For the circuit shown below,
Question: For the circuit shown below, calculate the value of $\mathrm{I}_{\mathrm{z}}$ : $25 \mathrm{~mA}$$0.15 \mathrm{~A}$$0.1 \mathrm{~A}$$0.05 \mathrm{~A}$Correct Option: 1 Solution: $I=\frac{50}{1000}=50 \mathrm{~mA}$ $I=\frac{50}{2000}=25 \mathrm{~mA}$ $\mathrm{I}_{\mathrm{Z}}=\mathrm{I}_{1000}-\mathrm{I}_{2000}$ $=50-25=25 \mathrm{~mA}$...
Read More →In the reported figure,
Question: In the reported figure, two bodies $A$ and $B$ of masses $200 \mathrm{~g}$ and $800 \mathrm{~g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _____________ $\mathrm{rad} / \mathrm{s}$ when $\mathrm{k}=20 \mathrm{~N} / \mathrm{m}$. Solution: $\omega=\sqrt{\frac{k_{e q}}{\mu}}$ $\mu=$ reduced mass springs are in series c...
Read More →What should be the height of transmitting antenna and
Question: What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of $150 \mathrm{~km}$ ? The average population density around the tower is $2000 / \mathrm{km}^{2}$ and the value of $\mathrm{R}_{\mathrm{e}}=6.5 \times 10^{6} \mathrm{~m}$. Height $=1731 \mathrm{~m}$ Population Covered $=1413 \times 10^{5}$Height $=1241 \mathrm{~m}$ Population Covered $=7 \times 10^{5}$Height $=1600 \mathrm{~m}$ Population Covered $=2 \times 10^...
Read More →The value of tension in a long thin metal wire has been changed
Question: The value of tension in a long thin metal wire has been changed from $\mathrm{T}_{1}$ to $\mathrm{T}_{2}$. The lengths of the metal wire at two different values of tension $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are $\ell_{1}$ and $\ell_{2}$ respectively. The actual length of the metal wire is :$\frac{T_{1} \ell_{2}-T_{2} \ell_{1}}{T_{1}-T_{2}}$$\frac{T_{1} \ell_{1}-T_{2} \ell_{2}}{T_{1}-T_{2}}$$\frac{\ell_{1}+\ell_{2}}{2}$$\sqrt{T_{1} T_{2} \ell_{1} \ell_{2}}$Correct Option: 1 Solution:...
Read More →A circular conducting coil
Question: A circular conducting coil of radius $1 \mathrm{~m}$ is being heated by the change of magnetic field $\overrightarrow{\mathrm{B}}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2 \mu \Omega$. The magnetic field is slowly switched off such that its magnitude changes in time as $\mathrm{B}=\frac{4}{\pi} \times 10^{-3} \mathrm{~T}\left(1-\frac{\mathrm{t}}{100}\right)$ The energy dissipated by the coil before the magnetic field is switched off...
Read More →A light cylindrical vessel is kept on a horizontal surface.
Question: A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a A) : $\frac{\mathrm{A}}{2 \mathrm{a}}$None of these$\frac{2 a}{A}$$\frac{\mathrm{a}}{\mathrm{A}}$Correct Option: , 3 Solution: For no sliding $f \geq \rho a v^{2}$ $\mu m g \geq \rho a v^{2}$ $\mu \rho A h g \geq \r...
Read More →Match List-I with List-II :
Question: Match List-I with List-II : Choose the correct answer from the options given below:$(\mathrm{a})-($ ii $) ;(\mathrm{b})-(\mathrm{i}) ;(\mathrm{c})-(\mathrm{iv}) ;(\mathrm{d})-(\mathrm{iii})$$(\mathrm{a})-($ ii $) ;(\mathrm{b})-(\mathrm{i}) ;(\mathrm{c})-($ (iii) $)$ (d) $-$ (iv)(a) $-($ iii $) ;(\mathrm{b})-($ i $) ;(\mathrm{c})-($ iv $) ;(\mathrm{d})-($ ii $)$$(a)-($ iv $) ;(b)-($ iii $) ;(\mathrm{c})-($ ii $) ;(\mathrm{d})-(\mathrm{i})$Correct Option: 1 Solution: (a) For $\mathrm{x}_...
Read More →An inductor of
Question: An inductor of $10 \mathrm{mH}$ is connected to a $20 \mathrm{~V}$ battery through a resistor of $10 \mathrm{k} \Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1 \mu \mathrm{s}$ is $\frac{\mathrm{x}}{100} \mathrm{~mA}$. Then $\mathrm{x}$ is equal to __________ (Take $\left.\mathrm{e}^{-1}=0.37\right)$ Solution: $\mathrm{I}_{\max }=\frac{\mathrm{V}}{\mathrm{R}}=\frac{20 \mathrm{~V}}{10...
