A person moved from $$A$$ to $$B$$ on a circular path as shown in figure. If the distance travelled by him is $$60 \text{ m}$$, then the magnitude of displacement would be: (Given $$\cos 135° = -0.7$$)
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A person moved from $$A$$ to $$B$$ on a circular path as shown in figure. If the distance travelled by him is $$60 \text{ m}$$, then the magnitude of displacement would be: (Given $$\cos 135° = -0.7$$)
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If momentum $$P$$, area $$A$$ and time $$T$$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is
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Which of the following physical quantities have the same dimensions?
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A body of mass $$0.5 \text{ kg}$$ travels on a straight line path with velocity $$v = (3x^2 + 4) \text{ m s}^{-1}$$. The net work done by the force during its displacement from $$x = 0$$ to $$x = 2 \text{ m}$$ is
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A solid cylinder and a solid sphere, having same mass $$M$$ and radius $$R$$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be
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Three identical particles $$A$$, $$B$$ and $$C$$ of mass $$100 \text{ kg}$$ each are placed in a straight line with $$AB = BC = 13 \text{ m}$$. The gravitational force on a fourth particle $$P$$ of the same mass is $$F$$, when placed at a distance $$13 \text{ m}$$ from the particle $$B$$ on the perpendicular bisector of the line $$AC$$. The value of $$F$$ will be approximately
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A certain amount of gas of volume $$V$$ at $$27°C$$ temperature and pressure $$2 \times 10^7 \text{ N m}^{-2}$$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $$\gamma = 1.5$$)
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Following statements are given:
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(3) The average kinetic energy of a gas molecule decreases with increase in volume.
(4) Pressure of a gas increases with increase in temperature at constant volume.
(5) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:
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In figure (A), mass $$2m$$ is fixed on mass $$m$$ which is attached to two springs of spring constant $$k$$. In figure (B), mass $$m$$ is attached to two springs of spring constant $$k$$ and $$2k$$. If mass $$m$$ in (A) and (B) are displaced by distance $$x$$ horizontally and then released, then time period $$T_1$$ and $$T_2$$ corresponding to (A) and (B) respectively follow the relation.
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A condenser of $$2 \mu F$$ capacitance is charged steadily from $$0$$ to $$5 \text{ C}$$. Which of the following graph represents correctly the variation of potential difference $$V$$ across its plates with respect to the charge $$Q$$ on the condenser?
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Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $$6:5$$ and their respective masses ratio is $$9:4$$. Then, the ratio of their charges will be
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The magnetic moment of an electron ($$e$$) revolving in an orbit around nucleus with an orbital angular momentum is given by
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A small square loop of wire of side $$l$$ is placed inside a large square loop of wire $$L$$ ($$L \gg l$$). Both loops are coplanar and their centres coincide at point $$O$$ as shown in figure. The mutual inductance of the system is
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To increase the resonant frequency in series LCR circuit,
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The RMS value of conduction current in a parallel plate capacitor is $$6.9 \mu A$$. The capacity of this capacitor, if it is connected to $$230 \text{ V}$$ AC supply with an angular frequency of $$600 \text{ rad s}^{-1}$$, will be
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Which of the following statement is correct?
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Time taken by light to travel in two different materials $$A$$ and $$B$$ of refractive indices $$\mu_A$$ and $$\mu_B$$ of same thickness is $$t_1$$ and $$t_2$$ respectively. If $$t_2 - t_1 = 5 \times 10^{-10} \text{ s}$$ and the ratio of $$\mu_A$$ to $$\mu_B$$ is $$1:2$$. Then the thickness of material, in meter is: (Given $$v_A$$ and $$v_B$$ are velocities of light in $$A$$ and $$B$$ materials respectively).
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A metal exposed to light of wavelength $$800 \text{ nm}$$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $$500 \text{ nm}$$ is used. The work function of the metal is (Take $$hc = 1230 \text{ eV nm}$$).
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The momentum of an electron revolving in $$n^{th}$$ orbit is given by: (Symbols have their usual meanings)
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In the circuit, the logical value of $$A = 1$$ or $$B = 1$$ when potential at $$A$$ or $$B$$ is $$5 \text{ V}$$ and the logical value of $$A = 0$$ or $$B = 0$$ when potential at $$A$$ or $$B$$ is $$0 \text{ V}$$.
The truth table of the given circuit will be:
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A car is moving with speed of $$150 \text{ km h}^{-1}$$ and after applying the brake it will move $$27 \text{ m}$$ before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ______ m distance.
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Four forces are acting at a point $$P$$ in equilibrium as shown in figure. The ratio of force $$F_1$$ to $$F_2$$ is $$1:x$$ where $$x =$$ ______.
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A wire of length $$L$$ and radius $$r$$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $$F$$, its length increases by $$5 \text{ cm}$$. Another wire of the same material of length $$4L$$ and radius $$4r$$ is pulled by a force $$4F$$ under same conditions. The increase in length of this wire is ______ cm.
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A unit scale is to be prepared whose length does not change with temperature and remains $$20 \text{ cm}$$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $$40 \text{ cm}$$ and length of iron will be ______ cm.
$$\alpha_{\text{iron}} = 1.2 \times 10^{-5} \text{ K}^{-1}$$ and $$\alpha_{\text{brass}} = 1.8 \times 10^{-5} \text{ K}^{-1}$$.
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An observer is riding on a bicycle and moving towards a hill at $$18 \text{ km h}^{-1}$$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $$640 \text{ Hz}$$ and velocity of the sound in air is $$320 \text{ m s}^{-1}$$, the beat frequency between the two sounds heard by observer will be ______ Hz.
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The volume charge density of a sphere of radius $$6 \text{ m}$$ is $$2 \mu C \text{ cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is ______ $$\times 10^{10} \text{ N C}^{-1}$$.
[Given: Permittivity of vacuum $$\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$]
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In the given figure, the value of $$V_0$$ will be ______ V.
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Eight copper wires of length $$l$$ and diameter $$d$$ are joined in parallel to form a single composite conductor of resistance $$R$$. If a single copper wire of length $$2l$$ has the same resistance $$R$$ then its diameter will be ______ $$d$$.
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The energy band gap of semiconducting material to produce violet (wavelength $$= 4000$$ $$\mathring{A}$$) LED is ______ eV. (Round off to the nearest integer).
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The required height of a TV tower which can cover the population of $$6.03$$ lakh is $$h$$. If the average population density is $$100$$ per square km and the radius of earth is $$6400 \text{ km}$$, then the value of $$h$$ will be ______ m.
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