Prove the following
Question: If $\overrightarrow{\mathrm{P}} \times \overrightarrow{\mathrm{Q}}=\overrightarrow{\mathrm{Q}} \times \overrightarrow{\mathrm{P}}$, the angle between $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ is $\theta\left(0^{\circ}\theta360^{\circ}\right)$. The value of ' $\theta^{\prime}$ will be_______ $\circ$. Solution: $-P Q \sin \theta$ $=P Q \sin \theta$ $\Rightarrow \theta=180^{\circ}$...
Read More →The percentage increase in the speed of transverse waves produced
Question: The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4 \%$, will be______ $\%$. Solution: $v=\sqrt{\frac{T}{\mu}}$ $\frac{\Delta V}{V}=\frac{1}{2} \frac{\Delta T}{T}$...
Read More →The equivalent resistance
Question: The equivalent resistance of series combination of two resistors is ' $s$ '. When they are connected in parallel, the equivalent resistance is ' $p$ '. If $s=n p$, then the minimum value for $n$ is (Round off to the Nearest Integer) Solution: $\mathrm{R}_{1}+\mathrm{R}_{2}=\mathrm{s}$...(1) $\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}=\mathrm{p}$...(2) $\mathrm{R}_{1} \mathrm{R}_{2}=\mathrm{sp}$ $\mathrm{R}_{1} \mathrm{R}_{2}=\mathrm{np}^{2}$ $\mathrm{R}_{1}+\ma...
Read More →A reversible heat engine converts one-fourth
Question: A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52 \mathrm{~K}$, its efficiency is doubled. The temperature in Kelvin of the source will be_______. Solution: $\eta=\frac{1}{4}=1-\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}$ $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{3}{4}$ $\frac{T_{2}-52}{T_{1}}=\frac{1}{2}$...
Read More →A reversible heat engine converts one-fourth
Question: A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by $52 \mathrm{~K}$, its efficiency is doubled. The temperature in Kelvin of the source will be_______. Solution: $\eta=\frac{1}{4}=1-\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}$ $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{3}{4}$ $\frac{T_{2}-52}{T_{1}}=\frac{1}{2}$...
Read More →Solve this following
Question: Draw the output signal $Y$ in the given combination of gates :- Correct Option: , 4 Solution: According to gates by Demorgan's law $\overline{\overline{\mathrm{A}}+\mathrm{B}}=\mathrm{A} \cdot \overline{\mathrm{B}}$ By observation....
Read More →The angular speed of truck
Question: The angular speed of truck wheel is increased from $900 \mathrm{rpm}$ to $2460 \mathrm{rpm}$ in 26 seconds. The number of revolutions by the truck engine during this time is (Assuming the acceleration to be uniform). Solution: We know, $\theta=\left(\frac{\omega_{1}+\omega_{2}}{2}\right) \mathrm{t}$ Let number of revolutions be $\mathrm{N}$ $\therefore 2 \pi N=2 \pi\left(\frac{900+2460}{60 \times 2}\right) \times 26$ $\mathrm{N}=728$...
Read More →The wavelength of an X-ray beam is
Question: The wavelength of an X-ray beam is 10A The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3} \mathrm{~h} \mathrm{~kg}$. The value of $x$ is__________. $(h=$ Planck's constant $)$ Solution: $\frac{\mathrm{hc}}{\lambda}=\mathrm{mc}^{2}$ $\mathrm{m}=\frac{\mathrm{h}}{\mathrm{c} \lambda}$...
Read More →For VHF signal broadcasting,
Question: For VHF signal broadcasting, ___________- $\mathrm{km}^{2}$ of maximum service area will be covered by an antenna tower of height $30 \mathrm{~m}$, if the receiving antenna is placed at ground. Let radius of the earth be $6400 \mathrm{~km}$. (Round off to the Nearest Integer) (Take $\pi$ as $3.14$ ) Solution: $\mathrm{d}=\sqrt{2 \mathrm{Rh}}$ $\mathrm{A}=\pi \mathrm{d}^{2}$ $\mathrm{~A}=\pi 2 \mathrm{Rh}$ $=3.14 \times 2 \times 6400 \times \frac{30}{1000}$ $\mathrm{A}=1205.76 \mathrm{~...
Read More →The initial velocity v_i required to project a body
Question: The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10 \mathrm{R}$, where $\mathrm{R}$ is the radius of the earth, may be described in terms of escape velocity $v_{\mathrm{e}}$ such that $v_{i}=\sqrt{\frac{x}{y}} \times v_{\mathrm{e}}$. The value of $x$ will be________. Solution: $\frac{-\mathrm{GMm}}{11 \mathrm{R}}=\frac{-\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$ $v=\sqrt{\frac{20 G M}{11 R}}$...
