An ideal gas is expanding
Question: An ideal gas is expanding such that $\mathrm{PT}^{3}=$ constant. The coefficient of volume expansion of the gas is:$\frac{1}{T}$$\frac{2}{\mathrm{~T}}$$\frac{4}{T}$$\frac{3}{\mathrm{~T}}$Correct Option: , 3 Solution: $\mathrm{PT}^{3}=\mathrm{constant}$ $\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right) \mathrm{T}^{3}=\mathrm{constant}$ $\mathrm{T}^{4} \mathrm{~V}^{-1}=\mathrm{constant}$ $\mathrm{T}^{4}=\mathrm{kV}$ $\Rightarrow 4 \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{\Delta \mathrm{V}}...
Read More →A mosquito is moving with a velocity
Question: A mosquito is moving with a velocity $\overrightarrow{\mathrm{v}}=0.5 \mathrm{t}^{2} \hat{\mathrm{i}}+3 \mathrm{t} \hat{\mathrm{j}}+9 \hat{\mathrm{k}}$ m/s and accelerating in uniform conditions. What will be the direction of mosquito after $2 \mathrm{~s}$ ?$\tan ^{-1}\left(\frac{2}{3}\right)$ from $x$-axis$\tan ^{-1}\left(\frac{2}{3}\right)$ from y-axis$\tan ^{-1}\left(\frac{5}{2}\right)$ from $y$-axis$\tan ^{-1}\left(\frac{5}{2}\right)$ from x-axisCorrect Option: , 2 Solution: Given ...
Read More →Solve this following
Question: If $\mathrm{E}, \mathrm{L}, \mathrm{M}$ and $\mathrm{G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of $P$ in the formula $\mathrm{P}=\mathrm{EL}^{2} \mathrm{M}^{-5} \mathrm{G}^{-2}$ are :- $\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{0}\right]$$\left[\mathrm{M}^{-1} \mathrm{~L}^{-1} \mathrm{~T}^{2}\right]$$\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \...
Read More →The correct relation between
Question: The correct relation between $\alpha$ (ratio of collector current to emitter current) and $\beta$ (ratio of collector current to base current) of a transistor is :$\beta=\frac{\alpha}{1+\alpha}$$\alpha=\frac{\beta}{1-\alpha}$$\beta=\frac{1}{1-\alpha}$$\alpha=\frac{\beta}{1+\beta}$Correct Option: , 4 Solution: $\alpha=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{E}}}, \beta=\frac{\mathrm{I}_{\mathrm{C}}}{\mathrm{I}_{\mathrm{B}}}$ $\mathrm{I}_{\mathrm{E}}=\mathrm{I}_{\mathrm{B}}+\m...
Read More →For a transistor in CE
Question: For a transistor in CE mode to be used as an amplifier, it must be operated in :Both cut-off and SaturationSaturation region onlyCut-off region onlyThe active region onlyCorrect Option: , 4 Solution: Active region of the CE transistor is linear region and is best suited for its use as an amplifier...
Read More →Moment of inertia
Question: Moment of inertia of a square plate of side $l$ about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :$\frac{\mathrm{M} l^{2}}{6}$$\mathrm{M} l^{2}$$\frac{\mathrm{M} l^{2}}{12}$$\frac{2}{3} \mathrm{M} l^{2}$Correct Option: , 4 Solution: According to perpendicular Axis theorem. $\mathrm{I}_{\mathrm{x}}+\mathrm{I}_{\mathrm{y}}=\mathrm{I}_{\mathrm{z}}$ $\mathrm{I}_{\mathrm{z}} \Rightarrow \frac{\mathrm{m} \ell^{2}}{3}+\frac{\mathrm{m}...
Read More →What will be the nature of flow of water from a circular tap,
Question: What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 \mathrm{~L} / \mathrm{min}$ to $0.48 \mathrm{~L} / \mathrm{min}$ ? The radius of the tap and viscosity of water are $0.5 \mathrm{~cm}$ and $10^{-3} \mathrm{~Pa} \mathrm{~s}$, respectively. (Density of water : $10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ )Unsteady to steady flowRemains steady flowRemains turbulent flowSteady flow to unsteady flowCorrect Option: , 4 Solution: The nature of flo...
