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An expression for a dimensionless quantity $$P$$ is given by $$P = \frac{\alpha}{\beta} \log_e\left(\frac{kT}{\beta x}\right)$$; where $$\alpha$$ and $$\beta$$ are constants, $$x$$ is distance; $$k$$ is Boltzmann constant and $$T$$ is the temperature. Then the dimensions of $$\alpha$$ will be
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A person is standing in an elevator. In which situation, he experiences weight loss?
An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?
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A ball is released from rest from point $$P$$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $$Q$$ is $$A$$ while angular position of point $$Q$$ is $$\alpha$$ with respect to point $$P$$. Which of the following graphs represent the correct relation between $$A$$ and $$\alpha$$ when ball goes from $$Q$$ to $$R$$?
A thin circular ring of mass $$M$$ and radius $$R$$ is rotating with a constant angular velocity $$2$$ rad s$$^{-1}$$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass $$m$$ be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rad s$$^{-1}$$).
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The variation of acceleration due to gravity $$(g)$$ with distance $$(r)$$ from the center of the earth is correctly represented by (Given $$R$$ = radius of earth)
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The efficiency of a Carnot's engine, working between steam point and ice point, will be
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A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$1.4$$. Vessel is moving with speed $$v$$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by :
($$R$$ = universal gas constant)
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Time period of a simple pendulum in a stationary lift is $$T$$. If the lift accelerates with $$\frac{g}{6}$$ vertically upwards then the time period will be
(Where $$g$$ = acceleration due to gravity)
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Two capacitors having capacitance $$C_1$$ and $$C_2$$ respectively are connected as shown in figure. Initially, capacitor $$C_1$$ is charged to a potential difference $$V$$ volt by a battery. The battery is then removed and the charged capacitor $$C_1$$ is now connected to uncharged capacitor $$C_2$$ by closing the switch $$S$$. The amount of charge on the capacitor $$C_2$$, after equilibrium, is
An aluminium wire is stretched to make its length, $$0.4\%$$ larger. The percentage change in resistance is
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Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A): Non-polar materials do not have any permanent dipole moment.
Reason (R): When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.
In the light of above statements, choose the most appropriate answer from the options given below.
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A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is
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The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5t^3 + 4t^2 + 2t - 5)$$ Weber. If the resistance of the coil is $$5$$ ohm, then the induced current through the coil at $$t = 2$$ s will be,
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If Electric field intensity of a uniform plane electro magnetic wave is given as
$$E = -301.6\sin(kz-\omega t)\hat{a}_x + 452.4\sin(kz-\omega t)\hat{a}_y$$ V m$$^{-1}$$. Then, magnetic intensity $$H$$ of this wave in A m$$^{-1}$$ will be [Given : Speed of light in vacuum $$c = 3 \times 10^8$$ m s$$^{-1}$$, Permeability of vacuum $$\mu_0 = 4\pi \times 10^{-7}$$ N A$$^{-2}$$]
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A wave of frequency $$= 3$$ GHz, strikes a particle of size $$\left(\frac{1}{100}\right)^{th}$$ of $$\lambda$$, then this phenomenon is called as
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An electron with speed $$v$$ and a photon with speed $$c$$ have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are $$E_e$$ and $$P_e$$ and that of photon are $$E_{ph}$$ and $$P_{ph}$$ respectively. Which of the following is correct?
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How many alpha and beta particles are emitted when Uranium $$_{92}U^{238}$$ decays to lead $$_{82}Pb^{206}$$?
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The I - V characteristics of a $$p - n$$ junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of $$2$$ V and $$4$$ V respective is
Choose the correct statement for amplitude modulation
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A ball of mass $$0.5$$ kg is dropped from the height of $$10$$ m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ______ m. [Use $$g = 10$$ m s$$^{-2}$$]
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A fighter jet is flying horizontally at a certain altitude with a speed of $$200$$ m s$$^{-1}$$. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $$\theta$$ with the horizontal, to hit the jet. If the bullet speed is $$400$$ m s$$^{-1}$$, the value of $$\theta$$ will be ______ °.
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The elongation of a wire on the surface of the earth is $$10^{-4}$$ m. The same wire of same dimensions is elongated by $$6 \times 10^{-5}$$ m on another planet. The acceleration due to gravity on the planet will be ______ m s$$^{-2}$$. (Take acceleration due to gravity on the surface of earth $$= 10$$ m s$$^{-2}$$)
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The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $$5 \times 10^{-4}$$ is ______ kJ m$$^{-3}$$. Assume that material is elastic upto the linear strain of $$5 \times 10^{-4}$$.
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An ideal fluid of density $$800$$ kg m$$^{-3}$$, flows smoothly through a bent pipe (as shown in the figure) that tapers in cross-sectional area from $$a$$ to $$\frac{a}{2}$$. The pressure difference between the wide and narrow sections of pipe is $$4100$$ Pa. At the wider section, the velocity of the fluid is $$\frac{\sqrt{x}}{6}$$ m s$$^{-1}$$ for $$x =$$ ______. (Given $$g = 10$$ m s$$^{-2}$$)
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A $$10$$ $$\Omega$$, $$20$$ mH coil carrying constant current is connected to a battery of $$20$$ V through a switch. Now after switch is opened current becomes zero in $$100$$ $$\mu$$s. The average e.m.f. induced in the coil is ______ V.
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A $$110$$ V, $$50$$ Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance $$55$$ $$\Omega$$, at resonance in the circuit, will be ______ A.
A light ray is incident, at an incident angle $$\theta_1$$, on the system of two plane mirrors $$M_1$$ and $$M_2$$ having an inclination angle $$75°$$ between them (as shown in figure). After reflecting from mirror $$M_1$$ it gets reflected back by the mirror $$M_2$$ with an angle of reflection $$30°$$. The total deviation of the ray will be ______ degree.
As per the given circuit, the value of current through the battery will be ______ A.
In a vernier callipers, each cm on the main scale is divided into $$20$$ equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be ______ $$\times 10^{-2}$$ mm
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