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Question: A $2 \mu \mathrm{F}$ capacitor $\mathrm{C}_{1}$ is first charged to a potential difference of $10 \mathrm{~V}$ using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor $\mathrm{C}_{2}$ of $8 \mu \mathrm{F}$. The charge in $\mathrm{C}_{2}$ on equilibrium condition is $\mu \mathrm{C}$. (Round off to the Nearest Integer) Solution: $20=\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right) \mathrm{V} \Rightarrow \mathrm{V}=2$ volt. $\mathrm{Q}_{2}=\mathrm{C}...
Read More →Two narrow bores of diameter
Question: Two narrow bores of diameter $5.0 \mathrm{~mm}$ and $8.0 \mathrm{~mm}$ are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water $\mathrm{T}=7.3 \times 10^{-2} \mathrm{Nm}^{-1}$, angle of contact $=0, \mathrm{~g}=10 \mathrm{~ms}^{-2}$ and density of water $=1.0 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ]$3.62 \mathrm{~mm}$$2.19 \mathrm{~mm}$$5.34 \mathrm{~...
Read More →The image of an object
Question: The image of an object placed in air formed by a convex refracting surface is at a distance of $10 \mathrm{~m}$ behind the surface. The image is real and is at $\frac{2^{\text {rd }}}{3}$ of the distance of the object from the surface .The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13} \mathrm{~m}$. the value of ' $x$ ' is Solution: $\lambda_{\mathrm{m}}=\frac{\lambda_{\mathrm{a}}}{\mu} \Rightarrow ...
Read More →A person is swimming with a speed of
Question: A person is swimming with a speed of $10 \mathrm{~m} /$ s at an angle of $120^{\circ}$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is ' $x$ ' $\mathrm{m} / \mathrm{s}$. The value of ' $x$ ' to the nearest integer is___________. Solution: $10 \sin 30^{\circ}=x$ $x=5 \mathrm{~m} / \mathrm{s}$...
Read More →The disc of mass
Question: The disc of mass $M$ with uniform surface mass density $\sigma$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{\mathrm{x}}{3} \frac{\mathrm{a}}{\pi}, \frac{\mathrm{x}}{3} \frac{\mathrm{a}}{\pi}$ where $\mathrm{x}$ is___________ (Round off to the Nearest Integer) [a is an area as shown in the figure] Solution: C.O.M of quarter disc is at $\frac{4 a}{3 \pi}, \frac{4 a}{3 \pi}$ $=4$...
Read More →The first three spectral lines of H-atom in the Balmer series are given
Question: The first three spectral lines of H-atom in the Balmer series are given $\lambda_{1}, \lambda_{2}, \lambda_{3}$ considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left(\frac{\lambda_{1}}{\lambda_{3}}\right)$ are related by a factor of approximately ' $x$ ' $\times 10^{-1}$. The value of $x$, to the nearest integer, is_____________ Solution: For $1^{\text {st }}$ line $\frac{1}{\lambda_{1}}=R z^{2}\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)$ $\frac{...
Read More →The electric field
Question: The electric field in a region is given by $\overrightarrow{\mathrm{E}}=\frac{2}{5} \mathrm{E}_{0} \hat{\mathrm{i}}+\frac{3}{5} \mathrm{E}_{0} \hat{\mathrm{j}}$ with $\mathrm{E}_{0}=4.0 \times 10^{3} \frac{\mathrm{N}}{\mathrm{C}}$. The flux of this field through a rectangular surface area $0.4 \mathrm{~m}^{2}$ parallel to the $\mathrm{Y}-\mathrm{Z}$ plane is _____$\mathrm{Nm}^{2} \mathrm{C}^{-1}$. Solution: $\phi=\mathrm{E}_{\mathrm{x}} \mathrm{A} \Rightarrow \frac{2}{5} \times 4 \time...
Read More →Two separate wires A and B are stretched by
Question: Two separate wires A and B are stretched by $2 \mathrm{~mm}$ and $4 \mathrm{~mm}$ respectively, when they are subjected to a force of $2 \mathrm{~N}$. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire $A$. The length of the wires $A$ and $B$ are in the ratio of $a: b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is________. Solution: For A $\frac{\mathrm{E}}{\pi \mathrm{r}^{2}}=\mathrm{y} \frac{2 \mathrm{~mm}}{...