Read More →The initial mass of a rocket is
Question: The initial mass of a rocket is $1000 \mathrm{~kg}$. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of $20 \mathrm{~ms}^{-2}$. The gases come out at a relative speed of $500 \mathrm{~ms}^{-1}$ with respect to the rocket :[Use $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ] $6.0 \times 10^{2} \mathrm{~kg} \mathrm{~s}^{-1}$$500 \mathrm{~kg} \mathrm{~s}^{-1}$$10 \mathrm{~kg} \mathrm{~s}^{-1}$$60 \mathrm{~kg} \mathrm{~s}^{-1}$Correct Option: , 4 Solution:...
Read More →The velocity-displacement graph of a particle is shown in the figure.
Question: The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by :Correct Option: , 3 Solution: $\mathrm{V}=-\left(\frac{\mathrm{V}_{0}}{\mathrm{x}_{0}}\right) \mathrm{x}+\mathrm{v}_{0}$ $a=\frac{v d v}{d x}$ $a=\left[-\left(\frac{v_{0}}{x_{0}}\right) x+v_{0}\right]\left[-\frac{v_{0}}{x_{0}}\right]$ $\mathrm{a}=\left(\frac{\mathrm{v}_{0}}{\mathrm{x}_{0}}\right)^{2} \mathrm{x}-\frac{\mathrm{v}_{0}^{2}}{\math...
Read More →Calculate the amount of charge
Question: Calculate the amount of charge on capacitor of $4 \mu \mathrm{F}$. The internal resistance of battery is $1 \Omega$ : $8 \mu \mathrm{C}$Zero$16 \mu \mathrm{C}$$4 \mu \mathrm{C}$Correct Option: 1 Solution: On simplifying circuit we get No current in upper wire. $\therefore \quad \mathrm{V}_{\mathrm{AB}}=\frac{5}{4+1} \times 4=4 \mathrm{v}$ $\therefore \quad \theta=\left(\mathrm{C}_{\mathrm{eq}}\right) \mathrm{v}$ $\Rightarrow 2 \times 4=8 \mu \mathrm{C}$...
Read More →What equal length of an iron wire and a copper-nickel alloy wire,
Question: What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \mathrm{~mm}$ diameter connected parallel to give an equivalent resistance of $3 \Omega$ ? (Given resistivities of iron and copper-nickel alloy wire are $12 \mu \Omega \mathrm{cm}$ and $51 \mu \Omega \mathrm{cm}$ respectively)$82 \mathrm{~m}$$97 \mathrm{~m}$$110 \mathrm{~m}$$90 \mathrm{~m}$Correct Option: , 2 Solution: $\frac{R_{1} R_{2}}{R_{1}+R_{2}}=3$ $\frac{\frac{\left(12 \times 10^{-6} \times 10^{-2}\righ...
Read More →Consider a uniform wire of mass M and length L.
Question: Consider a uniform wire of mass $M$ and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :$\frac{1}{4} \frac{\mathrm{ML}^{2}}{\pi^{2}}$$\frac{2}{5} \frac{\mathrm{ML}^{2}}{\pi^{2}}$$\frac{\mathrm{ML}^{2}}{\pi^{2}}$$\frac{1}{2} \frac{\mathrm{ML}^{2}}{\pi^{2}}$Correct Option: , 3 Solution: $\pi \mathrm{r}=\mathrm{L} \Rightarrow \mathrm{r}=\frac{\mathrm{L}}{\pi}$ $\mathrm{I}=\mathrm{Mr}^{2}=\frac...
