An X-ray tube is
Question: An X-ray tube is operated at $1.24$ million volt. The shortest wavelength of the produced photon will be :$10^{-3} \mathrm{~nm}$$10^{-1} \mathrm{~nm}$$10^{-2} \mathrm{~nm}$$10^{-4} \mathrm{~nm}$Correct Option: 1 Solution: $\lambda_{\text {min }}=\frac{1240}{\Delta V}(\mathrm{~nm})$ $=\frac{1240}{1.24 \times 10^{6}}=10^{-3} \mathrm{~nm}$ Option (1) is correct....
Read More →In the given circuit of potentiometer,
Question: In the given circuit of potentiometer, the potential difference $\mathrm{E}$ across $\mathrm{AB}$ (10m length) is larger than $\mathrm{E}_{1}$ and $\mathrm{E}_{2}$ as well. For key $\mathrm{K}_{1}$ (closed), the jockey is adjusted to touch the wire at point $\mathbf{J}_{1}$ so that there is no deflection in the galvanometer. Now the first battery $\left(\mathrm{E}_{1}\right)$ is replaced by second battery $\left(E_{2}\right)$ for working by making $\mathrm{K}_{1}$ open and $\mathrm{K}_...
Read More →If one mole of an ideal gas
Question: If one mole of an ideal gas at $\left(\mathrm{P}_{1}, \mathrm{~V}_{1}\right)$ is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B \rightarrow C)$. Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to : $\mathrm{RT}\left...
Read More →A small bob tied at one end of a thin string
Question: A small bob tied at one end of a thin string of length $1 \mathrm{~m}$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the height position is_________ $\mathrm{m} / \mathrm{s}$. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ ) Solution: Let the speed of bob at lowest position be $\mathrm{v}_{1}$ and at the highest position be $v_{2}$. Maximum tension is at lowest position and minimum tension i...
Read More →The de Broglie wavelength
Question: The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :$4: 3$$4: 1$$4: 2$$1: 4$Correct Option: , 2 Solution: $\lambda=\frac{\mathrm{h}}{\mathrm{mv}}$ $\lambda_{\mathrm{P}}=\lambda_{\alpha}$ $m_{P} v_{P}=m_{\alpha} v_{\alpha}$ $m_{P} v_{P}=4 m_{p} v_{\alpha} \quad\left(m_{\alpha}=4 m_{P}\right)$ $\frac{\mathrm{v}_{\mathrm{P}}}{\mathrm{v}_{\alpha}}=4 \quad($ Option 2) is correct...
Read More →Figure shows a circuit that
Question: Figure shows a circuit that contains four identical resistors with resistance $\mathrm{R}=2.0 \Omega$, two identical inductors with inductance $\mathrm{L}=2.0 \mathrm{mH}$ and an ideal battery with emf $\mathrm{E}=9 \mathrm{~V}$. The current ' $i$ ' just after the switch 'S' is closed will be : $2.25 \mathrm{~A}$$3.0 \mathrm{~A}$$3.37 \mathrm{~A}$$9 \mathrm{~A}$Correct Option: 1 Solution: Just after the switch is closed, inductor will behave like infinite resistance (open circuit) so t...
Read More →In a certain thermodynamical process,
Question: In a certain thermodynamical process, the pressure of a gas depends on its volume as $\mathrm{kV}^{3}$. The work done when the temperature changes from $100^{\circ} \mathrm{C}$ to $300^{\circ} \mathrm{C}$ will be_________ $\mathrm{nR}$, where $\mathrm{n}$ denotes number of moles of a gas. Solution: $\mathrm{P}=\mathrm{kV}^{3}$ $\mathrm{T}_{\mathrm{i}}=100^{\circ} \mathrm{C} \ \mathrm{~T}_{\mathrm{f}}=300^{\circ} \mathrm{C}$ $\Delta \mathrm{T}=300-100$ $\Delta \mathrm{T}=200^{\circ} \ma...
Read More →Five equal resistances are connected in a network as shown in figure.
Question: Five equal resistances are connected in a network as shown in figure. The net resistance between the points $\mathrm{A}$ and $\mathrm{B}$ is : $2 R$$\frac{\mathrm{R}}{2}$$\frac{3 R}{2}$$\mathrm{R}$Correct Option: , 4 Solution: This diagram can be drawn like It is a wheat stone bridge $\therefore \mathrm{R}_{\mathrm{eq}}=\frac{2 \mathrm{R} \times 2 \mathrm{R}}{2 \mathrm{R}+2 \mathrm{R}} \Rightarrow \mathrm{R}$...
