Consider the following statements :
Question: Consider the following statements : A. Atoms of each element emit characteristics spectrum. B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. C. The density of nuclear matter depends on the size of the nucleus. D. A free neutron is stable but a free proton decay is possible. E. Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below :A, B, C, D and EA, B and E onlyB and D...
Read More →A radioactive substance decays to
Question: A radioactive substance decays to $\left(\frac{1}{16}\right)^{\text {th }}$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is________. Solution: $4 \times t_{1 / 2}=80$ $t_{1 / 2}=20$ days...
Read More →Two identical particles of mass 1 kg each go round a circle of radius R,
Question: Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :$\sqrt{\frac{G}{2 R^{3}}}$$\frac{1}{2} \sqrt{\frac{\mathrm{G}}{\mathrm{R}^{3}}}$$\frac{1}{2 R} \sqrt{\frac{1}{G}}$$\sqrt{\frac{2 G}{R^{3}}}$Correct Option: , 2 Solution: $F=\frac{\mathrm{Gm}^{2}}{(2 \mathrm{R})^{2}}=m R \omega^{2}$ $\omega=\frac{1}{2} \sqrt{\frac{G}{R^{3}}}$...
Read More →A body rotating with an angular speed of
Question: A body rotating with an angular speed of $600 \mathrm{rpm}$ is uniformly accelerated to $1800 \mathrm{rpm}$ in $10 \mathrm{sec}$. The number of rotations made in the process is_________. Solution: $\omega_{f}=\omega_{0}+\alpha t$ $\alpha=1200 \times 6$ $\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$ $=600 \times \frac{10}{60}+\frac{1}{2} \times 1200 \times 6 \times \frac{1}{36}$ $\theta=200$...
Read More →A certain metallic surface is illuminated by
Question: A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is $3 \mathrm{~V}_{0}$. If the same surface is illuminated with a radiation of wavelength $2 \lambda$, the stopping potential is $\mathrm{V}_{0}$. The threshold wavelength of this surface for photoelectric effect is_________$\lambda$. Solution: $\mathrm{KE}=\frac{\mathrm{hc}}{\lambda}-\phi \mathrm{hc}$ $\mathrm{e}\left(3 \math...
Read More →Figure A and B shown two long straight wires of circular cross-section
Question: Figure $A$ and $B$ shown two long straight wires of circular cross-section ( $a$ and $b$ with $ab$ ), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius $r$ and can be represented as: Correct Option: , 3 Solution: Graph for wire of radius R : As $ba$ $\mathrm{B}_{\mathrm{a}}\mathrm{B}_{\mathrm{b}}$ $\mathrm{B}_{\mathrm{a}}=\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{a}}$ $\mathrm{B}_{\mathrm{b}}=\frac{\mu_{0} \ma...
Read More →One mole of an ideal gas at
Question: One mole of an ideal gas at $27^{\circ} \mathrm{C}$ is taken from $\mathrm{A}$ to $\mathrm{B}$ as shown in the given $\mathrm{PV}$ indicator diagram. The work done by the system will be________ $\times 10^{-1} \mathrm{~J}$. Solution: Process of isothermal $\mathrm{W}=\mathrm{nRT} \ell \mathrm{n}\left(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\right)$ $=1 \times 8.3 \times 300 \times \ln 2$ $=17258 \times 10^{-1} \mathrm{~J}$...
Read More →Find the truth table for the function Y of A and B represented in the following figure.
Question: Find the truth table for the function Y of A and B represented in the following figure. Correct Option: , 2 Solution: $\mathrm{Y}=\mathrm{A} \cdot \mathrm{B}+\overline{\mathrm{B}}$...
Read More →A series LCR circuit of
Question: A series $L C R$ circuit of $R=5 \Omega, L=20 \mathrm{mH}$ and $\mathrm{C}=0.5 \mu \mathrm{F}$ is connected across an AC supply of $250 \mathrm{~V}$, having variable frequency. The power dissipated at resonance condition is___________ $\times 10^{2} \mathrm{~W}$. Solution: $\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}}$ (due to resonance) $\mathrm{Z}=\mathrm{R}$ so $\mathrm{i}_{\mathrm{rms}}=\frac{\mathrm{V}}{\mathrm{Z}}=\frac{\mathrm{V}}{\mathrm{R}}$ $\frac{\mathrm{V}^{2}}{\mathrm{R...