Read More →A huge circular arc
Question: A huge circular arc of length $4.4$ ly subtends an angle ' $4 s^{\prime}$ at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second ? Given : $1 \mathrm{lv}=9.46 \times 10^{15} \mathrm{~m}$ $1 \mathrm{AU}=1.5 \times 10^{11} \mathrm{~m}$$4.1 \times 10^{8} \mathrm{~s}$$4.5 \times 10^{10} \mathrm{~s}$$3.5 \times 10^{6} \mathrm{~s}$$7.2 \times 10^{8} \mathrm{~s}$Correct Option: , 2 Solution: $\mathrm{R}=\frac{\ell}{\theta}$ $\op...
Read More →A charge Q is moving
Question: A charge $Q$ is moving $\overline{\mathrm{dI}}$ distance in the magnetic field $\overrightarrow{\mathrm{B}}$. Find the value of work done by $\overrightarrow{\mathrm{B}}$.1InfiniteZero$-1$Correct Option: , 3 Solution: Since force on a point charge by magnetic field is always perpendicular to $\overrightarrow{\mathrm{V}}[\overrightarrow{\mathrm{F}}=\mathrm{q} \overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}}]$ $\therefore$ Work by magnetic force on the point charge is zero....
Read More →In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed.
Question: In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by $0.5 \mathrm{~mm}$ on a complete rotation. For a particular observation the reading on the main scale is $5 \mathrm{~mm}$ and the $20^{\text {th }}$ division of the circular scale coincides with reference line. Calculate the true reading.$5.00 \mathrm{~mm}$$5.25 \mathrm{~mm}$$5.15 \mathrm{~mm}$$5.2...
Read More →A plane electromagnetic wave propagating
Question: A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\overrightarrow{\mathrm{E}})$ and magnetic field $(\overrightarrow{\mathrm{B}})$ components.$\mathrm{E}_{\mathrm{y}}, \mathrm{B}_{\mathrm{y}}$ or $\mathrm{E}_{\mathrm{z}}, \mathrm{B}_{\mathrm{z}}$$\mathrm{E}_{\mathrm{y}}, \mathrm{B}_{\mathrm{x}}$ or $\mathrm{E}_{\mathrm{x}}, \mathrm{B}_{\mathrm{y}}$$\mathrm{E}_{\mathrm{x}}, \mathrm{B}_{\mathrm{z}}$ or $\mathrm{E}_{z}, \mathrm{~B}_...
Read More →An object is placed
Question: An object is placed beyond the centre of curvature $\mathrm{C}$ of the given concave mirror. If the distance of the object is $\mathrm{d}_{1}$ from $\mathrm{C}$ and the distance of the image formed is $d_{2}$ from $C$, the radius of curvature of this mirror is :$\frac{2 \mathrm{~d}_{1} \mathrm{~d}_{2}}{\mathrm{~d}_{1}-\mathrm{d}_{2}}$$\frac{2 \mathrm{~d}_{1} \mathrm{~d}_{2}}{\mathrm{~d}_{1}+\mathrm{d}_{2}}$$\frac{\mathrm{d}_{1} \mathrm{~d}_{2}}{\mathrm{~d}_{1}+\mathrm{d}_{2}}$$\frac{\m...
Read More →A proton and an alpha - partical,
Question: A proton and an $\alpha$-particle, having kinetic energies $\mathrm{K}_{\mathrm{p}}$ and $\mathrm{K}_{\alpha}$, respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$-particle is $2: 1$. The ratio of $\mathrm{K}_{\mathrm{p}}: \mathrm{K}_{\alpha}$ is:$1: 8$$8: 1$$1: 4$$4: 1$Correct Option: , 4 Solution: $r=\frac{m v}{q B}=\frac{p}{q B} \quad \frac{m_{\alpha}}{m_{p}}=4$ $\frac{r_{p}}{r_{\alpha}}=\frac{p_{p}}{q_{p}} \f...
