A transistor is connected in common emitter circuit configuration, the collector supply voltage is 10 V
Question: A transistor is connected in common emitter circuit configuration, the collector supply voltage is $10 \mathrm{~V}$ and the voltage drop across a resistor of $1000 \Omega$ in the collector circuit is $0.6 \mathrm{~V}$. If the current gain factor $(\beta)$ is 24 , then the base current is________$\mu \mathrm{A} .$ (Round off to the Nearest Integer) Solution: $\beta=\frac{I_{C}}{I_{B}}=24 ; \quad R_{C}=1000$ $\Delta \mathrm{V}=0.6$ $\mathrm{I}_{\mathrm{C}}=\frac{0.6}{1000}$ $\mathrm{I}_{...
Read More →For a series LCR circuit with
Question: For a series LCR circuit with $\mathrm{R}=100 \Omega$, $\mathrm{L}=0.5 \mathrm{mH}$ and $\mathrm{C}=0.1 \mathrm{pF}$ connected across $220 \mathrm{~V}-50 \mathrm{~Hz} \mathrm{AC}$ supply, the phase angle between current and supplied voltage and the nature of the circuit is :$0^{\circ}$, resistive circuit$\approx 90^{\circ}$, predominantly inductive circuit$0^{\circ}$, resonance circuit$\approx 90^{\circ}$, predominantly capacitive circuitCorrect Option: , 4 Solution: $R=100 \Omega$ $\m...
Read More →When radiation of wavelength
Question: When radiation of wavelength $\lambda$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is $4.8 \mathrm{~V}$. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes $1.6 \mathrm{~V}$. The threshold wavelength of the metal is :$2 \lambda$$4 \lambda$$8 \lambda$$6 \lambda$Correct Option: , 2 Solution: $\mathrm{V}_{\mathrm{S}}=\mathrm{h} v-\phi$ $4.8=\frac{\mathrm{hc}}{\lambda}-\phi$..(1) $1....
Read More →A stone of mass 20 g is projected from a rubber catapult of length 0.1 m
Question: A stone of mass $20 \mathrm{~g}$ is projected from a rubber catapult of length $0.1 \mathrm{~m}$ and area of cross section $10^{-6} \mathrm{~m}^{2}$ stretched by an amount $0.04 \mathrm{~m}$. The velocity of the projected stone is $\mathrm{m} / \mathrm{s}$. (Young's modulus of rubber $=0.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ ) Solution: By energy conservation $\frac{1}{2} \cdot \frac{\mathrm{YA}}{\mathrm{L}} \cdot \mathrm{x}^{2}=\frac{1}{2} \mathrm{mv}^{2}$ $\frac{0.5 \times 10...
Read More →A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure).
Question: A prism of refractive index $n_{1}$ and another prism of refractive index $\mathrm{n}_{2}$ are stuck together (as shown in the figure). $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ depend on $\lambda$, the wavelength of light, according to the relation $\mathrm{n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}}$ and $\mathrm{n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}$ The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interfa...
Read More →A ray of light entering
Question: A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to : $\sin ^{-1} \frac{\sqrt{7}}{3}$$\sin ^{-1} \frac{\sqrt{5}}{4}$$\sin ^{-1} \frac{\sqrt{7}}{4}$$\sin ^{-1} \frac{\sqrt{5}}{3}$Correct Option: 1 Solution: At maximum angle $\theta$ ray at point B goes in gazing emergence, at all less values of $...
Read More →In an electromagnetic wave the electric field vector
Question: In an electromagnetic wave the electric field vector and magnetic field vector are given as $\vec{E}=E_{0} \hat{i}$ and $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{k}}$ respectively. The direction of propagation of electromagnetic wave is along : $(\hat{\mathrm{k}})$$\hat{J}$$(-\hat{\mathrm{k}})$$(-\hat{j})$Correct Option: , 4 Solution: Direction of propagation $=\overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{B}}=\hat{\mathrm{i}} \times \hat{\mathrm{k}}=-\hat{\...
