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Two trains $$A$$ and $$B$$ of length $$l$$ and $$4l$$ are travelling into a tunnel of length $$L$$ in parallel tracks from opposite directions with velocities $$108$$ km h$$^{-1}$$ and $$72$$ km h$$^{-1}$$, respectively. If train $$A$$ take $$35$$ s less time than train $$B$$ to cross the tunnel then, length $$L$$ of tunnel is:
(Given $$L = 60 \ l$$)
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A disc is rolling without slipping on a surface. The radius of the disc is $$R$$. At $$t = 0$$, the top most point on the disc is $$A$$ as shown in figure. When the disc completes half of its rotation, the displacement of point $$A$$ from its initial position is
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The ratio of powers of two motors is $$\frac{3\sqrt{x}}{\sqrt{x}+1}$$, that are capable of raising $$300$$ kg water in $$5$$ minutes and $$50$$ kg water in $$2$$ minutes respectively from a well of $$100$$ m deep. The value of $$x$$ will be
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A body of mass $$(5 \pm 0.5)$$ kg is moving with a velocity of $$(20 \pm 0.4)$$ m s$$^{-1}$$. Its kinetic energy will be
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Two bodies are having kinetic energies in the ratio $$16 : 9$$. If they have same linear momentum, the ratio of their masses respectively is:
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A bullet of $$10$$ g leaves the barrel of gun with a velocity of $$600$$ m s$$^{-1}$$. If the barrel of gun is $$50$$ cm long and mass of gun is $$3$$ kg, then value of impulse supplied to the gun will be:
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A planet having mass $$9 M_e$$ and radius $$4R_e$$, where $$M_e$$ and $$R_e$$ are mass and radius of earth respectively, has escape velocity in km s$$^{-1}$$ given by: (Given escape velocity on earth $$V_e = 11.2 \times 10^3$$ m s$$^{-1}$$)
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Under isothermal condition, the pressure of a gas is given by $$P = aV^{-3}$$, where $$a$$ is a constant and $$V$$ is the volume of the gas. The bulk modulus at constant temperature is equal to
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The figure shows a liquid of a given density flowing steadily in a horizontal tube of a varying cross-section. Cross-sectional area at A is $$1.5$$ cm$$^2$$, and that at B is $$25$$ mm$$^2$$, if the speed of liquid at B is $$60$$ cm s$$^{-1}$$ then $$(P_A - P_B)$$ is
(Given $$P_A$$ and $$P_B$$ are liquid pressures at A and B points. Density $$\rho = 1000$$ kg m$$^{-3}$$. A and B are on the axis of tube)
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The rms speed of oxygen molecule in a vessel at particular temperature is $$\left(1 + \frac{5}{x}\right)^{\frac{1}{2}}v$$, when $$v$$ is the average speed of the molecule. The value of $$x$$ will be:
(take $$\pi = \frac{22}{7}$$)
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Which graph represents the difference between total energy and potential energy of a particle executing SHM vs its distance from mean position?
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Two charges of each magnitude $$0.01$$ C and separated by a distance of $$0.4$$ mm constitute an electric dipole. If the dipole is placed in an uniform electric field $$\vec{E}$$ of $$10$$ dyne $$\cdot$$ C$$^{-1}$$ making $$30°$$ angle with $$\vec{E}$$, the magnitude of torque acting on dipole is:
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Different combination of 3 resistors of equal resistance $$R$$ are shown in the figures. The increasing order for power dissipation is:
(A)
(B)
(C)
(D)
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The source of time varying magnetic field may be
(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal
Choose the correct answer from the options given below.
