X different wavelengths
Question: $X$ different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number $\mathrm{n}=6$ ? The value of $\mathrm{X}$ is Solution: No. of different wavelengths $=\frac{\mathrm{n}(\mathrm{n}-1)}{2}$ $=\frac{6 \times(6-1)}{2}=\frac{6 \times 5}{2}=15$...
Read More →Four NOR gates are connected as shown in figure
Question: Four NOR gates are connected as shown in figure. The truth table for the given figure is : Correct Option: , 4 Solution: $y=\overline{(\overline{A+\overline{A+B}})+(\overline{B+\overline{A+B})}}$ $\mathrm{y}=(\mathrm{A}+\overline{\mathrm{A}+\mathrm{B}}) \cdot(\mathrm{B}+\overline{\mathrm{A}+\mathrm{B}})$ Ans. 4...
Read More →A body of mass M moving at speed
Question: A body of mass $M$ moving at speed $V_{0}$ collides elastically with a mass ' $m$ ' at rest. After the collision, the two masses move at angles $\theta_{1}$ and $\theta_{2}$ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio $\mathrm{M} / \mathrm{m}$, for which the angles $\theta_{1}$ and $\theta_{2}$ will be equal, is :4132Correct Option: , 3 Solution: given $\theta_{1}=\theta_{2}=\theta$ from momentum conservation in $\mathr...
Read More →Two simple harmonic motion,
Question: Two simple harmonic motion, are represented by the equations $\mathrm{y}_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right)$ $\mathrm{y}_{2}=5(\sin 3 \pi \mathrm{t}+\sqrt{3} \cos 3 \pi \mathrm{t})$ Ratio of amplitude of $y_{1}$ to $y_{2}=x: 1$. The value of $x$ is Solution: $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) \Rightarrow$ Amplitude $=10$ $y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$ $y_{2}=10\left(\frac{1}{2} \sin 3 \pi t+\frac{\sqrt{3}}{2} \cos 3 \pi t\right)$ $y_{2}=10\left...
Read More →A heat engine operates
Question: A heat engine operates between a cold reservoir at temperature $\mathrm{T}_{2}=400 \mathrm{~K}$ and a hot reservoir at temperature $\mathrm{T}_{1}$. It takes $300 \mathrm{~J}$ of heat from the hot reservoir and delivers $240 \mathrm{~J}$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be_____________K. Solution: $Q_{\text {in }}=300 \mathrm{~J} ; \mathrm{Q}_{\text {out }}=240 \mathrm{~J}$ Work done $=Q_{\text {in }}-Q_{\text {out }}=300-240...
Read More →A coil having N turns is wound tightly in the form of a spiral
Question: A coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. Find the magnetic field at centre, when a current I passes through coil:$\frac{\mu_{0} I N}{2(b-a)} \log _{e}\left(\frac{b}{a}\right)$$\frac{\mu_{0} \mathrm{I}}{8}\left[\frac{a+b}{a-b}\right]$$\frac{\mu_{0} I}{4(a-b)}\left[\frac{1}{a}-\frac{1}{b}\right]$$\frac{\mu_{0} I}{8}\left(\frac{a-b}{a+b}\right)$Correct Option: 1 Solution: No. of turns in $\mathrm{dx}$ width $=\fr...
Read More →Figure shows a rod
Question: Figure shows a rod $\mathrm{AB}$, which is bent in a $120^{\circ}$ circular arc of radius R. A charge (-Q) is uniformly distributed over rod $\mathrm{AB}$. What is the electric field $\vec{E}$ at the centre of curvature $O$ ? $\frac{3 \sqrt{3} \mathrm{Q}}{8 \pi \varepsilon_{0} \mathrm{R}^{2}}(\hat{\mathrm{i}})$$\frac{3 \sqrt{3} \mathrm{Q}}{8 \pi^{2} \varepsilon_{0} \mathrm{R}^{2}}(\hat{\mathrm{i}})$$\frac{3 \sqrt{3} \mathrm{Q}}{16 \pi^{2} \varepsilon_{0} \mathrm{R}^{2}}(\hat{\mathrm{i}...
Read More →The light waves from
Question: The light waves from two coherent sources have same intensity $\mathrm{I}_{1}=\mathrm{I}_{2}=\mathrm{I}_{0}$. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima ?$\mathrm{I}_{0}$$2 \mathrm{I}_{0}$$5 \mathrm{I}_{0}$$4 \mathrm{I}_{0}$Correct Option: , 4 Solution: $\mathrm{I}_{\max }=\left(\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}}\right)^{2}$ $=4 \mathrm{I}_{0}$...
Read More →A player kicks a
Question: A player kicks a football with an initial speed of $25 \mathrm{~ms}^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )$\mathrm{h}_{\max }=10 \mathrm{~m} \quad \mathrm{~T}=2.5 \mathrm{~s}$$\mathrm{h}_{\max }=15.625 \mathrm{~m} \quad \mathrm{~T}=3.54 \mathrm{~s}$$\mathrm{h}_{\max }=15.625 \mathrm{~m} \quad \mathrm{~T}=1.77 \mathrm{~s}$$\ma...