Read More →Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that
Question: Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}=4 \overrightarrow{\mathrm{AO}}+\overrightarrow{\mathrm{OB}}+\overrightarrow{\mathrm{OC}}$ Reason R : Polygon law of vector addition yields $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{BC}}+\overrightarrow{\mathrm{CD}}+\overrightarrow{\mathrm{AD}}=2 \overrightarrow{\mathrm{AO}}$ In the light of th...
Read More →A butterfly is flying with a velocity
Question: A butterfly is flying with a velocity $4 \sqrt{2} \mathrm{~m} / \mathrm{s}$ in North-East direction. Wind is slowly blowing at $1 \mathrm{~m} / \mathrm{s}$ from North to South. The resultant displacement of the butterfly in 3 seconds is :$3 \mathrm{~m}$$20 \mathrm{~m}$$12 \sqrt{2} \mathrm{~m}$$15 \mathrm{~m}$Correct Option: , 4 Solution: $\vec{V}_{B W}=4 \sqrt{2} \cos 45 \hat{i}+4 \sqrt{2} \sin 45 \hat{j}$ $=4 \hat{i}+4 \hat{j}$ $\overrightarrow{\mathrm{V}}_{\mathrm{W}}=-\hat{\mathrm{j...
Read More →Student A and Student B
Question: Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322 \mathrm{~cm}$. The absolute value of the difference between the final circular scale readings observed by the students A and $B$ is [Figure shows position of reference 'O' when jaws of screw gauge are closed] Given pitch $=0.1 \mathrm{~cm}$. Solution: For (A) Reading $=$ MSR $+$ CSR $+$ Error $0.322=0.3...
Read More →An electron of mass
Question: An electron of mass $m_{e}$ and a proton of mass $m_{p}$ are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is :-$\frac{m_{p}}{m_{e}}$1$\sqrt{\frac{m_{\mathrm{P}}}{\mathrm{m}_{e}}}$$\frac{m_{e}}{m_{p}}$Correct Option: , 3 Solution: $\mathrm{KE}=\mathrm{e} \Delta \mathrm{V}$ $\lambda_{e}=\frac{\mathrm{h}}{\sqrt{2 m_{e}(e \Delta V)}}$ $\lambda_{p}=\frac{h}{\sqrt{2 m_{p}(e \Delta V)}}$ $\Righta...
Read More →Consider a mixture of gas molecule of types
Question: Consider a mixture of gas molecule of types $A, B$ and $\mathrm{C}$ having masses $\mathrm{m}_{\mathrm{A}}\mathrm{m}_{\mathrm{B}}\mathrm{m}_{\mathrm{C}}$. The ratio of their root mean square speeds at normal temperature and pressure is :$\mathrm{v}_{\mathrm{A}}=\mathrm{v}_{\mathrm{B}}=\mathrm{v}_{\mathrm{C}}=0$$\frac{1}{\mathrm{~V}_{\mathrm{A}}}\frac{1}{\mathrm{~V}_{\mathrm{B}}}\frac{1}{\mathrm{v}_{\mathrm{C}}}$$\mathrm{v}_{\mathrm{A}}=\mathrm{v}_{\mathrm{B}} \neq \mathrm{v}_{\mathrm{C...
Read More →In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas.
Question: In the reported figure, there is a cyclic process ABCDA on a sample of $1 \mathrm{~mol}$ of a diatomic gas. The temperature of the gas during the process $\mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{C} \rightarrow \mathrm{D}$ are $\mathrm{T}_{1}$ and $\mathrm{T}_{2}\left(\mathrm{~T}_{1}\mathrm{T}_{2}\right)$ respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.$\mathrm{W}_{\mathrm{AB}}=\mathrm{W}_{\mathrm{DC}}$$W_{A D}=W_{B...
Read More →A body of mass
Question: A body of mass $2 \mathrm{~kg}$ moving with a speed of $4 \mathrm{~m} / \mathrm{s}$. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10} \mathrm{~m} / \mathrm{s}$. Then the value of $\mathrm{x}$ is Solution: $\mathrm{p}_{\mathrm{i}}=\mathrm{p}_{\mathrm{f}}$ $2 \times 4=2 \times 1+\mathrm{m}_{2} \times \mathrm{v}_{2}$ $\mathrm{m}_{2} \mathr...
Read More →A nucleus with mass number 184 initially at rest emits an
Question: A nucleus with mass number 184 initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is $5.5 \mathrm{MeV}$, calculate the kinetic energy of the $\alpha-$ particle.$5.0 \mathrm{MeV}$$5.5 \mathrm{MeV}$$0.12 \mathrm{MeV}$$5.38 \mathrm{MeV}$Correct Option: , 4 Solution: $\frac{1}{2}(4 \mathrm{~m}) \mathrm{v}^{2}+\frac{1}{2}(180 \mathrm{~m})\left(\frac{4 \mathrm{v}}{180}\right)^{2}=5.5 \mathrm{MeV}$ $\Rightarrow \quad \frac{1}{2} 4 \mathrm{mv}^{2}\left[1+45\left(\fr...
