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Motion of a particle in $$x-y$$ plane is described by a set of following equations $$x = 4\sin\left(\frac{\pi}{2} - \omega t\right)$$ m and $$y = 4\sin(\omega t)$$ m. The path of the particle will be
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A particle of mass $$m$$ is moving in a circular path of constant radius $$r$$ such that its centripetal acceleration $$a_c$$ is varying with time $$t$$ as $$a_c = k^2rt^2$$, where $$k$$ is a constant. The power delivered to the particle by the force acting on it is
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Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) M.I. of solid sphere of radius R about any tangent. | (I) $$\frac{5}{3}MR^2$$ |
| (B) M.I. of hollow sphere of radius R about any tangent. | (II) $$\frac{7}{5}MR^2$$ |
| (C) M.I. of circular ring of radius R about its diameter. | (III) $$\frac{1}{4}MR^2$$ |
| (D) M.I. of circular disc of radius R about any diameter. | (IV) $$\frac{1}{2}MR^2$$ |
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Two planets $$A$$ and $$B$$ of equal mass are having their period of revolutions $$T_A$$ and $$T_B$$ such that $$T_A = 2T_B$$. These planets are revolving in the circular orbits of radii $$r_A$$ and $$r_B$$ respectively. Which out of the following would be the correct relationship of their orbits?
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A water drop of diameter $$2$$ cm is broken into $$64$$ equal droplets. The surface tension of water is $$0.075$$ N m$$^{-1}$$. In this process the gain in surface energy will be
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A radar sends an electromagnetic signal of electric field $$(E_0) = 2.25$$ V m$$^{-1}$$ and magnetic field $$(B_0) = 1.5 \times 10^{-8}$$ T which strikes a target on line of sight at a distance of $$3$$ km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time $$t = 0$$ from radar, then after how much time echo will reach to the radar?
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The velocity of sound in a gas, in which two wavelengths $$4.08$$ m and $$4.16$$ m produce $$40$$ beats in $$12$$ s, will be
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Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero.
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The three charges $$\frac{q}{2}, q$$ and $$\frac{q}{2}$$ are placed at the corners $$A, D$$ and $$C$$ of a square of side $$a$$ as shown in figure. The magnitude of electric field ($$E$$) at the corner $$B$$ of the square, is
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An infinitely long hollow conducting cylinder with radius $$R$$ carries a uniform current along its surface. Choose the correct representation of magnetic field $$(B)$$ as a function of radial distance $$(r)$$ from the axis of cylinder.
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The refracting angle of a prism is $$A$$ and refractive index of the material of the prism is $$\cot\left(\frac{A}{2}\right)$$. Then the angle of minimum deviation will be
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The aperture of the objective is $$24.4$$ cm. The resolving power of this telescope, if a light of wavelength $$2440$$ Å is used to see the object will be
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The de Broglie wavelengths for an electron and a photon are $$\lambda_e$$ and $$\lambda_p$$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?
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The $$Q$$-value of a nuclear reaction and kinetic energy of the projectile particle, $$K_p$$ are related as
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In the following circuit, the correct relation between output ($$Y$$) and inputs $$A$$ and $$B$$ will be
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For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode
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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 : $$n - p - n$$ transistor permits more current than a $$p - n - p$$ transistor.
Reason R : Electrons have greater mobility as a charge carrier.
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Match List-I with List-II
| List-I | List-II |
|---|---|
| (A) Television signal | (I) 03 KHz |
| (B) Radio signal | (II) 20 KHz |
| (C) High Quality Music | (III) 02 MHz |
| (D) Human speech | (IV) 06 MHz |
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A hanging mass $$M$$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $$2Mg$$ force. In this situation, tension in the string is $$\frac{x}{5}Mg$$ for $$x =$$ ______. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
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A pendulum is suspended by a string of length $$250$$ cm. The mass of the bob of the pendulum is $$200$$ g. The bob is pulled aside until the string is at $$60°$$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ______ m s$$^{-1}$$. (if $$g = 10$$ m s$$^{-2}$$)
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A man of $$60$$ kg is running on the road and suddenly jumps into a stationary trolly car of mass $$120$$ kg. Then the trolly car starts moving with velocity $$2$$ m s$$^{-1}$$. The velocity of the running man was ______ m s$$^{-1}$$, when he jumps into the car.
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The position vector of $$1$$ kg object is $$\vec{r} = (3\hat{i} - \hat{j})$$ m and its velocity $$\vec{v} = (3\hat{j} + \hat{k})$$ m s$$^{-1}$$. The magnitude of its angular momentum is $$\sqrt{x}$$ N m s, where $$x$$ is ______
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The total internal energy of two mole monoatomic ideal gas at temperature $$T = 300$$ K will be ______ J. (Given $$R = 8.31$$ J mol$$^{-1}$$ K$$^{-1}$$)
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A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $$R$$ using a given resistor of $$15$$ $$\Omega$$. The galvanometer $$(G)$$ shows null deflection when tapping key is at $$43$$ cm mark from end $$A$$. If the end correction for end $$A$$ is $$2$$ cm, then the determined value of $$R$$ will be ______ $$\Omega$$.
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Current measured by the ammeter $$(A)$$ in the reported circuit when no current flows through $$10\Omega$$ resistance, will be ______ A.
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A singly ionized magnesium atom $$(A = 24)$$ ion is accelerated to kinetic energy $$5$$ keV, and is projected perpendicularly into a magnetic field $$B$$ of the magnitude $$0.5$$ T. The radius of path formed will be ______ cm.
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An AC source is connected to an inductance of $$100$$ mH, a capacitance of $$100$$ $$\mu$$F and a resistance of $$120$$ $$\Omega$$ as shown in figure. The time in which the resistance having a thermal capacity $$2$$ J °C$$^{-1}$$ will get heated by $$16°$$C is ______ s.
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A telegraph line of length $$100$$ km has a capacity of $$0.01$$ $$\mu$$F km$$^{-1}$$ and it carries an alternating current at $$0.5$$ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ______ mH. (If $$\pi = \sqrt{10}$$)
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