Read More →A particle of mass
Question: A particle of mass $\mathrm{m}$ moves in a circular orbit in a central potential field $\mathrm{U}(\mathrm{r})=\mathrm{U}_{0} \mathrm{r}^{4}$. If Bohr's quantization conditions are applied, radii of possible orbitals $r_{n}$ vary with $n^{1 / \alpha}$, where $\alpha$ is ___________ Solution: $\mathrm{F}=\frac{-\mathrm{dU}}{\mathrm{dr}}=-4 \mathrm{U}_{0} \mathrm{r}^{3}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$ $m v^{2}=4 U_{0} r^{4}$ $V \propto r^{2}$ $m v r=\frac{n h}{2 \pi}$ $\mathrm{r}^{3}...
Read More →The voltage across the
Question: The voltage across the $10 \Omega$ resistor in the given circuit is $\mathrm{x}$ volt. The value of ' $x$ ' to the nearest integer is________. Solution: $\mathrm{R}_{\mathrm{eq}_{1}}=\frac{50 \times 20}{70}=\frac{100}{7}$ $\mathrm{R}_{\mathrm{eq}}=\frac{170}{7}$ $v_{1}=\left[\frac{170}{\frac{170}{7}}\right] \times 10=70 \mathrm{v}$ Ans. $=70.00$...
Read More →Suppose you have taken
Question: Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01 \mathrm{~cm}^{3}$ of oleic acid per $\mathrm{cm}^{3}$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4 \mathrm{~cm}^{2}$ by considering 100 spherical drops of radius $\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3} \mathrm{~cm}$. Then the thickness of oleic acid layer will be $\mathrm{x} \times 10^{-14} \mathrm{~m}$. Where ...
Read More →Consider a 20 kg uniform circular disk of radius 0.2 m.
Question: Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50 \mathrm{rad} \mathrm{s}^{-1}$. The value of $\mathrm{n}$, to the nearest integer, is [Given : In one complete revolution, the disk rotates by $6.28 \mathrm{rad}...
Read More →Inside a uniform spherical shell :
Question: Inside a uniform spherical shell : (a) the gravitational field is zero (b) the gravitational potential is zero (c) the gravitational field is same everywhere (d) the gravitation potential is same everywhere (e) all of the above Choose the most appropriate answer from the options given below :(a), (c) and (d) only(e) only(a), (b) and (c) only(b), (c) and (d) onlyCorrect Option: 1 Solution: Inside a spherical shell, gravitational field is zero and hence potential remains same everywhere ...
Read More →A boy of mass
Question: A boy of mass $4 \mathrm{~kg}$ is standing on a piece of wood having mass $5 \mathrm{~kg}$. If the coefficient of friction between the wood and the floor is $0.5$, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is_________N.(Round off to the Nearest Integer) [Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ] Solution: $\mathrm{N}+\mathrm{T}=90$ $\mathrm{~T}=\mu \mathrm{N}=0.5(90-\mathrm{T})$ $1.5 \mathrm{~T}=45$ $\mathrm{T}=30$...
Read More →The circuit shown in the figure consists of
Question: The circuit shown in the figure consists of a charged capacitor of capacity $3 \mu \mathrm{F}$ and a charge of $30 \mu \mathrm{C}$. At time $\mathrm{t}=0$, when the key is closed, the value of current flowing through the $5 \mathrm{M} \Omega$ resistor is ' $x^{\prime} \mu-A$. The value of 'x to the nearest integer is_________. Solution: $\mathrm{i}_{0}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{30 / 3}{5 \times 10^{6}}=2 \times 10^{-6}$...
Read More →Car B overtakes another car A at a relative speed of
Question: Car B overtakes another car A at a relative speed of $40 \mathrm{~ms}^{-1}$. How fast will the image of car B appear to move in the mirror of focal length $10 \mathrm{~cm}$ fitted in car $\mathrm{A}$, when the car $\mathrm{B}$ is $1.9 \mathrm{~m}$ away from the car A? $4 \mathrm{~ms}^{-1}$$0.2 \mathrm{~ms}^{-1}$$40 \mathrm{~ms}^{-1}$$0.1 \mathrm{~ms}^{-1}$Correct Option: , 4 Solution: Mirror used is convex mirror (rear-view mirror) $\therefore \mathrm{V}_{\mathrm{L} / \mathrm{m}}=-\mat...
Read More →A body of mass
Question: A body of mass $1 \mathrm{~kg}$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F \mathrm{~N}$. The value of $F$ will be __________ (Round off to the Nearest Integer) [Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ] Solution: $\mathrm{F} \cos \theta=\mu \mathrm{N}$ $\mathrm{F} \sin \theta+\mathrm{N}=\mathrm{mg}$ $\Rightarrow \mathrm{F}=\frac{\mu \mathrm{mg}}{\cos \t...