Read More →Two Carnot engines A and B operate in series such that engine A absorbs heat
Question: Two Carnot engines A and B operate in series such that engine $A$ absorbs heat at $T_{1}$ and rejects heat to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by Engine A and rejects heat to the sink at $\mathrm{T}_{3}$. When workdone in both the cases is equal, to value of $T$ is :$\frac{2}{3} \mathrm{~T}_{1}+\frac{3}{2} \mathrm{~T}_{3}$$\frac{1}{3} \mathrm{~T}_{1}+\frac{2}{3} \mathrm{~T}_{3}$$\frac{3}{2} \mathrm{~T}_{1}+\frac{1}{3} \mathrm{~T}_{3}$$\frac{2}{3} ...
Read More →For the forward biased diode characteristics shown in the figure,
Question: For the forward biased diode characteristics shown in the figure, the dynamic resistance at $\mathrm{I}_{\mathrm{D}}=3 \mathrm{~mA}$ will be_____$\Omega .$ Solution: $\mathrm{R}_{\mathrm{d}}=\frac{\mathrm{dV}}{\mathrm{di}}=\frac{1}{\frac{\mathrm{di}}{\mathrm{dv}}}=\frac{1}{\frac{5-1 \times 10^{-3}}{0.75-0.65}}$ $\frac{100}{4}=25 \Omega$...
Read More →Two bodies, a ring and a solid cylinder of same material
Question: Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$. Then, the value of $x$ is__________. Solution: I in both cases is about point of contact Ring $\mathrm{mgh}=\frac{1}{2} \mathrm{I} \omega^{2}$ $\mathrm{mgh}=\frac{1}{2}\left(2 \mathrm{mR}^{2}\right) \frac{...
Read More →A simple pendulum of mass 'm',
Question: A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be $\tan ^{-1}\left[\frac{\mathrm{q}}{\mathrm{mg}} \times \frac{\mathrm{C}_{1}\left(\mathrm{~V}_{2}-\mathrm{V}_{1}\right)}{\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right)(\mathrm{d}-\mathrm{t})}\right]$$\tan ^{-1}\left[\frac{q}{m g} \times \frac{C_{2}\left(V_{2}-V_{1}\right)}{\left(C_{1...
Read More →In the given figure switches
Question: In the given figure switches $S_{1}$ and $S_{2}$ are in open condition. The resistance across ab when the Switches $S_{1}$ and $S_{2}$ are closed is________ $\Omega .$ Solution: when switch $S_{1}$ and $S_{2}$ are closed $\frac{12 \times 6}{12+6}+2+\frac{6 \times 12}{6+12}$ $\frac{72}{18}+2+\frac{72}{18}=4+2+4=10 \Omega$...
Read More →solve this
Question: A $100 \Omega$ resistance, a $0.1 \mu \mathrm{F}$ capacitor and an inductor are connected in series across a $250 \mathrm{~V}$ supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is $60 \mathrm{~Hz}$.0.70 H70.3 mH$7.03 \times 10^{-5} \mathrm{H}$70.3 HCorrect Option: , 4 Solution: $\mathrm{C}=0.1 \mu \mathrm{F}=10^{-7} \mathrm{~F}$ Resonant frequency = 60 Hz $\omega_{0}=\frac{1}{\sqrt{L C}}$ $2 \pi ...
Read More →A body of mass ' m ' is launched up on a rough inclined
Question: A body of mass ' $m$ ' is launched up on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$ if the time of ascent is half of the time of descent. The value of $x$ is_________. Solution: $\mathrm{t}_{\mathrm{a}}=\frac{1}{2} \mathrm{t}_{\mathrm{d}}$ $\sqrt{\frac{2 \mathrm{~s}}{\mathrm{a}_{\mathrm{a}}}}=\frac{1}{2} \sqrt{\frac{2 \mathrm{~s}}{\mathrm{a}_{\mathrm{d}}}}$ .............(i) $...
Read More →A zener diode having zener voltage
Question: A zener diode having zener voltage $8 \mathrm{~V}$ and power dissipation rating of $0.5 \mathrm{~W}$ is connected across a potential divider arranged with maximum potential drop across zener diode is as shown in the diagram. The value of protective resistance $R_{p}$ is............$\Omega$ Solution: $\mathrm{P}=\mathrm{Vi}$ $0.5=8 \mathrm{i}$ $\mathrm{i}=\frac{1}{16} \mathrm{~A}$ $E=20=8+i R_{P}$ $\mathrm{R}_{\mathrm{P}}=12 \times 16=192 \Omega$...