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Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions:
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A vessel of depth $$d$$ is half filled with oil of refractive index $$n_1$$ and the other half is filled with water of refractive index $$n_2$$. The apparent depth of this vessel when viewed from above will be-
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The difference between threshold wavelengths for two metal surfaces $$A$$ and $$B$$ having work function $$\phi_A = 9$$ eV and $$\phi_B = 4.5$$ eV in nm is:
{Given, $$hc = 1242$$ eV nm}
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$$^{238}_{92}$$A $$\to ^{234}_{90}$$B $$+ ^{4}_{2}$$D $$+ Q$$
In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of $$^{238}_{92}$$A $$= 238.05079 \times 931.5$$ MeV c$$^{-2}$$, mass of $$^{234}_{90}$$B $$= 234.04363 \times 931.5$$ MeV c$$^{-2}$$, mass of $$^{4}_{2}$$D $$= 4.00260 \times 931.5$$ MeV c$$^{-2}$$]
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For the following circuit and given inputs $$A$$ and $$B$$, choose the correct option for output 'Y'
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Match List-I with List-II
| List-I (Layer of atmosphere) | List-II (Approximate height over earth's surface) | ||
|---|---|---|---|
| A | F$$_1$$-Layer | I | 10 km |
| B | D-Layer | II | 170 - 190 km |
| C | Troposphere | III | 100 km |
| D | E-Layer | V | 65 - 75 km |
Choose the correct answer from the options given below.
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A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $$\pi : 22$$ then, the value of its angular speed will be _____ rad s$$^{-1}$$.
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The elastic potential energy stored in a steel wire of length $$20$$ m stretched through $$2$$ cm is $$80$$ J. The cross sectional area of the wire is _____ mm$$^2$$. (Given, $$Y = 2.0 \times 10^{11}$$ N m$$^{-2}$$)
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At a given point of time the value of displacement of a simple harmonic oscillator is given as $$y = A \cos(30°)$$. If amplitude is $$40$$ cm and kinetic energy at that time is $$200$$ J, the value of force constant is $$1.0 \times 10^x$$ N m$$^{-1}$$. The value of $$x$$ is _____.
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A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5$$ m distance from each other. Points P and Q are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, respectively. $$E_P$$ and $$E_Q$$ are the magnitudes of resultant electric field intensities at point P and Q respectively. If $$\frac{E_P}{E_Q} = \frac{4}{a}$$ for $$2|\sigma| = |\lambda|$$, then the value of $$a$$ is _____.
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A potential $$V_0$$ is applied across a uniform wire of resistance $$R$$. The power dissipation is $$P_1$$. The wire is then cut into two equal halves and a potential of $$V_0$$ is applied across the length of each half. The total power dissipation across two wires is $$P_2$$. The ratio of $$P_2 : P_1$$ is $$\sqrt{x} : 1$$. The value of $$x$$ is _____.
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When a resistance of $$5 \ \Omega$$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $$250$$ mA, however when $$1050 \ \Omega$$ resistance is connected with it in series, it gives full scale deflection for $$25$$ volt. The resistance of galvanometer is _____ $$\Omega$$.
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In the given figure, an inductor and resistor are connected in series with a battery of emf $$E$$ volt. $$\frac{E^a}{2b}$$ J s$$^{-1}$$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $$\frac{b}{a}$$ will be _____.
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A fish rising vertically upward with a uniform velocity of $$8$$ m s$$^{-1}$$, observes that a bird is diving vertically downward towards the fish with the velocity of $$12$$ m s$$^{-1}$$. If the refractive index of water is $$\frac{4}{3}$$, then the actual velocity of the diving bird to pick the fish, will be _____ m s$$^{-1}$$.
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The radius of 2$$^{\text{nd}}$$ orbit of He$$^+$$ of Bohr's model is $$r_1$$ and that of fourth orbit of Be$$^{3+}$$ is represented as $$r_2$$. Now the ratio $$\frac{r_2}{r_1}$$ is $$x : 1$$. The value of $$x$$ is _____.
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From the given transfer characteristic of a transistor in CE configuration, the value of power gain of this configuration is $$10^x$$, for $$R_B = 10$$ k$$\Omega$$, and $$R_C = 1$$ k$$\Omega$$. The value of $$x$$ is _____.
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