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$$P + \frac{a}{V^2}(V - b) = RT$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^2}{a}$$, will be:
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An object moves with speed $$v_1$$, $$v_2$$ and $$v_3$$ along a line segment $$AB$$, $$BC$$ and $$CD$$ respectively as shown in the figure, where $$AB = BC$$ and $$AD = 3AB$$, then the average speed of the object will be:
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A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of 5 m s$$^{-1}$$. Neglecting the air resistance, the speed with which the stone hits the ground will be _____ m s$$^{-1}$$ (given, $$g = 10$$ m s$$^{-2}$$).
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A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, $$g = 10$$ m s$$^{-2}$$):
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If earth has a mass nine times and radius twice to the of a planet $$P$$. Then $$\frac{v_e}{3}\sqrt{x}$$ ms$$^{-1}$$ will be the minimum velocity required by a rocket to pull out of gravitational force of $$P$$, where $$v_e$$ is escape velocity on earth. The value of $$x$$ is
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Given below are two statements:
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below
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A mercury drop of radius $$10^{-3}$$ m is broken into 125 equal size droplets. Surface tension of mercury is 0.45 N m$$^{-1}$$. The gain in surface energy is:
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A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. The work done by the gas in the process is, (given $$\gamma = \frac{3}{2}$$):
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The average kinetic energy of a molecule of the gas is
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A steel wire with mass per unit length $$7.0 \times 10^{-3}$$ kg m$$^{-1}$$ is under tension of 70 N. The speed of transverse waves in the wire will be:
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Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets as shown in the figure. Then the electric fields in three different regions, $$E_I$$, $$E_{II}$$ and $$E_{III}$$ are:
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The equivalent resistance between A and B of the network shown in the figure:
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Find the magnetic field at point P as shown in the figure. The curved portion is a semicircle connected to two long straight wires.
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Match the List-I with List-II.
A. AC generator I. Presence of both L and C
B. Transformer II. Electromagnetic Induction
C. Resonance phenomenon to occur III. Quality factor
D. Sharpness of resonance IV. Mutual Inductance
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Match the List-I with List-II:
A. Microwaves I. Radioactive decay of the nucleus
B. Gamma rays II. Rapid acceleration and deceleration of electron in aerials
C. Radio waves III. Inner shell electrons
D. X-rays IV. Klystron valve
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'$$n$$' polarizing sheets are arranged such that each makes an angle 45° with the proceeding sheet. An unpolarized light of intensity $$I$$ is incident into this arrangement. The output intensity is found to be $$\frac{I}{64}$$. The value of $$n$$ will be:
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A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $$\lambda$$. An alpha particle having certain kinetic energy has the same de-Broglie wavelength $$\lambda$$. The ratio of kinetic energy of proton and that of alpha particle is:
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The mass of proton, neutron and helium nucleus are respectively 1.0073 u, 1.0087 u and 4.0015u. The binding energy of helium nucleus is:
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Match the List I with List II
A. Intrinsic Semiconductor I. Fermi-level near valence band
B. n-type semiconductor II. Fermi-level at middle of valence and conduction band
C. p-type semiconductor III. Fermi-level near conduction band
D. Metals IV. Fermi-level inside conduction band
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Which of the following frequencies does not belong to FM broadcast.
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A small particle moves to position $$5\hat{i} - 2\hat{j} + \hat{k}$$ from its initial position $$2\hat{i} + 3\hat{j} - 4\hat{k}$$ under the action of force $$5\hat{i} + 2\hat{j} + 7\hat{k}$$ N. The value of work done will be _____ J.
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A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is _____ m s$$^{-1}$$.
(Given $$g = 10$$ m s$$^{-2}$$)
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A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is _____.
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The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: _____ cm.
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Two equal positive point charges are separated by a distance $$2a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$q_0$$ becomes maximum is $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is _____.
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In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5 V is found to be 60 cm. If this cell is replaced by another cell of emf $$E$$, the length-of null point increases by 40 cm. The value of $$E$$ is $$\frac{x}{10}$$ V. The value of $$x$$ is _____.
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A charge particle of 2 $$\mu$$C accelerated by a potential difference of 100 V enters a region of uniform magnetic field of magnitude 4 mT at right angle to the direction of field. The charge particle completes semicircle of radius 3 cm inside magnetic field. The mass of the charge particle is _____ $$\times 10^{-18}$$ kg.
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A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain a resistance $$R = 100$$ $$\Omega$$ and an inductor of inductive reactance $$X_L = 79.6$$ $$\Omega$$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _____ $$\mu$$F.
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A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be $$\frac{x}{3}$$ cm. The value of $$x$$ is _____.
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A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $$\frac{x}{\pi} \times 10^{-17}$$ eVs. The value of $$x$$ is _____ (use $$h = 4.14 \times 10^{-15}$$ eVs, $$c = 3 \times 10^8$$ m s$$^{-1}$$)
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