Match List-I with List-II.
Question: Match List-I with List-II. Choose the most appropriate answer from the option given below :(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)Correct Option: 1 Solution: torque $\tau \rightarrow \mathrm{ML}^{2} \mathrm{~T}^{-2}$ (III) Impulse I $\Rightarrow \mathrm{MLT}^{-1}$ (I) Tension force $\Rightarrow \mathrm{MLT}^{-2}$ (IV) Surface tension $\Rightarrow \mathrm{MT}^{-2}$ (II) Optio...
Read More →If the maximum value of accelerating potential provided by a ratio frequency oscillator is
Question: If the maximum value of accelerating potential provided by a ratio frequency oscillator is $12 \mathrm{kV}$. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is $\left[\mathrm{m}_{\mathrm{p}}=1.67 \times 10^{-27} \mathrm{~kg}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right.$ Speed of light $\left.=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right]$ Solution: $\mathrm{V}=12 \mathrm{kV}$ Number of revolution $=\mathrm{n}$ $\mathrm{n}\left[...
Read More →A source of light is placed in front of a screen.
Question: A source of light is placed in front of a screen. Intensity of light on the screen is I. Two Polaroids $P_{1}$ and $P_{2}$ are so placed in between the source of light and screen that the intensity of light on screen is $\mathrm{I} / 2 . \mathrm{P}_{2}$ should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3 \mathrm{I}}{8}$. Solution: $I=\frac{I_{0}}{2} \cos ^{2} \phi$ $\frac{I}{2} \cos ^{2} \phi=\frac{3 I}{8}$ $\cos ^{2} \phi=\frac{3}{4...
Read More →A tuning fork is vibrating
Question: A tuning fork is vibrating at $250 \mathrm{~Hz}$. The length of the shortest closed organ pipe that will resonate with the tuning fork will be $\mathrm{cm}$. (Take speed of sound in air as $340 \mathrm{~ms}^{-1}$ ) Solution: $\frac{\lambda}{4}=\ell \Rightarrow \lambda=4 \ell$ $\mathrm{f}=\frac{\mathrm{V}}{\lambda}=\frac{\mathrm{V}}{4 \ell}$ $\Rightarrow 250=\frac{340}{4 \ell}$ $\Rightarrow \ell=\frac{34}{4 \times 25}=0.34 \mathrm{~m}$ $\ell=34 \mathrm{~cm}$...
Read More →A plane electromagnetic wave
Question: A plane electromagnetic wave with frequency of $30 \mathrm{MHz}$ travels in free space. At particular point in space and time, electric field is $6 \mathrm{~V} / \mathrm{m}$. The magnetic field at this point will be $x \times 10^{-8} \mathrm{~T}$. The value of $x$ is Solution: $|\mathrm{B}|=\frac{|\mathrm{E}|}{\mathrm{C}}=\frac{6}{3 \times 10^{8}}$ $=2 \times 10^{-8} \mathrm{~T}$ $\therefore x=2$...
Read More →Two waves are simultaneously passing through a string and their equations are :
Question: Two waves are simultaneously passing through a string and their equations are : $\mathrm{y}_{1}=\mathrm{A}_{1} \sin \mathrm{k}(\mathrm{x}-\mathrm{vt}), \mathrm{y}_{2}=\mathrm{A}_{2} \sin \mathrm{k}\left(\mathrm{x}-\mathrm{vt}+\mathrm{x}_{0}\right)$. Given amplitudes $\mathrm{A}_{1}=12 \mathrm{~mm}$ and $\mathrm{A}_{2}=5 \mathrm{~mm}$, $\mathrm{x}_{0}=3.5 \mathrm{~cm}$ and wave number $\mathrm{k}=6.28 \mathrm{~cm}^{-1}$. The amplitude of resulting wave will be ........ $\mathrm{mm}$. So...