Read More →A particle performs simple harmonic motion
Question: A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{\mathrm{a}} \mathrm{s}$. The value of 'a' to the nearest integer is___________. Solution: $t=\frac{2}{12}=\frac{1}{6}$ $\therefore$ Correct answer $=6.00$...
Read More →A fringe width of 6 mm was produced for two slits separated by 1 mm apart.
Question: A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x' to the nearest integer is ______. Solution: $\beta=\frac{\lambda \mathrm{D}}{\mathrm{d}}$ $\lambda=\frac{\beta \mathrm{d}}{\mathrm{D}}$ $\lambda=\frac{6 \times 10^{-3} \times 10^{-3}}{10}$ $\lambda=6 \times 10^{-7} \mathrm{~m}=600 \times 10^{-9} \mathrm{~m}$ $\lambda=600 \mathrm{~nm}$...
Read More →The electric field intensity
Question: The electric field intensity produced by the radiation coming from a $100 \mathrm{~W}$ bulb at a distance of $3 \mathrm{~m}$ is E. The electric field intensity produced by the radiation coming from $60 \mathrm{~W}$ at the same distance is $\sqrt{\frac{\mathrm{x}}{5}} \mathrm{E}$. Where the value of $x=$ Solution: $\mathrm{c} \in_{0} \mathrm{E}^{2}=\frac{100}{4 \pi \times 3^{2}}$ $c \in_{0}\left(\sqrt{\frac{\mathrm{x}}{5}} \mathrm{E}\right)^{2}=\frac{60}{4 \pi \times 3^{2}}$ $\Rightarro...
Read More →The time period of a satellite in a circular orbit
Question: The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9 \mathrm{R}$ is :$9 \mathrm{~T}$$27 \mathrm{~T}$$12 \mathrm{~T}$$3 \mathrm{~T}$Correct Option: , 2 Solution: $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\left(\frac{T^{\prime}}{T}\right)^{2}=\left(\frac{9 R}{R}\right)^{3}$ $T^{\prime 2}=T^{2} \times 9^{3}$ $T^{\prime}=T \times 3^{3}$ $T^{\prime}=27 T$...
Read More →A sphere of mass
Question: A sphere of mass $2 \mathrm{~kg}$ and radius $0.5 \mathrm{~m}$ is rolling with an initial speed of $1 \mathrm{~ms}^{-1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How low will the sphere take to return to the starting point $\mathrm{A}$ ? $0.60 \mathrm{~s}$$0.52 \mathrm{~s}$$0.57 \mathrm{~s}$$0.80 \mathrm{~s}$Correct Option: , 3 Solution: (3) $\mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^{2}}}...
Read More →In the figure given, the electric current flowing
Question: In the figure given, the electric current flowing through the $5 \mathrm{k} \Omega$ resistor is ' $\mathrm{x}$ ' $\mathrm{mA}$. The value of x to the nearest integer is_________ Solution: $I=\frac{21}{5+1+1}=3 \mathrm{~mA}$...
Read More →The magnitude of vectors
Question: The magnitude of vectors $\overrightarrow{\mathrm{OA}}, \overrightarrow{\mathrm{OB}}$ and $\overrightarrow{\mathrm{OC}}$ in the given figure are equal. The direction of $\overrightarrow{\mathrm{OA}}+\overrightarrow{\mathrm{OB}}-\overrightarrow{\mathrm{OC}}$ with $\mathrm{x}$-axis will be :- $\tan ^{-1} \frac{(1-\sqrt{3}-\sqrt{2})}{(1+\sqrt{3}+\sqrt{2})}$$\tan ^{-1} \frac{(\sqrt{3}-1+\sqrt{2})}{(1+\sqrt{3}-\sqrt{2})}$$\tan ^{-1} \frac{(\sqrt{3}-1+\sqrt{2})}{(1-\sqrt{3}+\sqrt{2})}$$\tan ...
Read More →A loop of flexible wire of irregular shape carrying current
Question: A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.Loop assumes circular shape with its plane normal to the field.Loop assumes circular shape with its plane parallel to the field.Wire gets stretched to become straight.Shape of the loop remains unchanged.Correct Option: 1 Solution: Every part $(\mathrm{d} \ell)$ of the wire is pulled by force $\mathrm{i}(\mathrm{d} \ell) \mathrm{B}$ acting per...
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