Read More →A particle of mass
Question: A particle of mass $9.1 \times 10^{-31} \mathrm{~kg}$ travels in a medium with a speed of $10^{6} \mathrm{~m} / \mathrm{s}$ and a photon of a radiation of linear momentum $10^{-27} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$ travels in vacuum. The wavelength of photon is times the wavelength of the particle. Solution: For photon $\lambda_{1}=\frac{\mathrm{h}}{\mathrm{P}}=\frac{6.6 \times 10^{-34}}{10^{-27}}$ For particle $\lambda_{2}=\frac{\mathrm{h}}{\mathrm{mv}}=\frac{6.6 \times 10^{-34}}...
Read More →The length of a metal wire is l1,
Question: The length of a metal wire is $\ell_{1}$, when the tension in it is $T_{1}$ and is $\ell_{2}$ when the tension is $T_{2}$. The natural length of the wire is :$\sqrt{\ell_{1} \ell_{2}}$$\frac{\ell_{1} \mathrm{~T}_{2}-\ell_{2} \mathrm{~T}_{1}}{\mathrm{~T}_{2}-\mathrm{T}_{1}}$$\frac{\ell_{1} \mathrm{~T}_{2}+\ell_{2} \mathrm{~T}_{1}}{\mathrm{~T}_{2}+\mathrm{T}_{1}}$$\frac{\ell_{1}+\ell_{2}}{2}$Correct Option: , 2 Solution: $\mathrm{T}_{1}=\mathrm{k}\left(\ell_{1}-\ell_{0}\right)$ $\mathrm{...
Read More →The instantaneous velocity
Question: The instantaneous velocity of a particle moving in a straight line is given as $\mathrm{v}=\alpha \mathrm{t}+\beta \mathrm{t}^{2}$, where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between $1 \mathrm{~s}$ and $2 \mathrm{~s}$ is :$3 \alpha+7 \beta$$\frac{3}{2} \alpha+\frac{7}{3} \beta$$\frac{\alpha}{2}+\frac{\beta}{3}$$\frac{3}{2} \alpha+\frac{7}{2} \beta$Correct Option: , 2 Solution: $\mathrm{V}=\alpha \mathrm{t}+\beta \mathrm{t}^{2}$ $\frac{\mathrm{ds}}...
Read More →A radioactive sample has an average life of 30 ms and is decaying.
Question: A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of ' $R$ ' should be_____________$\Omega .$ Solution: $\mathrm{T}_{\mathrm{m}}=30 \mathrm{~ms}$ $\mathrm{C}=200 \mu \mathrm{F}$ $\frac{\mathrm{q}}{\mathrm{N}}=\frac{\mathrm{Q}_{0} \mathrm{e}^{-\mathrm{t} / \mathrm{...
Read More →An electron moving
Question: An electron moving with speed $\mathrm{v}$ and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is:$\frac{3 c}{v}$$\frac{\mathrm{v}}{3 \mathrm{c}}$$\frac{v}{2 c}$$\frac{2 \mathrm{c}}{\mathrm{v}}$Correct Option: , 3 Solution: $\lambda_{\mathrm{e}}=\lambda_{\mathrm{Ph}}$ $\frac{\mathrm{h}}{\mathrm{p}_{\mathrm{e}}}=\frac{\mathrm{h}}{\mathrm{p}_{\mathrm{ph}}}$ $\sqrt{2 \mathrm{mk}_{\mathrm{e}}}=\frac{\mathrm{E}_{\mathrm...
Read More →The given potentiometer
Question: The given potentiometer has its wire of resistance $10 \Omega$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across $2 \Omega$ resistor is : $10 \mathrm{~V}$$5 \mathrm{~V}$$\frac{40}{9} \mathrm{~V}$$\frac{40}{11} \mathrm{~V}$Correct Option: , 3 Solution: $\frac{20-\mathrm{V}_{0}}{5}+\frac{0-\mathrm{V}_{0}}{5}+\frac{20-\mathrm{V}_{0}}{2}=0$ $4+10=\frac{2 \mathrm{~V}_{0}}{5}+\frac{\mathrm{V}_{0}}{2}$ $14=\frac{4 \mathrm{~V}_{0}+5 \mathrm{~V}_{0}...