Read More →Solve this following
Question: An electric bulb of 500 watt at 100 volt is used in a circuit having a $200 \mathrm{~V}$ supply. Calculate the resistance $R$ to be connected in series with the bulb so that the power delivered by the bulb is $500 \mathrm{~W}$. $20 \Omega$$30 \Omega$$5 \Omega$$10 \Omega$Correct Option: 1 Solution: 500 watt at $100 \mathrm{v}$ $\mathrm{P}=\mathrm{V}_{1}$ $500=V_{i}$ $\mathrm{i}=5 \mathrm{Amp}$ $\mathrm{V}=\mathrm{i} \times \mathrm{R}$ $\mathrm{R}=20$ Ans. 1...
Read More →A sample of a radioactive nucleus A disintegrates
Question: A sample of a radioactive nucleus A disintegrates to another radioactive nucleus $B$, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B vesus time is : (Assume that at $\mathrm{t}=0$, there are no $\mathrm{B}$ atoms in the sample)Correct Option: , 2 Solution: Initially no. of atoms of $\mathrm{B}=0$ after $\mathrm{t}=0$, no. of atoms of $B$ will starts increasing \ reaches maximum value when rate of decay o...
Read More →The height of victoria falls
Question: The height of victoria falls is $63 \mathrm{~m}$. What is the difference in temperature of water at the top and at the bottom of fall? [Given $1 \mathrm{cal}=4.2 \mathrm{~J}$ and specific heat of water $\left.=1 \mathrm{cal} \mathrm{g}^{-1} \mathrm{C}^{-1}\right]$$0.147^{\circ} \mathrm{C}$$14.76^{\circ} \mathrm{C}$$1.476^{\circ}$$0.014^{\circ} \mathrm{C}$Correct Option: 1 Solution: Change in P.E. = Heat energy $\mathrm{mgh}=\mathrm{mS} \Delta \mathrm{T}$ $\Delta \mathrm{T}=\frac{\mathr...
Read More →For an ideal heat engine, the temperature of the source
Question: For an ideal heat engine, the temperature of the source is $127^{\circ} \mathrm{C}$. In order to have $60 \%$ efficiency the temperature of the sink should be___________ ${ }^{\circ} \mathrm{C}$. (Round off to the Nearest Integer) Solution: Ans. (-113) $\mathrm{n}=0.60=1=\frac{\mathrm{T}_{\mathrm{L}}}{\mathrm{T}_{\mathrm{H}}}$ $\frac{\mathrm{T}_{\mathrm{L}}}{\mathrm{T}_{\mathrm{H}}}=0.4 \Rightarrow \mathrm{T}_{\mathrm{L}}=0.4 \times 400$ $=160 \mathrm{~K}$ $=-113^{\circ} \mathrm{C}$...
Read More →A refrigerator consumes an average
Question: A refrigerator consumes an average $35 \mathrm{~W}$ power to operate between temperature $-10^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. If there is no loss of energy then how much average heat per second does it transfer ?$263 \mathrm{~J} / \mathrm{s}$$298 \mathrm{~J} / \mathrm{s}$$350 \mathrm{~J} / \mathrm{s}$$35 \mathrm{~J} / \mathrm{s}$Correct Option: 1 Solution: $\frac{T_{L}}{T_{H}-T_{L}}=$ C.O.P. $=\frac{\frac{d H}{d t}}{\frac{d W}{d t}}$ $\frac{263}{35} \times 35=\frac{\mat...
Read More →A coaxial cable consists
Question: A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii ' $b$ ' and 'c' respectively. The inner wire carries an electric current $\mathrm{i}_{0}$, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance $x$ from the axis when (i) $\mathrm{x}\mathrm{a}$ and (ii) $\mathrm{a}\mathrm{x}...
Read More →An object is placed at the focus of concave lens having
Question: An object is placed at the focus of concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?$1, \infty$Very high, $\infty$$\frac{1}{2}, \frac{f}{2}$$\frac{1}{4}, \frac{f}{4}$Correct Option: , 3 Solution: $U=-f$ $\frac{1}{V}-\frac{1}{U}=\frac{1}{-f} \Rightarrow \frac{1}{V}=-\frac{2}{f}$ $V=\frac{-f}{2}$ $\mathrm{m}=\frac{\mathrm{V}}{\mathrm{U}}=\frac{1}{2}$ distance $=\frac{f}{2}$ Option (3)...
Read More →A solid disc of radius 'a' and mass ' $m$ ' rolls down without slipping on anclined plane making an angle
Question: A solid disc of radius 'a' and mass ' $m$ ' rolls down without slipping on anclined plane making an angle $\theta$ with the horizontal. The acceleration of the disc will be $\frac{2}{b} g \sin \theta$ where $b$ is__________ (Round off to the Nearest Integer) $(g=$ acceleration due to gravity) $(\theta=$ angle as shown in figure $)$ Solution: Ans. (3) $\mathrm{a}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}}{\mathrm{mR}^{2}}}=\frac{\mathrm{g} \sin \theta}{1+\frac{1}{2}}=\frac{2}{3} ...
