Prove the following
Question: $\int \frac{x^{2}}{1-x^{4}} d x$ put $x^{2}=t$ Solution:...
Read More →A prism of angle
Question: A prism of angle $\mathrm{A}=1^{\circ}$ has a refractive index $\mu=1.5$. A good estimate for the minimum angle of deviation (in degrees) is close to $\mathrm{N} /$ 10 . Value of $N$ is__________. Solution:...
Read More →A body of mass 2 kg is driven by an engine delivering a constant power
Question: A body of mass $2 \mathrm{~kg}$ is driven by an engine delivering a constant power $1 \mathrm{~J} / \mathrm{s}$. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in $\mathrm{m}$ )_________. Solution:...
Read More →A thin rod of mass
Question: A thin rod of mass $0.9 \mathrm{~kg}$ and length $1 \mathrm{~m}$ is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move $0.1 \mathrm{~kg}$ moving in a straight line with velocity $80 \mathrm{~m} / \mathrm{s}$ hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in $\mathrm{rad} / \mathrm{s}$ ) of the rod immediately after the collision will be________. Solution:...
Read More →Nitrogen gas is at 300° C temperature.
Question: Nitrogen gas is at $300^{\circ} \mathrm{C}$ temperature. The temperature (in K) at which the rms speed of a $\mathrm{H}_{2}$ molecule would be equal to the rms speed of a nitrogen molecule, is_______. (Molar mass of $\mathrm{N}_{2}$ gas $28 \mathrm{~g}$ ) Solution:...
Read More →The surface of a metal is illuminated alternately
Question: The surface of a metal is illuminated alternately with photons of energies $E_{1}=4 \mathrm{eV}$ and $\mathrm{E}_{2}=2.5 \mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2 . The work function of the metal in (eV) is__________. Solution:...
Read More →The correct match between the entries in column I and column II are :
Question: The correct match between the entries in column I and column II are : (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)(a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)Correct Option: , 4 Solution:...
Read More →Two Zener diodes (A and B) having breakdown voltages of
Question: Two Zener diodes (A and B) having breakdown voltages of $6 \mathrm{~V}$ and $4 \mathrm{~V}$ respectively, are connected as shown in athe circuit below. The output voltage $V_{0}$ variation with input voltage linearly increasing with time, is given by : $\left(V_{\text {input }}=0 \mathrm{~V}\right.$ at $\mathrm{t}=0$ ) (figures are qualitative) Correct Option: , 4 Solution:...
Read More →A spaceship in space sweeps stationary interplanetary dust.
Question: A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{\mathrm{dM}(\mathrm{t})}{\mathrm{dt}}=\mathrm{bv}^{2}(\mathrm{t})$, where $\mathrm{v}(\mathrm{t})$ is its instantaneous velocity. The instantaneous acceleration of the satellite is:$-\frac{2 b v^{3}}{M(t)}$$-\frac{b v^{3}}{2 M(t)}$$-b v^{3}(t)$$-\frac{b v^{3}}{M(t)}$Correct Option: , 4 Solution:...
Read More →The velocity (v) and time (t) graph of a body in a straight line
Question: The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point $\mathrm{S}$ is at $4.333$ seconds. The total distance covered by the body in $6 \mathrm{~s}$ is : $12 \mathrm{~m}$$\frac{49}{4} \mathrm{~m}$$11 \mathrm{~m}$$\frac{37}{3} \mathrm{~m}$Correct Option: , 4 Solution: $=\frac{37}{3}$...
Read More →A galvanometer is used in laboratory for detecting
Question: A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of $6 \mathrm{~mA}$ it produces a deflection of $2^{\circ}$, its figure of merit is close to:$3 \times 10^{-3} \mathrm{~A} /$ div.$333^{\circ} \mathrm{A} /$ div.$6 \times 10^{-3} \mathrm{~A} /$ div.$666^{\circ} \mathrm{A} / \mathrm{div}$.Correct Option: 1 Solution:...