Read More →Two plane mirrors M_1 and M_2 are at right angle to
Question: Two plane mirrors $M_{1}$ and $M_{2}$ are at right angle to each other shown. A point source ' $P$ ' is placed at ' $a$ ' and ' $2 a^{\prime}$ meter away from $\mathrm{M}_{1}$ and $\mathrm{M}_{2}$ respectively. The shortest distance between the images thus formed is : (Take $\sqrt{5}=2.3$ ) $3 a$$4.6 \mathrm{a}$$2.3 \mathrm{a}$$2 \sqrt{10} \mathrm{a}$Correct Option: , 2 Solution: Shortest distance is $2 \mathrm{a}$ between $\mathrm{I}_{1} \ \mathrm{I}_{3}$ But answer given is for $\mat...
Read More →Two blocks of masses
Question: Two blocks of masses $3 \mathrm{~kg}$ and $5 \mathrm{~kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2} \mathrm{Nm}^{-2}$. What is the minimum radius of the wire? $\left(\right.$ Take $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$ $125 \mathrm{~cm}$$1250 \mathrm{~cm}$$12.5 \mathrm{~cm}$$1.25 \mathrm{~cm}$Correct Option: , 3 Solution: $\mathrm{T}=\frac{2 \mathrm{~m}_{1} \mathrm{~m}_{2} \mathrm{~g}}{\mathrm{~m...
Read More →The ratio of the equivalent
Question: The ratio of the equivalent resistance of the network (shown in figure) between the points a and $b$ when switch is open and switch is closed is $\mathrm{x}: 8$. The value of $\mathrm{x}$ is Solution: $\mathrm{R}_{\text {eq open }}=\frac{3 \mathrm{R}}{2}$ $\mathrm{R}_{\text {eq closed }}=2 \times \frac{\mathrm{R} \times 2 \mathrm{R}}{3 \mathrm{R}}=\frac{4 \mathrm{R}}{3}$ $\frac{\mathrm{R}_{\mathrm{cq} \text { opcn }}}{\mathrm{R}_{\text {cq closed }}}=\frac{3 \mathrm{R}}{2} \times \frac...
Read More →The ranges and heights for two projectiles projected with the same initial velocity at angles
Question: The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $\mathrm{R}_{1}, \mathrm{R}_{2}$ and $\mathrm{H}_{1}$, $\mathrm{H}_{2}$ respectively. Choose the correct option:$\mathrm{R}_{1}\mathrm{R}_{2}$ and $\mathrm{H}_{1}=\mathrm{H}_{2}$$\mathrm{R}_{1}=\mathrm{R}_{2}$ and $\mathrm{H}_{1}\mathrm{H}_{2}$$\mathrm{R}_{1}\mathrm{R}_{2}$ and $\mathrm{H}_{1}\mathrm{H}_{2}$$\mathrm{R}_{1}=\mathrm{R}_{2}$ a...
Read More →An ac circuit has an inductor
Question: An ac circuit has an inductor and a resistor of resistance $\mathrm{R}$ in series, such that $\mathrm{X}_{\mathrm{L}}=3 \mathrm{R}$. Now, a capacitor is added in series such that $X_{C}=2 R$. The ratio of new power factor with the old power factor of the circuit is $\sqrt{5}: \mathrm{x}$. The value of $\mathrm{x}$ is Solution:...
Read More →A body of mass ' m ' dropped from a height ' h '
Question: A body of mass ' $m$ ' dropped from a height ' $h$ ' reaches the ground with a speed of $0.8 \sqrt{\mathrm{gh}}$. The value of workdone by the air-friction is :$-0.68 \mathrm{mgh}$$\mathrm{mgh}$$1.64 \mathrm{mgh}$$0.64 \mathrm{mgh}$Correct Option: 1 Solution: Work done $=$ Change in kinetic energy $\mathrm{W}_{\mathrm{mg}}+\mathrm{W}_{\text {air-friction }}=\frac{1}{2} \mathrm{~m}(.8 \sqrt{\mathrm{gh}})^{2}-\frac{1}{2} \mathrm{~m}(0)^{2}$ $\mathrm{~W}_{\text {air }-\text { friction }}=...
