statement (II) : Concave lens always forms a virtual and erect image.
In the light of the above statements, choose the correct answer from the options given below :
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A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :
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The energy equivalent of $$1$$ g of substance is :
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A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $$1.42$$ eV. The wavelength of light emitted from the LED is :
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One main scale division of a vernier caliper is equal to $$m$$ units. If $$n^{th}$$ division of main scale coincides with $$(n+1)^{th}$$ division of vernier scale, the least count of the vernier caliper is :
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If $$\vec{a}$$ and $$\vec{b}$$ makes an angle $$\cos^{-1}\left(\frac{5}{9}\right)$$ with each other, then for $$|\vec{a} + \vec{b}| = \sqrt{2}|\vec{a} - \vec{b}|$$, $$|\vec{a}| = n|\vec{b}|$$. The integer value of $$n$$ is ____
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A string is wrapped around the rim of a wheel of moment of inertia $$0.40$$ kg m$$^2$$ and radius $$10$$ cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $$40$$ N. The angular velocity of the wheel after $$10$$ s is $$x$$ rad/s, where $$x$$ is _______
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Two persons pull a wire towards themselves. Each person exerts a force of $$200$$ N on the wire. Young's modulus of the material of wire is $$1 \times 10^{11}$$ N m$$^{-2}$$. Original length of the wire is $$2$$ m and the area of cross section is $$2$$ cm$$^2$$. The wire will extend in length by ______ $$\mu$$m.
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The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $$4$$ m, $$2$$ ms$$^{-1}$$ and $$16$$ ms$$^{-2}$$ at a certain instant. The amplitude of the motion is $$\sqrt{x}$$ m, where $$x$$ is ________
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At the centre of a half ring of radius $$R = 10$$ cm and linear charge density $$4$$ nCm$$^{-1}$$, the potential is $$x\pi$$ V. The value of $$x$$ is _______
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The current flowing through the $$1\Omega$$ resistor is $$\frac{n}{10}$$ A. The value of $$n$$ is ________
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A square loop of edge length $$2$$ m carrying current of $$2$$ A is placed with its edges parallel to the $$x$$-$$y$$ axis. A magnetic field is passing through the $$x - y$$ plane and expressed as $$\vec{B} = B_0(1 + 4x)\hat{k}$$, where $$B_0 = 5$$ T. The net magnetic force experienced by the loop is _______ N.
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When a coil is connected across a $$20$$ V dc supply, it draws a current of $$5$$ A. When it is connected across $$20$$ V, $$50$$ Hz ac supply, it draws a current of $$4$$ A. The self inductance of the coil is ______ mH. (Take $$\pi = 3$$)
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In a Young's double slit experiment, the intensity at a point is $$\left(\frac{1}{4}\right)^{th}$$ of the maximum intensity, the minimum distance of the point from the central maximum is _______ $$\mu$$m. (Given : $$\lambda = 600$$ nm, $$d = 1.0$$ mm, $$D = 1.0$$ m)
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A star has $$100\%$$ helium composition. It starts to convert three $$^4$$He into one $$^{12}$$C via triple alpha process as $$^4$$He $$+ ^4$$He $$+ ^4$$He $$\rightarrow ^{12}$$C $$+ Q$$. The mass of the star is $$2.0 \times 10^{32}$$ kg and it generates energy at the rate of $$5.808 \times 10^{30}$$ W. The rate of converting these $$^4$$He to $$^{12}$$C is $$n \times 10^{42}$$ s$$^{-1}$$, where n is ________ [Take, mass of $$^4$$He $$= 4.0026$$ u, mass of $$^{12}$$C $$= 12$$ u]
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