Read More →Solve this following
Question: Two masses $A$ and $B$, each of mass $M$ are fixed together by a massless spring. A force acts on the mass $\mathrm{B}$ as shown in figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B wil be :- $\frac{\mathrm{Ma}-\mathrm{F}}{\mathrm{M}}$$\frac{\mathrm{MF}}{\mathrm{F}+\mathrm{Ma}}$$\frac{\mathrm{F}+\mathrm{Ma}}{\mathrm{M}}$$\frac{\mathrm{F}-\mathrm{Ma}}{\mathrm{M}}$Correct Option: , 4 Solution: $a_{c m}=\frac{m_{1} a_{1}+m_{2} a_{2...
Read More →Two small spheres each of mass 10mg
Question: Two small spheres each of mass $10 \mathrm{mg}$ are suspended from a point by threads $0.5 \mathrm{~m}$ long. They are equally charged and repel each other to a distance of $0.20 \mathrm{~m}$. The charge on each of the sphere is $\frac{\mathrm{a}}{21} \times 10^{-8} \mathrm{C}$. The value of 'a' will is_________. [Given $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ] Solution: $\mathrm{T} \cos \theta=\mathrm{mg}=10 \times 10^{-6} \times 10=10^{-4}$ $\mathrm{T} \sin \theta=\frac{9 \times 10^{9} \ti...
Read More →A current of
Question: A current of $10 \mathrm{~A}$ exists in a wire of crosssectional area of $5 \mathrm{~mm}^{2}$ with a drift velocity of $2 \times 10^{-3} \mathrm{~ms}^{-1}$. The number of free electrons in each cubic meter of the wire is$2 \times 10^{6}$$625 \times 10^{25}$$2 \times 10^{25}$$1 \times 10^{23}$Correct Option: , 2 Solution: $\mathrm{i}=10 \mathrm{~A}, \mathrm{~A}=5 \mathrm{~mm}^{2}=5 \times 10^{-6} \mathrm{~m}^{2}$ and $v_{d}=2 \times 10^{-3} \mathrm{~m} / \mathrm{s}$ We know, $\quad \mat...
Read More →Solve this following
Question: The recoil speed of a hydrogen atom after it emits a photon in going from $\mathrm{n}=5$ state to $\mathrm{n}=1$ state will be :-$4.17 \mathrm{~m} / \mathrm{s}$$2.19 \mathrm{~m} / \mathrm{s}$$3.25 \mathrm{~m} / \mathrm{s}$$4.34 \mathrm{~m} / \mathrm{s}$Correct Option: 1 Solution: ( $\Delta \mathrm{E})$ Releases when photon going from $\mathrm{n}=5$ to $\mathrm{n}=\Delta \mathrm{E}=(13.6-0.54) \mathrm{eV}=13.06 \mathrm{eV}$ $\mathrm{P}_{\mathrm{i}}=\mathrm{P}_{\mathrm{f}}($ By linear mo...
Read More →The peak electric field produced by the radiation coming from
Question: The peak electric field produced by the radiation coming from the $8 \mathrm{~W}$ bulb at a distance of $10 \mathrm{~m}$ is $\frac{x}{10} \sqrt{\frac{\mu_{0} \mathrm{c}}{\pi}} \frac{\mathrm{V}}{\mathrm{m}}$. The efficiency of the bulb is $10 \%$ and it is a point source. The value of $x$ is_________. Solution: $I=\frac{1}{2} \mathrm{c} \in_{0} \mathrm{E}_{0}^{2}$ $\frac{8}{4 \pi \times 10^{2}} \times \frac{1}{2}=\frac{1}{4} \times \mathrm{c} \times \frac{1}{\mu_{0} c^{2}} \times \mathr...
Read More →Two ideal polyatomic gases
Question: Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed so that there is no loss of energy. If $F_{1}$ and $F_{2}, m_{1}$ and $m_{2}, n_{1}$ and $n_{2}$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :$\frac{\mathrm{n}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \mathrm{~T}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$$\frac{\mathrm{n}_{1} \mathrm{~F}_{1} \mathrm{~T}_{1}+\mathrm{n}_{2} \ma...
Read More →Consider the diffraction pattern obtained from the sunlight
Question: Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter $0.1 \mu \mathrm{m}$. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such thtat :its size decreases, and intensity decreasesits size increases, and intensity increasesits size increases, but intensity decreasesits size decreases, but intensity increasesCorrect Option: , 4 Solution: $\sin \theta=\frac{m \lambda}{a}$ when a increases, $\theta$ decrea...