Read More →The magnetic susceptibility of a material
Question: The magnetic susceptibility of a material of a rod is 499 . Permeability in vacuum is $4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$. Absolute permeability of the material of the rod is :$4 \pi \times 10^{-4} \mathrm{H} / \mathrm{m}$$2 \pi \times 10^{-4} \mathrm{H} / \mathrm{m}$$3 \pi \times 10^{-4} \mathrm{H} / \mathrm{m}$$\pi \times 10^{-4} \mathrm{H} / \mathrm{m}$Correct Option: , 2 Solution: $\mu=\mu_{0}\left(1+x_{m}\right)$ $=4 \pi \times 10^{-7} \times 500$ $=2 \pi \times 10^{-4}...
Read More →Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion,
Question: Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is : at $\mathrm{x}\mathrm{x}_{4}, \mathrm{~K}$.E. is constant throughout the region.at $xx_{1}, K . E$. is smallest and the particle is moving at the slowest speed.at $x=x_{2}, K . E$. is greatest and the particle is moving at the fastest speed.at $x=x_{3...
Read More →Two small drops of mercury each of radius R coalesce
Question: Two small drops of mercury each of radius $R$ coalesce to form a single large drop. The ratio of total surface energy before and after the change is :$2^{\frac{1}{3}}: 1$$1: 2^{\frac{1}{3}}$$2: 1$$1: 2$Correct Option: 1 Solution: $\frac{4}{3} \pi \mathrm{R}^{3}+\frac{4}{3} \pi \mathrm{R}^{3}=\frac{4}{3} \pi \mathrm{R}^{13}$ $R^{\prime}=2^{\frac{1}{3}} R$ ............(i) $\mathrm{A}_{\mathrm{i}}=2\left[4 \pi \mathrm{R}^{2}\right]$ $\mathrm{A}_{\mathrm{f}}=4 \pi \mathrm{R}^{\prime 2}$ $\...
Read More →Match List I with List II
Question: Match List I with List II Choose the correct answer from the options given below(a) $\rightarrow$ (iii), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iv), (d) $\rightarrow$ (i)(a) $\rightarrow$ (iii), (b) $\rightarrow$ (iv), (c) $\rightarrow$ (ii), (d) $\rightarrow$ (i)(a) $\rightarrow$ (iv), (b) $\rightarrow$ (ii), (c) $\rightarrow$ (iii), (d) $\rightarrow$ (i)(a) $\rightarrow$ (iv), (b) $\rightarrow$ (iii), (c) $\rightarrow($ ii $)$, (d) $\rightarrow$ (i)Correct Option: 1 Solution: q =...
Read More →Two vectors P and Q have equal magnitudes.
Question: Two vectors $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ have equal magnitudes. If the magnitude of $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}$ is $n$ times the magnitude of $\vec{P}-\vec{Q}$, then angle between $\vec{P}$ and $\vec{Q}$ is :$\sin ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)$$\cos ^{-1}\left(\frac{\mathrm{n}-1}{\mathrm{n}+1}\right)$$\sin ^{-1}\left(\frac{n^{2}-1}{n^{2}+1}\right)$$\cos ^{-1}\left(\frac{n^{2}-1}{n^{2}+1}\right)$Corre...
Read More →An object of mass 0.5 kg is executing simple harmonic motion.
Question: An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $t=\frac{T}{4} s$ starting from mean position. Assume that the initial phase of the oscillation is zero.0.62 J$6.2 \times 10^{-3} \mathrm{~J}$$1.2 \times 10^{3} \mathrm{~J}$$6.2 \times 10^{3} \mathrm{~J}$Correct Option: 1 Solution: $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$ $0.2=2 \pi \sqrt{\frac{0.5}...
Read More →A body at rest is moved along a horizontal straight line by
Question: A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time ' $t$ ' is proportional to:$t^{\frac{3}{2}}$$t^{\frac{1}{2}}$$t^{\frac{1}{4}}$$t^{\frac{3}{4}}$Correct Option: 1 Solution: $\mathrm{P}=$ constant $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{Pt}$ $\Rightarrow \mathrm{v} \propto \sqrt{\mathrm{t}}$ $\frac{d x}{d t}=C \sqrt{t}$ $\mathrm{C}=\mathrm{constant}$ by integration. $\mathrm{x}=\mathrm{C} \frac{\mathrm{...
Read More →One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C.
Question: One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27C to 37C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? $\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{k}^{-1}\right]$work done by the gas is close to 332 Jwork done on the gas is close to 582 Jwork done by the gas is close to 582 Jwork done on the gas is close to 332 JCorrect Option: , 4 Solution: Since, e...
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