Read More →In the given figure,
Question: In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k$, the frequency of oscillation of given body is : $\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{2 \mathrm{M}}}$$\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k}}{\mathrm{Mg} \sin \alpha}}$$\frac{1}{2 \pi} \sqrt{\frac{2 k}{M}}$$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{k}}{\mathrm{Mg} \sin \alpha}}$Correc...
Read More →The electric field in a region is given
Question: The electric field in a region is given $\overrightarrow{\mathrm{E}}=\left(\frac{3}{5} \mathrm{E}_{0} \hat{\mathrm{i}}+\frac{4}{5} \mathrm{E}_{0} \hat{\mathrm{j}}\right) \frac{\mathrm{N}}{\mathrm{C}}$. The ratio of flux of reported field through the rectangular surface of area $0.2 \mathrm{~m}^{2}$ (parallel to $\mathrm{y}-\mathrm{z}$ plane) to that of the surface of area $0.3 \mathrm{~m}^{2}$ (parallel to $x-z$ plane) is $a: b$, where $a=$_________. [Here $\hat{\mathrm{i}}, \hat{\math...
Read More →A large number of water drops, each of radius
Question: A large number of water drops, each of radius $r$, combine to have a drop of radius $R$. If the surface tension is $\mathrm{T}$ and mechanical equivalent of heat is $J$, the rise in heat energy per unit volume will be:$\frac{2 \mathrm{~T}}{\mathrm{~J}}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$$\frac{2 \mathrm{~T}}{\mathrm{rJ}}$$\frac{3 \mathrm{~T}}{\mathrm{rJ}}$$\frac{3 \mathrm{~T}}{\mathrm{~J}}\left(\frac{1}{\mathrm{r}}-\frac{1}{\mathrm{R}}\right)$Correct Option: , 4 Solu...
Read More →Given below are two statements :
Question: Given below are two statements : Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement II : In the study of transistor, the amplification factor $\beta$ indicates ratio of the collector current to the base current. In the light of the above statements, choose the correct answer from the options given below:Statement I is false but Statement II is trueBoth Statement I and Statemen...
Read More →A transmitting station releases waves of wavelength
Question: A transmitting station releases waves of wavelength $960 \mathrm{~m}$. A capacitor of $2.56 \mu \mathrm{F}$ is used in the resonant circuit. The self inductance of coil necessary for resonance is__________ $\times 10^{-8} \mathrm{H}$. Solution: $\lambda=960 \mathrm{~m}$ $\mathrm{C}=2.56 \mu \mathrm{F}=2.56 \times 10^{-6} \mathrm{~F}$ $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ $L=?$ Now at resonance, $\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}$ [Resoant frequency] $2 \pi \mathrm...
Read More →The period of oscillation
Question: The period of oscillation of a simple pendulum is $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$. Measured value of 'L' is $1.0 \mathrm{~m}$ from meter scale having a minimum division of $1 \mathrm{~mm}$ and time of one complete oscillation is $1.95 \mathrm{~s}$ measured from stopwatch of $0.01 \mathrm{~s}$ resolution. The percentage error in the determination of ' $g$ ' will be :$1.13 \%$$1.03 \%$$1.33 \%$$1.30 \%$Correct Option: 1 Solution: $T=2 \pi \sqrt{\frac{\ell}{g}}$ $\...
Read More →Solve this following
Question: LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is $1.9 \mathrm{eV}$. Calculate the wavelength of light emitted and its colour. $\left[h=6.63 \times 10^{-34} \mathrm{Js}\right.$ and $\left.\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right]$$1046 \mathrm{~nm}$ and red colour$654 \mathrm{~nm}$ and orange colour$1046 \mathrm{~nm}$ and blue colour$654 \mathrm{~nm}$ and red colourCorrect Option: , 4 Solution: $\lambda=\frac{\mathrm{hc}}{\mathrm{E}}=\frac...
Read More →Two coherent light sources having intensity
Question: Two coherent light sources having intensity in the ratio $2 x$ produce an interference pattern. The ratio $\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}$ will be :$\frac{2 \sqrt{2 x}}{x+1}$$\frac{\sqrt{2 x}}{2 x+1}$$\frac{\sqrt{2 x}}{x+1}$$\frac{2 \sqrt{2 x}}{2 x+1}$Correct Option: , 4 Solution: Given that, $\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=2 \mathrm{x}$ We know, $I_{\max }=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2} \ I_{\min }=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}$ $\there...