Read More →With what speed should a galaxy move outward with respect to
Question: With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength $5890 A$ is observed at $5896 A$ ?$306 \mathrm{~km} / \mathrm{sec}$$322 \mathrm{~km} / \mathrm{sec}$$296 \mathrm{~km} / \mathrm{sec}$$336 \mathrm{~km} / \mathrm{sec}$Correct Option: 1, Solution: $f=f_{0} \sqrt{\frac{1+\beta}{1-\beta}} \quad \beta=\frac{v}{c}$ $\beta=\frac{v}{c}$ $\frac{f}{f_{0}} \sqrt{\frac{1+\beta}{1-\beta}}$ $\left(1+\frac{\Delta f}{f_{0}}\right)^{2}=(1+\beta)(1...
Read More →In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å.
Question: In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5 A$. If the speed of electron is $2.2 \times 16^{6} \mathrm{~m} / \mathrm{s}$, then the current associated with the electron will be_______ $\times 10^{-2} \mathrm{~mA} .\left[\right.$ Take $\pi$ as $\left.\frac{22}{7}\right]$ Solution: Sol. $\mathrm{I}=\frac{\mathrm{e}}{\mathrm{T}}=\frac{e \omega}{2 \pi}=\frac{\mathrm{eV}}{2 \pi}$ $I=\frac{1.6 \times 10^{-19} \times 2.2 \times 10^{6} \times 7}...
Read More →The force is given
Question: The force is given in terms of time $t$ and displacement $x$ by the equation $F=A \cos B x+C \sin D t$ $\mathrm{F}=\mathrm{A} \cos \mathrm{Bx}+\mathrm{C} \sin \mathrm{Dt}$ The dimensional formula of $\frac{\mathrm{AD}}{\mathrm{B}}$ is :$\left[\mathrm{M}^{0} \mathrm{~L} \mathrm{~T}^{-1}\right]$$\left[\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-3}\right]$$\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$$\left[\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-3}\right]$Correct Option:...
Read More →A satellite is launched into a circular orbit of radius
Question: A satellite is launched into a circular orbit of radius $\mathrm{R}$ around earth, while a second satellite is launched into a circular orbit of radius $1.02 \mathrm{R}$. The percentage difference in the time periods of the two satellites is:$1.5$$2.0$$0.7$$3.0$Correct Option: , 4 Solution: $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\mathrm{T}=\mathrm{kR}^{3 / 2}$ $\frac{\mathrm{dT}}{\mathrm{T}}=\frac{3}{2} \frac{\mathrm{dR}}{\mathrm{R}}$ $=\frac{3}{2} \times 0.02=0.03$ $\%$ Change $=3 \...
Read More →Two spherical soap bubbles
Question: Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:$\frac{\mathrm{r}_{1} \mathrm{r}_{2}}{\mathrm{r}_{1}+\mathrm{r}_{2}}$$\sqrt{\mathrm{r}_{1} \mathrm{r}_{2}}$$\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}$$\frac{\mathrm{r}_{1}+\mathrm{r}_{2}}{2}$Correct Option: , 3 Solution: no. of moles is conserved $\mathrm{n}_{1}+\mathrm{n}_{2}=\mathrm{n}_{3}$ $\mathrm{P}_{1} \mathrm{~V}_{1}+\mathrm{P}_{2} ...