Read More →A reversible engine has an efficiency of
Question: A reversible engine has an efficiency of $\frac{1}{4}$. If the temperature of the sink is reduced by $58^{\circ} \mathrm{C}$, its efficiency becomes double. Calculate the temperature of the $\sin k$ :$174^{\circ} \mathrm{C}$$280^{\circ} \mathrm{C}$$180.4^{\circ} \mathrm{C}$$382^{\circ} \mathrm{C}$Correct Option: 1 Solution: $T_{2}=\operatorname{sink}$ temperature $\eta=1-\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}$ $\frac{1}{4}=1-\frac{T_{2}}{T_{1}}$ $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=...
Read More →If force
Question: If force $(\mathrm{F})$, length (L) and time $(\mathrm{T})$ are taken as the fundamental quantities. Then what will be the dimension of density :${\left[\mathrm{FL}^{-4} \mathrm{~T}^{2}\right] }$${\left[\mathrm{FL}^{-3} \mathrm{~T}^{2}\right] }$${\left[\mathrm{FL}^{-5} \mathrm{~T}^{2}\right] }$${\left[\mathrm{FL}^{-3} \mathrm{~T}^{3}\right] }$Correct Option: 1 Solution: Density $=\left[F^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}\right]$ ${\left[\mathrm{ML}^{-3}\right...
Read More →A transmitting antenna at top of a tower has a height of
Question: A transmitting antenna at top of a tower has a height of $50 \mathrm{~m}$ and the height of receiving antenna is $80 \mathrm{~m}$. What is range of communication for Line of Sight (LoS) mode ? [use radius of earth $=6400 \mathrm{~km}$ ]$45.5 \mathrm{~km}$$80.2 \mathrm{~km}$$144.1 \mathrm{~km}$$57.28 \mathrm{~km}$Correct Option: , 4 Solution: $\mathrm{d}_{\mathrm{t}}=\sqrt{2 \mathrm{Rh}_{1}}+\sqrt{2 \mathrm{Rh}_{2}}$ $=\sqrt{2 \mathrm{R}}\left(\sqrt{\mathrm{h}_{1}}+\sqrt{\mathrm{h}_{2}}...
Read More →Two particles A and B having charges
Question: Two particles A and B having charges $20 \mu \mathrm{C}$ and $-5 \mu \mathrm{C}$ respectively are held fixed with a separation of $5 \mathrm{~cm}$. At what position a third charged particle should be placed so that it does not experience a net electric force? At $5 \mathrm{~cm}$ from $20 \mu \mathrm{C}$ on the left side of systemAt $5 \mathrm{~cm}$ from $-5 \mu \mathrm{C}$ on the right sideAt $1.25 \mathrm{~cm}$ from $-5 \mu \mathrm{C}$ between two chargesAt midpoint between two charge...
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), (b)-(iii), (c)-(iv), (d)-(i)(a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)(a) -(iv), (b)-(ii), (c)-(i), (d)-(iii)(a) -(iii), (b)-(ii), (c)-(i), (d)-(iv)Correct Option: , 2 Solution: SI unit of Rydberg const. $=\mathrm{m}^{-1}$ SI unit of Plank's const. $=\mathrm{kg} \mathrm{m}^{2} \mathrm{~s}^{-1}$ SI unit of Magnetic field energy density $=k \mathrm{k} \mathrm{m}^{-1} \mathrm{~s}^{-2}$ SI un...
Read More →A closed organ pipe of length L and an open organ pipe contain gases
Question: A closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}$ where $x$ is__________ (Round off to the Nearest Integer) Solution: Ans. (4) $\mathrm{f}_{\mathrm{c}}=\mathrm{f}_{0}$ $\frac{3 \mathrm{~V}_{\mathrm{C}}}{4...
Read More →Solve this following
Question: At time $\mathrm{t}=0$, a material is composed of two radioactive atoms $A$ and $B$, where $\mathrm{N}_{\mathrm{A}}(0)=2 \mathrm{~N}_{\mathrm{B}}(0)$. The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to $B$ and $B$ disintegrates to $\mathrm{C}$. Which of the following figures represents the evolution of $\mathrm{N}_{\mathrm{B}}(\mathrm{t}) / \mathrm{N}_{\mathrm{B}}(0)$ with respect to time $\mathrm{t}$ ? $\left[\begin{array}{l}\mathrm{N}_{\mat...
Read More →A monochromatic neon
Question: A monochromatic neon lamp with wavelength of $670.5 \mathrm{~nm}$ illuminates a photo-sensitive material which has a stopping voltage of $0.48 \mathrm{~V}$. What will be the stopping voltage if the source light is changed with another source of wavelength of $474.6 \mathrm{~nm}$ ?$0.96 \mathrm{~V}$$1.25 \mathrm{~V}$$0.24 \mathrm{~V}$$1.5 \mathrm{~V}$Correct Option: , 2 Solution: $\mathrm{kE}_{\max }=\frac{\mathrm{hc}}{\lambda_{\mathrm{i}}}+\phi$ or $\quad \mathrm{eV}_{\mathrm{o}}=\frac...
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