Read More →Solve this
Question: The logic circuit shown above is equivalent to :Correct Option: , 4 Solution: Since option (1) has same truth table, hence answer is option (4) is correct. Alternative solution : Given Boolean expression can be written as $\overline{\mathrm{A}+\overline{\mathrm{B}}}=\mathrm{C}$ $\therefore \mathrm{C}=\overline{\mathrm{A}} \cdot \overline{\mathrm{B}}=\overline{\mathrm{A}} \cdot \mathrm{B}$...
Read More →Given below are two statements : one is labelled
Question: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : An electron microscope can achieve better resolving power than an optical microscope. Reason $\mathbf{R}$ : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below:$A$ is true but $R$ is false.Both $A$ and $R$ are t...
Read More →A soft ferromagnetic material
Question: A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :increase in size but no change in orientation.have no relation with external magnetic field.decrease in size and changes orientation.may increase or decrease in size and change its orientation.Correct Option: , 4 Solution: Soft ferromagnetic materials are materials which can be easily magnetised and demagnetised by external magnetic field. When external field is applied, the domains experiences...
Read More →The current (i) at time t = 0 and t = ∞ respectively for
Question: The current (i) at time $t=0$ and $t=\infty$ respectively for the given circuit is : $\frac{18 \mathrm{E}}{55}, \frac{5 \mathrm{E}}{18}$$\frac{10 \mathrm{E}}{33}, \frac{5 \mathrm{E}}{18}$$\frac{5 \mathrm{E}}{18}, \frac{18 \mathrm{E}}{55}$$\frac{5 \mathrm{E}}{18}, \frac{10 \mathrm{E}}{33}$Correct Option: , 4 Solution: At $\mathrm{t}=0$, current through inductor is zero, hence $\mathrm{R}_{\mathrm{eq}}=(5+1) \|(5+4)=\frac{18}{5}$ $i_{1}=\frac{E}{18 / 5}=\frac{5 E}{18}$ At $\mathrm{t}=\in...
Read More →The temperature
Question: The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $\mathrm{R}_{1}$ and $R_{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by : $\frac{\theta_{2} R_{2}-\theta_{1} R_{1}}{R_{2}-R_{1}}$$\frac{\theta_{1} R_{2}-\theta_{2} R_{1}}{R_{2}-R_{1}}$$\frac{\theta_{1} R_{2}+\theta_{2} R_{1}}{R_{1}+R_{2}}$$\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$Correct Option: , 3 Solution: Heat flow rat...
Read More →On the basis of kinetic theory of gases
Question: On the basis of kinetic theory of gases, the gas exerts pressure because its molecules :continuously lose their energy till it reaches wall.are attracted by the walls of container.continuously stick to the walls of container.suffer change in momentum when impinge on the walls of container.Correct Option: , 4 Solution: From the assumption of KTG, the molecules of gas collide with the walls and suffers momentum change which results in force on the wall and hence pressure. Hence option (4...
Read More →Two electrons each are fixed
Question: Two electrons each are fixed at a distance ' $2 d$ '. A third charge proton placed at the midpoint is displaced slightly by a distance $\mathrm{x}(\mathrm{x}\mathrm{d})$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : $(\mathrm{m}=$ mass of charged particle)$\left(\frac{2 \mathrm{q}^{2}}{\pi \varepsilon_{0} m d^{3}}\right)^{\frac{1}{2}}$$\left(\frac{\pi \varepsilon_{0} m d^{3}}{2 q^{2}}\right)^{\frac{1}{2}}$...
Read More →Given below are two statements : one is labelled as Assertion
Question: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass. Reason $R$ : The product of their mass and radius must be same, $\mathrm{M}_{1} \mathrm{R}_{1}=\mathrm{M}_{2} \mathrm{R}_{2}$ In the light of the above statements, choose the most appropriate answer from the options given below:Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\m...
Read More →If two similar springs each of spring constant
Question: If two similar springs each of spring constant $\mathrm{K}_{1}$ are joined in series, the new spring constant and time period would be changed by a factor:$\frac{1}{2}, \sqrt{2}$$\frac{1}{4}, \sqrt{2}$$\frac{1}{4}, 2 \sqrt{2}$$\frac{1}{2}, 2 \sqrt{2}$Correct Option: 1 Solution: $\frac{1}{\mathrm{k}_{e q}}=\frac{1}{\mathrm{k}_{1}}+\frac{1}{\mathrm{k}_{2}}$ $\frac{1}{k_{e q}}=\frac{1}{k}+\frac{1}{k} \Rightarrow k_{e q}=\frac{k}{2}$ $k^{\prime}=\frac{k}{2}$ $\mathrm{T}=2 \pi \sqrt{\frac{\...
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