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In the equation $$X + \frac{a}{Y^2}\left[Y - b\right] = RT$$, $$X$$ is pressure, $$Y$$ is volume, $$R$$ is universal gas constant and $$T$$ is temperature. The physical quantity equivalent to the ratio $$\frac{a}{b}$$ is:
The distance travelled by an object in time $$t$$ is given by $$s = 2.5t^2$$. The instantaneous speed of the object at $$t = 5$$ s will be :
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A passenger sitting in a train A moving at $$90$$ km h$$^{-1}$$ observes another train B moving in the opposite direction for $$8$$ s. If the velocity of the train B is $$54$$ km h$$^{-1}$$, then length of train B is:
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A vehicle of mass $$200$$ kg is moving along a levelled curved road of radius $$70$$ m with angular velocity of $$0.2$$ rad s$$^{-1}$$. The centripetal force acting on the vehicle is:
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Two planets A and B of radii $$R$$ and $$1.5R$$ have densities $$\rho$$ and $$\frac{\rho}{2}$$ respectively. The ratio of acceleration due to gravity at the surface of B to A is:
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Given below are two statements:
Statement I : For a planet, if the ratio of mass of the planet to its radius increase, the escape velocity from the planet also increase.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : A spherical body of radius $$(5 \pm 0.1)$$ mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%.
Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below
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The initial pressure and volume of an ideal gas are $$P_0$$ and $$V_0$$. The final pressure of the gas when the gas is suddenly compressed to volume $$\frac{V_0}{4}$$ will be:
(Given $$\gamma$$ = ratio of specific heats at constant pressure and at constant volume.)
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The mean free path of molecules of a certain gas at STP is $$1500d$$, where $$d$$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $$373$$ K is approximately:
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A particle executes SHM of amplitude $$A$$. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:
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A $$10 \ \mu$$C charge is divided into two parts and placed at $$1$$ cm distance so that the repulsive force between them is maximum. The charges of the two parts are:
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In the network shown below, the charge accumulated in the capacitor in steady state will be:
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An electron is moving along the positive x-axis. If uniform magnetic field is applied parallel to the negative z-axis, then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experience magnetic force along negative y-axis
C. The electron will not experience any force in magnetic field
D. The electron will continue to move along the positive x-axis
E. The electron will move along circular path in magnetic field
Choose the correct answer from the option given below:
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Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below:
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Given below are two statements:
Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface
Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light
In the light of above statements, choose the correct answer from the options given below
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In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is:
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In a Young's double slit experiment, the ratio of amplitude of light coming from slits is $$2 : 1$$. The ratio of the maximum to minimum intensity in the interference pattern is
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170.
Reason R : Nuclear force is short ranged.
In the light of the above statements, choose the correct answer from the options given below
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The output from a NAND gate having inputs A and B given below will be,
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To radiate EM signal of wavelength $$\lambda$$ with high efficiency, the antennas should have a minimum size equal to:
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