The angle between vector $$\vec{Q}$$ and the resultant of $$(2\vec{Q} + 2\vec{P})$$ and $$(2\vec{Q} - 2\vec{P})$$ is :
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The angle between vector $$\vec{Q}$$ and the resultant of $$(2\vec{Q} + 2\vec{P})$$ and $$(2\vec{Q} - 2\vec{P})$$ is :
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Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $$4.62 \text{ s}, 4.632 \text{ s}, 4.6 \text{ s}$$ and $$4.64 \text{ s}$$. The arithmetic mean of these readings in correct significant figure is :
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If $$G$$ be the gravitational constant and $$u$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{uG}$$ :
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A wooden block of mass $$5 \text{ kg}$$ rests on a soft horizontal floor. When an iron cylinder of mass $$25 \text{ kg}$$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $$0.1 \text{ ms}^{-2}$$. The action force of the system on the floor is equal to:
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A body of mass $$50 \text{ kg}$$ is lifted to a height of $$20 \text{ m}$$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :
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Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $$\sqrt{8/x}$$. The value of $$x$$ is :
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A simple pendulum doing small oscillations at a place R height above earth surface has time period of $$T_1 = 4 \text{ s}$$. $$T_2$$ would be its time period if it is brought to a point which is at a height $$2R$$ from earth surface. Choose the correct relation $$[R = \text{radius of earth}]$$ :
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In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :
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Match List I with List II :
(Where $$a$$ = radius of planet orbit, $$r$$ = radius of planet, $$M$$ = mass of Sun, $$m$$ = mass of planet)
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Given below are two statements :
Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $$0°$$.
Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
In the light of the above statement, choose the correct answer from the options given below.
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The heat absorbed by a system in going through the given cyclic process is :
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If the collision frequency of hydrogen molecules in a closed chamber at $$27°C$$ is $$Z$$, then the collision frequency of the same system at $$127°C$$ is :
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In the given figure $$R_1 = 10\Omega, R_2 = 8\Omega, R_3 = 4\Omega$$ and $$R_4 = 8\Omega$$. Battery is ideal with emf $$12 \text{ V}$$. Equivalent resistance of the circuit and current supplied by battery are respectively :
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In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :
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Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in figure. The mutual inductance between them is :
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An alternating voltage of amplitude $$40 \text{ V}$$ and frequency $$4 \text{ kHz}$$ is applied directly across the capacitor of $$12\mu\text{F}$$. The maximum displacement current between the plates of the capacitor is nearly :
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Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :
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Given below are two statements :
Statement I :
Figure shows the variation of stopping potential $$(V_0)$$ with frequency $$(\nu)$$ for the two photosensitive materials $$M_1$$ and $$M_2$$. The slope gives value of $$\frac{h}{e}$$, where $$h$$ is Planck's constant, $$e$$ is the charge of electron.
Statement II : $$M_2$$ will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency.
In the light of the above statements, choose the most appropriate answer from the options given below.
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An electron rotates in a circle around a nucleus having positive charge $$Ze$$. Correct relation between total energy $$(E)$$ of electron to its potential energy $$(U)$$ is :
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Following gates section is connected in a complete suitable circuit.
For which of the following combination, bulb will glow (ON) :
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A body moves on a frictionless plane starting from rest. If $$S_n$$ is distance moved between $$t = n - 1$$ and $$t = n$$ and $$S_{n-1}$$ is distance moved between $$t = n - 2$$ and $$t = n - 1$$, then the ratio $$\frac{S_{n-1}}{S_n}$$ is $$\left(1 - \frac{2}{x}\right)$$ for $$n = 10$$. The value of $$x$$ is ______.
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Three blocks $$M_1, M_2, M_3$$ having masses $$4 \text{ kg}, 6 \text{ kg}$$ and $$10 \text{ kg}$$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $$T_1$$ when they are moving upward with acceleration of $$2 \text{ ms}^{-2}$$ is ______ N (if $$g = 10 \text{ m/s}^2$$).
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The density and breaking stress of a wire are $$6 \times 10^4 \text{ kg/m}^3$$ and $$1.2 \times 10^8 \text{ N/m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{rd}$$ of the value on the surface of earth. The maximum length of the wire with breaking is ______ m (take, $$g = 10 \text{ m/s}^2$$).
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Three capacitors of capacitances $$25\mu\text{F}, 30\mu\text{F}$$ and $$45\mu\text{F}$$ are connected in parallel to a supply of $$100 \text{ V}$$. Energy stored in the above combination is $$E$$. When these capacitors are connected in series to the same supply, the stored energy is $$\frac{9}{x}E$$. The value of $$x$$ is ______.
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The electric field between the two parallel plates of a capacitor of capacitance $$1.5\mu\text{F}$$ drops to one third of its initial value in $$6.6\mu s$$ when the plates are connected by a thin wire. The resistance of this wire is ______ $$\Omega$$. (Given, $$\log 3 = 1.1$$)
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In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $$1/\theta$$ vs the resistance $$(R)$$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is ______ $$\times 10^{-1} \text{ A/division}$$. [The source has emf 2V]
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A $$2 \text{ A}$$ current carrying straight metal wire of resistance $$1\Omega$$, resistivity $$2 \times 10^{-6}\Omega\text{m}$$, area of cross-section $$10 \text{ mm}^2$$ and mass $$500 \text{ g}$$ is suspended horizontally in mid air by applying a uniform magnetic field $$\vec{B}$$. The magnitude of $$B$$ is ______ $$\times 10^{-1} \text{ T}$$ (given, $$g = 10 \text{ m/s}^2$$).
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An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $$20\mu\text{F}$$ is ______ V.
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In Young's double slit experiment, carried out with light of wavelength $$5000 \text{ \AA}$$, the distance between the slits is $$0.3 \text{ mm}$$ and the screen is at $$200 \text{ cm}$$ from the slits. The central maximum is at $$x = 0 \text{ cm}$$. The value of $$x$$ for third maxima is ______ mm.
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If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ______ $$\times 10^{-2} \text{ MeV}$$. (Given $$1\text{u} = 931 \text{ MeV/c}^2$$, atomic mass of helium $$= 4.002603 \text{ u}$$)
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