Read More →A balloon carries
Question: A balloon carries a total load of $185 \mathrm{~kg}$ at normal pressure and temperature of $27^{\circ} \mathrm{C}$. What load will the balloon carry on rising to a height at which the barometric pressure is $45 \mathrm{~cm}$ of $\mathrm{Hg}$ and the temperature is $-7^{\circ} \mathrm{C}$. Assuming the volume constant ?$181.46 \mathrm{~kg}$$214.15 \mathrm{~kg}$$219.07 \mathrm{~kg}$$123.54 \mathrm{~kg}$Correct Option: , 4 Solution: $\mathrm{P}_{\mathrm{m}}=\rho \mathrm{RT}$ $\therefore \...
Read More →Solve this following
Question: The rms speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are $\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{O}}$ and $\mathrm{V}_{\mathrm{C}}$ respectively then : $\mathrm{V}_{\mathrm{H}}\mathrm{V}_{\mathrm{O}}\mathrm{V}_{\mathrm{C}}$$\mathrm{V}_{\mathrm{C}}\mathrm{V}_{\mathrm{O}}\mathrm{V}_{\mathrm{H}}$$\mathrm{V}_{\mathrm{H}}=\mathrm{V}_{\mathrm{O}}\mathrm{V}_{\mathrm{C}}$$V_{H}=V_{O}=V_{C}$Correct Option: 1 Solution: $\mathrm{V}_{\mathrm{RMS}}=\sq...
Read More →The resultant of these forces
Question: The resultant of these forces $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}, \overrightarrow{\mathrm{OR}}, \overrightarrow{\mathrm{OS}}$ and $\overrightarrow{\mathrm{OT}}$ is approximately ...... $\mathrm{N}$. [Take $\sqrt{3}=1.7, \sqrt{2}=1.4$ Given $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ unit vectors along $\mathrm{x}, \mathrm{y}$ axis] $9.25 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}$$3 \hat{i}+15 \hat{j}$$2.5 \hat{\mathrm{i}}-14.5 \hat{\mathrm{j}}$$-1.5 \hat{\mathrm{i}}-15...
Read More →A large block of wood of mass M=5.99 kg is hanging from two long massless cords.
Question: A large block of wood of mass $\mathrm{M}=5.99 \mathrm{~kg}$ is hanging from two long massless cords. A bullet of mass $m=10 \mathrm{~g}$ is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance $\mathrm{h}=9.8 \mathrm{~cm}$ before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is : (Take $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$ ) $841...
Read More →For an adiabatic expansion of an ideal gas,
Question: For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):$-\gamma \frac{d \mathrm{~V}}{\mathrm{~V}}$$-\gamma \frac{V}{d V}$$-\frac{1}{\gamma} \frac{\mathrm{dV}}{\mathrm{V}}$$\frac{d V}{V}$Correct Option: 1 Solution: $\mathrm{PV} \gamma=$ constant Differentiating $\frac{\mathrm{dP}}{\mathrm{dV}}=-\frac{\gamma \mathrm{P}}{\mathrm{V}}$ $\frac{\mathrm{dP}}{\mathrm{P}}=-\frac{\gamma \mathrm{dV}}{\mathrm{V}}...
Read More →A solid metal sphere of radius
Question: A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in figure. The approximate variation electric field $\overrightarrow{\mathrm{E}}$ as a function of distance $r$ from centre $O$ is given by Correct Option: 1 Solution: Considering outer spherical shell is nonconducting Electric field inside a metal sphere is zero. $\mathrm{r}\mathrm{R} \Rightarrow \mathrm{E}=0$ $rR \Rightarrow E=\frac{...
Read More →An object of mass m_1 collides with another object
Question: An object of mass $m_{1}$ collides with another object of mass $\mathrm{m}_{2}$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $\mathrm{m}_{2}: \mathrm{m}_{1}$ is:$3: 1$$2: 1$$1: 2$$1: 1$Correct Option: 1 Solution: $m_{1} v_{1}=-m_{1} v+m_{2} v$ $v_{1}=-v+\frac{m_{2}}{m_{1}} v$ $\mathrm{v}_{1}=-\mathrm{v}+\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}} \mathrm{v}$ $\frac{\left(v_{1}+v\right)}{v}=\frac{m_{2}}{m_{1}}$ $\mat...
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