Read More →A current of 5 A is passing through a non-linear
Question: A current of $5 \mathrm{~A}$ is passing through a non-linear magnesium wire of cross-section $0.04 \mathrm{~m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (Resistivity of magnesium $\rho=44 \times 10^{-8} \Omega \mathrm{m}$ )$11 \times 10^{-2} \mathrm{~V} / \mathrm{m}$$11 \times 10^{-7} \mathrm{~V} / \mathrm{m}$$11 \times 10^{-5} \m...
Read More →The minimum and maximum
Question: The minimum and maximum distances of a planet revolving around the Sun are $x_{1}$ and $x_{2}$. If the minimum speed of the planet on its trajectory is $v_{0}$ then its maximum speed will be :$\frac{\mathrm{v}_{0} \mathrm{x}_{1}^{2}}{\mathrm{x}_{2}^{2}}$$\frac{\mathrm{v}_{0} \mathrm{x}_{2}^{2}}{\mathrm{x}_{1}^{2}}$$\frac{\mathrm{V}_{0} \mathrm{x}_{1}}{\mathrm{x}_{2}}$$\frac{\mathrm{V}_{0} \mathrm{X}_{2}}{\mathrm{X}_{1}}$Correct Option: , 4 Solution: Angular momentum conservation equati...
Read More →Consider a situation in which reverse biased current of a particular P-N
Question: Consider a situation in which reverse biased current of a particular P-N junction increases when it is exposed to a light of wavelength $\leq 621 \mathrm{~nm}$. During this process, enhancement in carrier concentration takes place due to generation of hole-electron pairs. The value of band gap is nearly.$2 \mathrm{eV}$$4 \mathrm{eV}$$1 \mathrm{eV}$$0.5 \mathrm{eV}$Correct Option: 1 Solution: Band gap $=\frac{h c}{\lambda_{0}}$ $\lambda_{0} ;$ threshold wavelength Band gap $=\frac{1242 ...
Read More →In Young's double slit experiment, if the source of light changes from orange to blue then :
Question: In Young's double slit experiment, if the source of light changes from orange to blue then :the central bright fringe will become a dark fringe.the distance between consecutive fringes will decreasethe distance between consecutive fringes will increase.the intensity of the minima will increase.Correct Option: , 2 Solution: Sol. Fringe width $=\lambda \mathrm{D} / \mathrm{d}$ as $\lambda$ decreases, fringe width also decreases...
Read More →Water droplets are coming from
Question: Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{\text {th }}$ second after its fall to the next droplet is $34.3 \mathrm{~m}$. At what rate the droplets are coming from the tap ? (Take $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$ )3 drops / 2 seconds2 drops / second1 drop / second1 drop $/ 7$ secondsCorrect Option: , 3 Solution: In 4 sec. $1^{\text {st }}$ drop will travel $\Rightarrow \frac{1}{2} \times(9.8) \times(4)^{2}...
Read More →A certain charge Q is divided into two parts
Question: A certain charge $\mathrm{Q}$ is divided into two parts $\mathrm{q}$ and (Q-q). How should the charges Q and $q$ be divided so that $\mathrm{q}$ and $(\mathrm{Q}-\mathrm{q})$ placed at a certain distance apart experience maximum electrostatic repulsion?$\mathrm{Q}=\frac{\mathrm{q}}{2}$$Q=2 q$$Q=4 q$$Q=3 q$Correct Option: , 2 Solution: $\mathrm{F}_{\mathrm{q}}=\frac{\mathrm{kq}(\mathrm{Q}-\mathrm{q})}{\mathrm{L}^{2}}=\frac{\mathrm{k}}{\mathrm{L}^{2}}\left(\mathrm{qQ}-\mathrm{q}^{2}\righ...
Read More →The figure shows two solid discs with radius R and r respectively.
Question: The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia) $\mathrm{R}^{2}: \mathrm{r}^{2}$$2 r^{4}: R^{4}$$2 R^{2}: r^{2}$$2 R^{4}: r^{4}$Correct Option: , 4 Solution: Rati...
Read More →Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping.
Question: Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:-The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plan...
Read More →In amplitude modulation,
Question: In amplitude modulation, the message signal $\mathrm{V}_{\mathrm{m}}(\mathrm{t})=10 \sin \left(2 \pi \times 10^{5} \mathrm{t}\right)$ volts and Carrier signal $V_{C}(t)=20 \sin \left(2 \pi \times 10^{7} t\right)$ volts The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is $\alpha \mathrm{kHz}$. The value of $\alpha$ is :$200 \mathrm{kHz}$$50 \mathrm{kHz}$$100 \mathrm{kHz}$0Correct Option: ...
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