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A particle moves in $$x - y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\vec{p}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$$. If $$k$$ is constant, the angle between $$\vec{F}$$ and $$\vec{p}$$ will be :
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What is the dimensional formula of $$ab^{-1}$$ in the equation $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$, where letters have their usual meaning.
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A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $$9$$ m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$m/s^2$$) :
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A heavy box of mass $$50$$ kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :
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A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $$t$$ is proportional to :
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A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given = Radius of geo-stationary orbit for earth is $$4.2 \times 10^4$$ km)
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Match List-I with List-II :
Choose the correct answer from the options given below :
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During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $$\frac{C_P}{C_V}$$ for the gas is :
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If $$n$$ is the number density and $$d$$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :
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The vehicles carrying inflammable fluids usually have metallic chains touching the ground :
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A galvanometer of resistance $$100\Omega$$ when connected in series with $$400\Omega$$ measures a voltage of upto $$10$$ V. The value of resistance required to convert the galvanometer into ammeter to read upto $$10$$ A is $$x \times 10^{-2} \Omega$$. The value of $$x$$ is :
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The ratio of heat dissipated per second through the resistors $$5\Omega$$ and $$10\Omega$$ in the circuit given below is
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The electrostatic force $$(\vec{F_1})$$ and magnetic force $$(\vec{F_2})$$ acting on a charge $$q$$ moving with velocity $$v$$ can be written :
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A series LCR circuit is subjected to an ac signal of $$200$$ V, $$50$$ Hz. If the voltage across the inductor $$(L = 10 \text{ mH})$$ is $$31.4$$ V, then the current in this circuit is :
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Match List-I with List-II :
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Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, choose the correct answer from the options given below :
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Which of the following statement is not true about stopping potential $$(V_0)$$ ?
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The angular momentum of an electron in a hydrogen atom is proportional to : (Where $$r$$ is the radius of orbit of electron)
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The output $$(Y)$$ of logic circuit given below is 0 only when
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A vernier callipers has 20 divisions on the vernier scale, which coincides with $$19^{th}$$ division on the main scale. The least count of the instrument is $$0.1$$ mm. One main scale division is equal to ______ mm.
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The maximum height reached by a projectile is $$64$$ m. If the initial velocity is halved, the new maximum height of the projectile is ______ m.
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A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $$\frac{x}{5}$$. The value of $$x$$ is ______.
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A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $$10$$ N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ______ N.
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A sonometer wire of resonating length $$90$$ cm has a fundamental frequency of $$400$$ Hz when kept under some tension. The resonating length of the wire with fundamental frequency of $$600$$ Hz under same tension ______ cm.
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The electric field at point $$p$$ due to an electric dipole is $$E$$. The electric field at point $$R$$ on equitorial line will be $$\frac{E}{x}$$. The value of $$x$$
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A wire of resistance $$20\Omega$$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ______ $$\Omega$$.
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A solenoid of length $$0.5$$ m has a radius of $$1$$ cm and is made up of '$$m$$' number of turns. It carries a current of $$5$$ A. If the magnitude of the magnetic field inside the solenoid is $$6.28 \times 10^{-3}$$ T then the value of $$m$$ is ______.
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The current in an inductor is given by $$I = (3t + 8)$$ where $$t$$ is in second. The magnitude of induced emf produced in the inductor is $$12$$ mV. The self-inductance of the inductor ______ mH.
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In a single slit experiment, a parallel beam of green light of wavelength $$550$$ nm passes through a slit of width $$0.20$$ mm. The transmitted light is collected on a screen $$100$$ cm away. The distance of first order minima from the central maximum will be $$x \times 10^{-5}$$ m. The value of $$x$$ is :
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The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $$915$$ Å. The longest wavelength of spectral lines in the Balmer series will be ______ Å.
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