Read More →If the length of the pendulum in pendulum clock increases
Question: If the length of the pendulum in pendulum clock increases by $0.1 \%$, then the error in time per day is: $86.4 \mathrm{~s}$$4.32 \mathrm{~s}$$43.2 \mathrm{~s}$$8.64 \mathrm{~s}$Correct Option: , 3 Solution: $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$ $\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{1}{2} \frac{\Delta \ell}{\ell}$ $\Delta \mathrm{T}=\frac{1}{2} \times \frac{0.1}{100} \times 24 \times 3600$ $\Delta \mathrm{T}=43.2$ Ans. 3...
Read More →A bullet of
Question: A bullet of $10 \mathrm{~g}$, moving with velocity $v$, collides head-on with the stationary bob of a pendulum and recoils with velocity $100 \mathrm{~m} / \mathrm{s}$. The length of the pendulum is $0.5 \mathrm{~m}$ and mass of the bob is $1 \mathrm{~kg}$. The minimum value of $v=$ $\mathrm{m} / \mathrm{s}$ so that the pendulum describes a circle. (Assume the string to be inextensible and $g=10 \mathrm{~m} / \mathrm{s}^{2}$ ) Solution: $V^{\prime}=\sqrt{5 \mathrm{gR}}=\sqrt{5 \times 1...
Read More →A uniform heavy rod of weight
Question: A uniform heavy rod of weight $10 \mathrm{~kg} \mathrm{~ms}^{-2}$, crosssectional area $100 \mathrm{~cm}^{2}$ and length $20 \mathrm{~cm}$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \mathrm{Nm}^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight.$2 \times 10^{-9} \mathrm{~m}$$5 \times 10^{-8} \mathrm{~m}$$4 \times 10^{-8} \mathrm{~m}$$5 \times 10^{-10} \mathrm{~m}$Correct Option: , 4 Solution: W...
Read More →The temperature of an ideal gas in 3 -dimensions is 300K.
Question: The temperature of an ideal gas in 3 -dimensions is $300 \mathrm{~K}$. The corresponding de-Broglie wavelength of the electron approximately at $300 \mathrm{~K}$, is: ${\left[\mathrm{m}_{\mathrm{e}}=\right.$ mass of electron $=9 \times 10^{-31} \mathrm{~kg}}$ $\mathrm{h}=$ Planck constant $=6.6 \times 10^{-34} \mathrm{Js}$ $\mathrm{k}_{\mathrm{B}}=$ Boltzmann constant $\left.=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right]$$6.26 \mathrm{~nm}$$8.46 \mathrm{~nm}$$2.26 \mathrm{~nm}$$3.25 \ma...
Read More →In the given circuit the
Question: In the given circuit the $\mathrm{AC}$ source has $\omega=100 \mathrm{rad} \mathrm{} \mathrm{s}^{-1}$. Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit? $5.9 \mathrm{~A}$$4.24 \mathrm{~A}$$0.94 \mathrm{~A}$$6 \mathrm{~A}$Correct Option: , 2 Solution: $Z_{C}=\sqrt{\left(\frac{1}{\omega C}\right)^{2}+R^{2}}$ $=\sqrt{\left(\frac{1}{100 \times 100 \times 10^{-6}}\right)^{2}+100^{2}}$ $Z_{\mathrm{C}}=\sqrt{(100)^{2}+(100)^{2}}$ $=100...
Read More →Choose the correct waveform that can represent the voltage
Question: Choose the correct waveform that can represent the voltage across $R$ of the following circuit, assuming the diode is ideal one: Correct Option: , 3 Solution: When $\mathrm{V}_{\mathrm{i}}3$ volt, $\mathrm{V}_{\mathrm{R}}0$ Because diode will be in forward biased state When $\mathrm{V}_{\mathrm{i}} \leq 3$ volt $; \mathrm{V}_{\mathrm{R}}=0$ Because diode will be in reverse biased state....