Read More →Which level of the
Question: Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?1648Correct Option: , 2 Solution: Energy of H-atom is $\mathrm{E}=-13.6 \mathrm{Z}^{2} / \mathrm{n}^{2}$ for $H$-atom $Z=1$ \ for ground state, $n=1$ $\Rightarrow \mathrm{E}=-13.6 \times \frac{1^{2}}{1^{2}}=-13.6 \mathrm{eV}$ Now for carbon atom (single ionised), $Z=6$ $E=-13.6 \frac{Z^{2}}{n^{2}}=-13.6$ $\Rightarrow n^{2}=6^{2} \Rightarrow n=6$...
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)-(ii), (b)-(iv), (c)-(i), (d)-(iii)(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)Correct Option: 1 Solution: (a) Rectifier $\rightarrow$ AC to DC (b) Stabilizer $\rightarrow$ used for constant output voltage even when input voltage or current change. (c) Transformer $\rightarrow$ Step - up or step - down ac voltage. (d) Filter $\right...
Read More →An inclined plane making an angle of
Question: An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field $200 \frac{\mathrm{N}}{\mathrm{C}}$ as shown in the figure. A body of mass $1 \mathrm{~kg}$ and charge $5 \mathrm{mC}$ is allowed to slide down from rest at a height of $1 \mathrm{~m}$. If the coefficient of friction is $0.2$, find the time taken by the body to reach the bottom. $\left[g=9.8 \mathrm{~m} / \mathrm{s}^{2}, \sin 30^{\circ}=\frac{1}{2}\right.$ $\left.\cos ...
Read More →A boy is rolling a
Question: A boy is rolling a $0.5 \mathrm{~kg}$ ball on the frictionless floor with the speed of $20 \mathrm{~ms}^{-1}$. The ball gets deflected by an obstacle on the way. After deflection it moves with $5 \%$ of its initial kinetic energy. What is the speed of the ball now ?$19.0 \mathrm{~ms}^{-1}$$4.47 \mathrm{~ms}^{-1}$$14.41 \mathrm{~ms}^{-1}$$1.00 \mathrm{~ms}^{-1}$Correct Option: , 2 Solution: Given, $\mathrm{m}=0.5 \mathrm{~kg}$ and $\mathrm{u}=20 \mathrm{~m} / \mathrm{s}$ Initial kinetic...
Read More →The stopping potential for electrons emitted from
Question: The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength $491 \mathrm{~nm}$ is $0.710 \mathrm{~V}$. When the incident wavelength is changed to a new value, the stopping potential is $1.43 \mathrm{~V}$. The new wavelength is :$329 \mathrm{~nm}$$309 \mathrm{~nm}$$382 \mathrm{~nm}$$400 \mathrm{~nm}$Correct Option: , 3 Solution: $\frac{\mathrm{hc}}{\lambda}=\phi+\mathrm{eV}_{\mathrm{s}}$ $\frac{1240}{491}=\phi+0.71$......(1) $\frac{1240}...
Read More →The output of the
Question: The output of the given combination gates represents : XOR GateNAND GateAND GateNOR GateCorrect Option: , 2 Solution: By De Morgan's theorem, we have...
Read More →The truth table for the followng logic circuit is:
Question: The truth table for the followng logic circuit is: Correct Option: , 2 Solution: $y=\overline{(A \bar{B}+\bar{A} B)}$ $\mathrm{y}=\overline{\mathrm{A} \overline{\mathrm{B}}} \cdot \overline{\overline{\mathrm{A}} \mathrm{B}}$ $y=(\overline{\mathrm{A}}+\mathrm{B}) \cdot(\mathrm{A}+\overline{\mathrm{B}})$ $\mathrm{y}=\overline{\mathrm{A}} \cdot \mathrm{A}+\overline{\mathrm{A}} \overline{\mathrm{B}}+\mathrm{A} \cdot \mathrm{B}+\mathrm{B} \overline{\mathrm{B}}$ $\mathrm{y}=\mathrm{AB}+\over...
Read More →Find the peak current and resonant frequency of the following circuit (as shown in figure).
Question: Find the peak current and resonant frequency of the following circuit (as shown in figure). $0.2 \mathrm{~A}$ and $50 \mathrm{~Hz}$$0.2 \mathrm{~A}$ and $100 \mathrm{~Hz}$$2 \mathrm{~A}$ and $100 \mathrm{~Hz}$$2 \mathrm{~A}$ and $50 \mathrm{~Hz}$Correct Option: 1 Solution: as given $\mathrm{z}=\sqrt{\left(\mathrm{x}_{\mathrm{L}}-\mathrm{x}_{\mathrm{C}}\right)^{2}+\mathrm{R}^{2}}$ $\mathrm{x}_{\mathrm{L}}=\omega_{\mathrm{L}}=100 \times 100 \times 10^{-3}=10 \Omega$ $\mathrm{x}_{\mathrm{...
Read More →