Read More →The quantities
Question: The quantities $\quad x=\frac{1}{\sqrt{\mu_{0} \in_{0}}}, y=\frac{E}{B} \quad$ and $\mathrm{z}=\frac{1}{\mathrm{CR}}$ are defined where $\mathrm{C}$-capacitance, R-Resistance, $l$-length, E-Electric field, $B$-magnetic field and $\in_{0}, \mu_{0},-$ free space permittivity and permeability respectively. Then: Only $x$ and $y$ have the same dimension$x, y$ and $z$ have the same dimensionOnly $x$ and $z$ have the same dimensionOnly y and z have the same dimensionCorrect Option: , 2 Solut...
Read More →Two different wires having lengths
Question: Two different wires having lengths $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, and respective temperature coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :$4 \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}} \frac{\mathrm{L}_{2} \mathrm{~L}_{1}}{\left(\mathrm{~L}_{2}+\mathrm{L}_{1}\right)^{2}}$$2 \sqrt{\alpha_{1} \alpha_{2}}$$\frac{\alpha_{1}+\alpha_{2}}{2}$$\frac{\alpha_{1} L_{1}+\alph...
Read More →In an experiment to verify Stokes law,
Question: In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $\mathrm{h}$ is proportional to : (ignore viscosity of air)$\mathrm{r}$$r^{4}$$r^{3}$$r^{2}$Correct Option: , 2 Solution:...
Read More →In the circuit shown,
Question: In the circuit shown, charge on the $5 \mu \mathrm{F}$ capacitor is : $5.45 \mu \mathrm{C}$$16.36 \mu \mathrm{C}$$10.90 \mu \mathrm{C}$$18.00 \mu \mathrm{C}$Correct Option: , 2 Solution:...
Read More →A ring is hung on a nail.
Question: A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_{1}$ and, (ii) back and forth in a direction perpendicular to its plane, with a period $T_{2}$. the ratio $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}$ will be : $\frac{2}{\sqrt{3}}$$\frac{\sqrt{2}}{3}$$\frac{2}{3}$$\frac{3}{\sqrt{2}}$Correct Option: 1 Solution:...
Read More →A radioactive nucleus decays by two different processes.
Question: A radioactive nucleus decays by two different processes. The half life for the first process is $10 \mathrm{~s}$ and that for the second is $100 \mathrm{~s}$. the effective half life of the nucleus is close to:$9 \mathrm{sec}$$55 \mathrm{sec}$$6 \mathrm{sec}$$12 \mathrm{sec}$Correct Option: 1 Solution:...
Read More →In an adiabatic process,
Question: In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $\mathrm{n}$ is:326$\frac{1}{32}$32128Correct Option: , 4 Solution:...
Read More →A driver in a car, approaching a vertical wall notices
Question: A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from $440 \mathrm{~Hz}$ to $480 \mathrm{~Hz}$, when it gets reflected from the wall. If the speed of sound in air is $345 \mathrm{~m} / \mathrm{s}$, then the speed of the car is$36 \mathrm{~km} / \mathrm{hr}$$24 \mathrm{~km} / \mathrm{hr}$$18 \mathrm{~km} / \mathrm{hr}$$54 \mathrm{~km} / \mathrm{hr}$Correct Option: , 4 Solution:...
Read More →Two coherent sources of sound,
Question: Two coherent sources of sound, $S_{1}$ and $S_{2}$, produce sound waves of the same wavelength, $\lambda=1 \mathrm{~m}$, in phase. $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are placed $1.5 \mathrm{~m}$ apart (see fig.) A listener, located at $\mathrm{L}$, directly in front of $S_{2}$ fi nds that the intensity is at a minimum when he is $2 \mathrm{~m}$ away from $\mathrm{S}_{2}$. The listener moves away from $S_{1}$, keeping his distance from $S_{2}$ fixed. The adjacent maximum of intensity...
Read More →The acceleration due to gravity on the earth's surface
Question: The acceleration due to gravity on the earth's surface at the poles is $\mathrm{g}$ and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weighed at the equator and at a height $\mathrm{h}$ above the poles by using a spring balance. If the weights are found to be same, then $h$ is : $(hR$, where $R$ is the radius of the earth)$\frac{\mathrm{R}^{2} \omega^{2}}{8 \mathrm{~g}}$$\frac{\mathrm{R}^{2} \omega^{2}}{4 \mathrm{~g}}$$\frac{\mathrm{R}^...
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