Read More →Solve this
Question: Wires $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ are made of same material having the breaking stress of $1.25 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ have cross-sectional area of $8 \times 10^{-7} \mathrm{~m}^{2}$ and $4 \times 10^{-7} \mathrm{~m}^{2}$, respectively. Masses of $20 \mathrm{~kg}$ and $10 \mathrm{~kg}$ hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is $\mathrm{kg} ____...
Read More →A square loop of side 20cm and resistance
Question: A square loop of side $20 \mathrm{~cm}$ and resistance $1 \Omega$ is moved towards right with a constant speed $v_{0}$. The right arm of the loop is in a uniform magnetic field of $5 \mathrm{~T}$. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value $4 \Omega$. What should be the value of $v_{0}$ so that a steady current of $2 \mathrm{~mA}$ flows in the loop ? $1 \mathrm{~m} / \mathrm{s}$$1 \mathrm{~cm} ...
Read More →Match List-I with List-II.
Question: Match List-I with List-II. Choose the most appropriate answer from the options given below : (a)-(ii) $,(\mathrm{b})-(\mathrm{iv}),(\mathrm{c})-(\mathrm{i}),(\mathrm{d})-($ iii $)$(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)Correct Option: , 4 Solution: (a) Magnetic Induction $=\mathrm{MT}^{-2} \mathrm{~A}^{-1}$ (b) Magnetic Flux $=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}$ (c) Magnetic Permeability $=\mathrm...
Read More →A zener diode of power rating
Question: A zener diode of power rating $2 \mathrm{~W}$ is to be used as a voltage regulator. If the zener diode has a breakdown of $10 \mathrm{~V}$ and it has to regulate voltage fluctuated between $6 \mathrm{~V}$ and $14 \mathrm{~V}$, the value of $\mathrm{R}_{\mathrm{s}}$ for safe operation should be $\Omega .$ Solution: When unregulated voltage is $14 \mathrm{~V}$ voltage across zener diode must be $10 \mathrm{~V}$ So potential difference across resistor $\Delta \mathrm{V}_{\mathrm{Rs}}=4 \m...
Read More →A small square loop of side ' a ' and one turn is placed
Question: A small square loop of side ' $a$ ' and one turn is placed inside a larger square loop of side $b$ and one turn $(ba)$. The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side ' $b$ ', then the coefficient of mutual inductance between the two loops is :$\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{\mathrm{a}^{2}}{\mathrm{~b}}$$\frac{\mu_{0}}{4 \pi} \frac{8 \sqrt{2}}{a}$$\frac{\mu_{0}}{4 \pi} 8 \sqrt{2} \frac{b^{2}}{a}$$\frac{\mu_{0}}{4 ...
Read More →A cube is placed inside an electric field,
Question: A cube is placed inside an electric field, $\overrightarrow{\mathrm{E}}=150 \mathrm{y}^{2} \hat{\mathrm{j}}$. The side of the cube is $0.5 \mathrm{~m}$ and is placed in the field as shown in the given figure. The charge inside the cube is: $3.8 \times 10^{-11} \mathrm{C}$$8.3 \times 10^{-11} \mathrm{C}$$3.8 \times 10^{-12} \mathrm{C}$$8.3 \times 10^{-12} \mathrm{C}$Correct Option: , 2 Solution: As electric field is in y-direction so electric flux is only due to top and bottom surface B...
Read More →The masses and radii of the earth and moon are
Question: The masses and radii of the earth and moon are $\left(\mathrm{M}_{1}, \mathrm{R}_{1}\right)$ and $\left(\mathrm{M}_{2}, \mathrm{R}_{2}\right)$ respectively. Their centres are at a distance ' $r$ ' apart. Find the minimum escape velocity for a particle of mass ' $m$ ' to be projected from the middle of these two masses:$V=\frac{1}{2} \sqrt{\frac{4 G\left(M_{1}+M_{2}\right)}{r}}$$\mathrm{V}=\sqrt{\frac{4 \mathrm{G}\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}{\mathrm{r}}}$$\mathrm{V}=\frac...
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