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A physical quantity $$P$$ is given as $$P = \frac{a^2 b^3}{c\sqrt{d}}$$. The percentage error in the measurement of $$a$$, $$b$$, $$c$$ and $$d$$ are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity $$P$$ will be
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The position-time graphs for two students A and B returning from the school to their homes are shown in figure.
(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster than B
(E) B travels faster than A
Choose the correct answer from the options given below
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The range of the projectile projected at an angle of 15$$^\circ$$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45$$^\circ$$ with horizontal, then its range will be
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A particle of mass $$m$$ moving with velocity $$v$$ collides with a stationary particle of mass $$2m$$. After collision, they stick together and continue to move together with velocity
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Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is
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Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $$d = \frac{R}{2}$$ from the surface of earth, if its weight on the surface of earth is 200 N, will be : (Given $$R$$ = radius of earth)
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Given below are two statements:
Statement I: Pressure in a reservoir of water is same at all points at the same level of water.
Statement II: The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below:
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Consider two containers A and B containing monoatomic gases at the same Pressure $$P$$, Volume $$V$$ and Temperature $$T$$. The gas in A is compressed isothermally to $$\frac{1}{8}$$ of its original volume while the gas in B is compressed adiabatically to $$\frac{1}{8}$$ of its original volume. The ratio of final pressure of gas in B to that of gas in A is
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Match List I with List II:
| List I | List II | ||
|---|---|---|---|
| (A) | 3 Translational degrees of freedom | (I) | Monoatomic gases |
| (B) | 3 Translational, 2 rotational degrees of freedom | (II) | Polyatomic gases |
| (C) | 3 Translational, 2 rotational and 1 vibrational degrees of freedom | (III) | Rigid diatomic gases |
| (D) | 3 Translational, 3 rotational and more than one vibrational degrees of freedom | (IV) | Nonrigid diatomic gases |
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A particle executes S.H.M. of amplitude $$A$$ along $$x$$-axis. At $$t = 0$$, the position of the particle is $$x = \frac{A}{2}$$ and it moves along positive $$x$$-axis. The displacement of particle in time $$t$$ is $$x = A\sin(\omega t + \delta)$$, then the value $$\delta$$ will be
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The equivalent capacitance of the combination shown is
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The equivalent resistance of the circuit shown below between points a and b is:
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Given below are two statements:
Statement I: If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II: Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio
In the light of the above statements, choose the correct answer from the options given below:
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The energy of an electromagnetic wave contained in a small volume oscillates with
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Given below are two statements:
Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs.
Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below:
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An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image would be shifted, will be
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The de Broglie wavelength of a molecule in a gas at room temperature 300 K is $$\lambda_1$$. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes
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The angular momentum for the electron in Bohr's orbit is $$L$$. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be
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A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has a breakdown of 8 V and it has to regulate voltage fluctuating between 3 V and 10 V. The value of resistance $$R_s$$ for safe operation of diode will be
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A carrier wave of amplitude 15 V is modulated by a sinusoidal base band signal of amplitude 3 V. The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is
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A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m s$$^{-1}$$, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is _______ J. (Given $$g = 10$$ m s$$^{-2}$$).
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If the earth suddenly shrinks to $$\frac{1}{64}$$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $$\frac{24}{x}$$ h. The value of x is _______.
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Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is _______ $$\times 10^{-6}$$ m. [Young's modulus for steel $$= 2 \times 10^{11}$$ N m$$^{-2}$$ and $$g = 10$$ m s$$^{-2}$$]
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A transverse harmonic wave on a string is given by $$y(x, t) = 5\sin6t + 0.003x$$ where $$x$$ and $$y$$ are in cm and $$t$$ in sec. The wave velocity is _______ m s$$^{-1}$$.
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Three concentric spherical metallic shells $$X$$, $$Y$$ and $$Z$$ of radius $$a$$, $$b$$ and $$c$$ respectively $$a < b < c$$ have surface charge densities $$\sigma$$, $$-\sigma$$ and $$\sigma$$, respectively. The shells $$X$$ and $$Z$$ are at same potential. If the radii of $$X$$ & $$Y$$ are 2 cm and 3 cm, respectively. The radius of shell Z is _______ cm.
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10 resistors each of resistance 10 $$\Omega$$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be _______.
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The current required to be passed through a solenoid of 15 cm length and 60 turns in order to demagnetise a bar magnet of magnetic intensity $$2.4 \times 10^3$$ A m$$^{-1}$$ is _______ A.
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A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5 $$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m s$$^{-1}$$ will be _______ $$\times 10^{-3}$$ N.
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Unpolarised light of intensity 32 W m$$^{-2}$$ passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is 3 W m$$^{-2}$$, then the angle between pass axis of first two polaroids is _______ $$^\circ$$.
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The decay constant for a radioactive nuclide is $$1.5 \times 10^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, $$N_A = 6 \times 10^{23}$$. The activity of 1.0 $$\mu$$g of the substance is _______ $$\times 10^{10}$$ Bq.
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