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Given below are two statements:
Statement I: Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statement II: Au < Parsec (Pc) < ly
In the light of the above statements, choose the most appropriate answer from the options given below:
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From the $$v - t$$ graph shown, the ratio of distance to displacement in 25 s of motion is:
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A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _______ from the centre:
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An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m s$$^{-1}$$ to keep it in position. The number of bullets fired per second by the machine gun is:
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The radii of two planets A and B are R and 4R and their densities are $$\rho$$ and $$\frac{\rho}{3}$$ respectively. The ratio of acceleration due to gravity at their surfaces $$g_A : g_B$$ will be
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1 kg of water at 100$$^\circ$$C is converted into steam at 100$$^\circ$$C by boiling at atmospheric pressure. The volume of water changes from $$1.00 \times 10^{-3}$$ m$$^3$$ as a liquid to 1.671 m$$^3$$ as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation = 2257 kJ/kg, Atmospheric pressure $$= 1 \times 10^5$$ Pa)
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On a temperature scale 'X', the boiling point of water is 65$$^\circ$$X and the freezing point is $$-15^\circ$$X. Assuming that the X scale is linear. The equivalent temperature corresponding to $$-95^\circ$$X on the Fahrenheit scale would be
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Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $$v_{rms}$$ and choose the correct answer from the options given below:
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The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by
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The electric field in an electromagnetic wave is given as $$\vec{E} = 20\sin(\omega t - \frac{x}{c})\hat{j}$$ N C$$^{-1}$$, where $$\omega$$ and $$c$$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $$5 \times 10^{-4}$$ m$$^3$$ will be
(Given $$\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)
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A parallel plate capacitor of capacitance 2 F is charged to a potential $$V$$. The energy stored in the capacitor is $$E_1$$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $$E_2$$. The ratio $$\frac{E_2}{E_1}$$ is
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Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:
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The current sensitivity of moving coil galvanometer is increased by 25%. This increase is achieved only changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:
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The free space inside a current carrying toroid is filled with a material of susceptibility $$2 \times 10^{-2}$$. The percentage increase in the value of magnetic field inside the toroid will be
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As per the given graph, choose the correct representation for curve A and curve B
{Where $$X_C$$ = Reactance of pure capacitive circuit connected with A.C. source
$$X_L$$ = Reactance of pure inductive circuit connected with A.C. source
$$R$$ = Impedance of pure resistive circuit connected with A.C. source
$$Z$$ = Impedance of the LCR series circuit}
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The critical angle for a denser-rarer interface is 45$$^\circ$$. The speed of light in rarer medium is $$3 \times 10^8$$ m s$$^{-1}$$. The speed of light in the denser medium is:
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A metallic surface is illuminated with radiation of wavelength $$\lambda$$, the stopping potential is $$V_0$$. If the same surface is illuminated with radiation of wavelength $$2\lambda$$, the stopping potential becomes $$\frac{V_0}{4}$$. The threshold wavelength for this metallic surface will be
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Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_A$$ and $$\lambda_B$$ are decay constants of A and B respectively, then choose the correct relation from the given options.
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The logic performed by the circuit shown in figure is equivalent to
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A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is $$x \times 10^{-2}$$ m. The value of $$x$$ is _____.
(Let, radius of earth R = 6400 km)
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A projectile fired at 30$$^\circ$$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is _______ m s$$^{-1}$$.
(Given $$g = 10$$ m s$$^{-2}$$)
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A force $$\vec{F} = (2 + 3x)\hat{i}$$ acts on a particle in the $$x$$ direction where $$F$$ is in Newton and $$x$$ is in meter. The work done by this force during a displacement from $$x = 0$$ to $$x = 4$$ m is _______ J.
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A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s$$^{-1}$$. If the moment of inertia of the sphere about its tangent is $$x \times 10^{-2}$$ times its angular momentum about the diameter. Then the value of $$x$$ will be _______
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The length of a wire becomes $$l_1$$ and $$l_2$$ when 100 N and 120 N tension are applied respectively. If $$10l_2 = 11l_1$$, then the natural length of wire will be $$\frac{1}{x}l_1$$. Here the value of $$x$$ is _______
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The equation of wave is given by $$Y = 10^{-2}\sin 2\pi(160t - 0.5x + \frac{\pi}{4})$$, where $$x$$ and $$Y$$ are in m and $$t$$ in s. The speed of the wave is _______ km h$$^{-1}$$.
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As shown in the figure, a configuration of two equal point charges $$q_0 = +2\mu C$$ is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $$h = x \times 10^{-3}$$ m. The value of x is _______
Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$, $$g = 10$$ m s$$^{-2}$$
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In the circuit diagram shown in figure given below, the current flowing through resistance 3 $$\Omega$$ is $$\frac{x}{3}$$ A. The value of $$x$$ is _______.
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The magnetic field B, crossing normally a square metallic plate of area 4 m$$^2$$, is changing with time as shown in the figure. The magnitude of the induced emf in the plate during $$t = 2$$ s to $$t = 4$$ s, is _______ mV.
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The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $$x$$ : 1. The value of $$x$$ is _______
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A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $$x \times 10^{15}$$ Hz. The value of x is _______.
(Given $$h = 4.25 \times 10^{-15}$$ eVs)
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