Read More →A boy reaches the airport and finds that the escalator
Question: A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time $t_{1}$. If he remains stationary on a moving escalator then the escalator takes him up in time $t_{2}$. The time taken by him to walk up on the moving escalator will be :$\frac{t_{1} t_{2}}{t_{2}-t_{1}}$$\frac{t_{1}+t_{2}}{2}$$\frac{t_{1} t_{2}}{t_{2}+t_{1}}$$t_{2}-t_{1}$Correct Option: , 3 Solution: $\mathrm{L}=$ Length of escalator $\mathrm{V}_{\mathrm{b} / \mathrm{exc...
Read More →Two ideal electric dipoles
Question: Two ideal electric dipoles $\mathrm{A}$ and $\mathrm{B}$, having their dipole moment $p_{1}$ and $p_{2}$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $\mathrm{C}$ on the axis of dipole $\mathrm{A}$, the resultant electric field is making an angle of $37^{\circ}$ with the axis. The ratio of the dipole moment of $\mathrm{A}$ and $\mathrm{B}, \frac{\mathrm{p}_{1}}{\mathrm{p}_{2}}$ is : $\left(\right.$ take $\left.\sin 37^{\circ}=\frac{3}{5}...
Read More →Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively
Question: Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $\sqrt{\frac{a}{7} \frac{G M}{R}}$ then the value of 'a' is ________. [Given : The two planets are fixed in the...
Read More →Consider a planet in some
Question: Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be:$2 \mathrm{~W}$$\mathrm{W}$$2^{\frac{1}{3}} \mathrm{~W}$$\sqrt{2} \mathrm{~W}$Correct Option: , 3 Solution: Density is same $\mathrm{M}=\frac{4}{3} \pi \mathrm{R}^{3} \rho, 2 \mathrm{~m}=\frac{4}{3} \pi \mathrm{R}^{13} \rho$ $R^{\prime}=2^{1 / 3} R$ $\omega=\frac...
Read More →Consider an electrical circuit containing a two way switch ' S '.
Question: Consider an electrical circuit containing a two way switch ' $S$ '. Initially $S$ is open and then $T_{1}$ is connected to $\mathrm{T}_{2}$. As the current in $\mathrm{R}=6 \Omega$ attains a maximum value of steady state level, $T_{1}$ is disconnected from $\mathrm{T}_{2}$ and immediately connected to $\mathrm{T}_{3}$. Potential drop across $\mathrm{r}=3 \Omega$ resistor immediately after $T_{1}$ is connected to $T_{3}$ is__________ $\mathrm{V} .$ (Round off to the Nearest Integer) Sol...
Read More →If the Kinetic energy of a moving body becomes
Question: If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :$100 \%$$200 \%$$300 \%$$400 \%$Correct Option: 1 Solution: $\mathrm{K}_{2}=4 \mathrm{~K}_{1}$ $\frac{1}{2} \mathrm{mv}_{2}^{2}=4 \frac{1}{2} \mathrm{mv}_{1}^{2}$ $\mathrm{v}_{2}=2 \mathrm{v}_{1}$ $\mathrm{P}=\mathrm{mv}$ $\mathrm{P}_{2}=\mathrm{mv}_{2}=2 m \mathrm{v}_{1}$ $\mathrm{P}_{1}=\mathrm{mv}_{1}$ $\%$ change $=\frac{\Delta \mathrm{P}}{\mathr...
Read More →Solve this following
Question: In 5 minutes, a body cools from $75^{\circ} \mathrm{C}$ to $65^{\circ} \mathrm{C}$ at room temperature of $25^{\circ} \mathrm{C}$. The temperature of Solution: By newton's law of cooling (with approximation) $\frac{\Delta \mathrm{T}}{\Delta \mathrm{t}}=-\mathrm{C}\left(\mathrm{T}_{\text {avg }}-\mathrm{T}_{\mathrm{s}}\right)$ $1^{\mathrm{st}} \frac{-10^{\circ} \mathrm{C}}{5 \min }=-\mathrm{C}\left(70^{\circ} \mathrm{C}-25^{\circ} \mathrm{C}\right)$ $\Rightarrow \quad C=\frac{2}{45} \mi...
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