Solve this following
Question: Take the breakdown voltage of the zener diode used in the given circuit as 6V. For the input voltage shown in figure below, the time variation of the output voltage is : (Graphs drawn are schematic and not to scale) Correct Option: 2, Solution: As there are two zener diodes in reverse polarity so if one is in forward bias the other will be in reverse bias and above $6 \mathrm{~V}$ the reverse bias will too be in conduction mode. Therefore when voltage is more than $6 \mathrm{~V}$ the o...
Read More →Three different processes that can occur in an ideal monoatomic
Question: Three different processes that can occur in an ideal monoatomic gas are shown in the $\mathrm{P}$ vs $\mathrm{V}$ diagram. The paths are labelled as $\mathrm{A} \rightarrow \mathrm{B}, \mathrm{A} \rightarrow \mathrm{C}$ and $\mathrm{A} \rightarrow \mathrm{D}$. The change in internal energies during these process are taken as $\mathrm{E}_{\mathrm{AB}}, \mathrm{E}_{\mathrm{AC}}$ and $\mathrm{E}_{\mathrm{AD}}$ and the workdone as $\mathrm{W}_{\mathrm{AB}}$, $\mathrm{W}_{\mathrm{AC}}$ and ...
Read More →Two charged thin infinite plane sheets of uniform surface charge density
Question: Two charged thin infinite plane sheets of uniform surface charge density $\sigma_{+}$and $\sigma_{-}$ where $\left|\sigma_{+}\right|\left|\sigma_{-}\right|$intersect at right angle. Which of the following best represents the electric field lines for this system : Correct Option: 1 Solution: Thin infinite uniformly charged planes produces uniform electric field therefore option 2 and option 3 are obviously wrong. And as positive charge density is bigger in magnitude so its field along $...
Read More →A hollow spherical shell at outer radius
Question: A hollow spherical shell at outer radius $\mathrm{R}$ floats just submerged under the water surface. The inner radius of the shell is $\mathrm{r}$. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t. water, the value of $r$ is :$\frac{4}{9} \mathrm{R}$$\frac{8}{9} R$$\frac{1}{3} \mathrm{R}$$\frac{2}{3} \mathrm{R}$Correct Option: , 2 Solution: $\frac{4}{3} \pi\left(R^{3}-r^{3}\right) \rho_{m} g=\frac{4}{3} \pi R^{3} \rho_{w} g$ $1-\left(\frac{\mathrm{r}}{\mathrm{R}}\r...
Read More →In a Young's double slit experiment,
Question: In a Young's double slit experiment, light of $500 \mathrm{~nm}$ is used to produce an interference pattern. When the distance between the slits is $0.05 \mathrm{~mm}$, the angular width (in degree) of the fringes formed on the distance screen is close to :$0.07^{\circ}$$0.17^{\circ}$$1.7^{\circ}$$0.57^{\circ}$Correct Option: , 4 Solution: $\Delta \theta_{0}=\left(\frac{\lambda}{\mathrm{d}} \times \frac{180}{\pi}\right)^{0}$ $=0.57^{\circ}$...
Read More →A block of mass m = 1 slides with velocity v = 6 m/s
Question: A block of mass $m=1 \mathrm{~kg}$ slides with velocity $v=6 \mathrm{~m} / \mathrm{s}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $\mathrm{O}$ and swings as a result of the collision making angle $\theta$ before momentarily coming to rest. If the rod has mass $\mathrm{M}=2 \mathrm{~kg}$, and length $l=1 \mathrm{~m}$, the value of $\theta$ is approximately : (Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )...
Read More →Activities of three radioactive substances
Question: Activities of three radioactive substances A, B and $\mathrm{C}$ are represented by the curves $\mathrm{A}, \mathrm{B}$ and C, in the figure. Then their half-lives $\mathrm{T}_{\frac{1}{2}}(\mathrm{~A}): \mathrm{T}_{\frac{1}{2}}(\mathrm{~B}): \mathrm{T}_{\frac{1}{2}}(\mathrm{C})$ are in the ratio : $3: 2: 1$$4: 3: 1$$2: 1: 3$$2: 1: 1$Correct Option: 3, Solution: $\mathrm{R}=\mathrm{R}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$ $\ln \mathrm{R}=\ln \mathrm{R}_{0}-\lambda \mathrm{t}$ $\lambda_...
Read More →Solve this following
Question: A two point charges $4 \mathrm{q}$ and $-\mathrm{q}$ are fixed on the $x$-axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2}$, respectively. If a third point charge ' $q$ ' is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will: increase by $\frac{2 q^{2}}{3 \pi \varepsilon_{0} d}$increase by $\frac{3 q^{2}}{4 \pi \varepsilon_{0} d}$decrease by $\frac{4 \mathrm{q}^{2}}{3 \pi \varepsilon_{0} \mathrm{~d}}$decrease by $\frac{\mathrm{q}^{2}}{4...
Read More →A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it
Question: A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{\mathrm{h}}{2}$. The velocity versus height of the ball during its motion may be represented graphically by : (graph are drawn schematically and on not to scale) Correct Option: , 3 Solution: Velocity at ground (means zero height) is nonzero therefore one is incorrect and velocity versus height is non-linear therefore two is also incorrect. $v^{2}=2 g h$ $\mathrm...
Read More →A uniform thin rope of length
Question: A uniform thin rope of length $12 \mathrm{~m}$ and mass $6 \mathrm{~kg}$ hangs vertically from a rigid support and a block of mass $2 \mathrm{~kg}$ is attached to its free end. A transverse short wavetrain of wavelength $6 \mathrm{~cm}$ is produced at the lower end of the rope. What is the wavelength of the wavetrain (in $\mathrm{cm}$ ) when it reaches the top of the rope ?91263Correct Option: , 2 Solution: $\mathrm{V} \propto \lambda \quad \mathrm{T}_{2}=8 \mathrm{~g}$ $\mathrm{T}_{1}...
Read More →A helicopter reises from rest on the ground vertically upwards with a constant acceleration g
Question: A helicopter reises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is a height $h$. The time taken by the packet to reach the ground is close to $[g$ is the acceleration due to gravity] :$\mathrm{t}=\sqrt{\frac{2 \mathrm{~h}}{3 \mathrm{~g}}}$$\mathrm{t}=1.8 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}$$\mathrm{t}=3.4 \sqrt{\left(\frac{\mathrm{h}}{\mathrm{g}}\right)}$$\mathrm{t}=\frac{2}{3} \sqrt{\left(\frac{\mathr...
Read More →When a diode is forward biased, it has a voltage drop of 0.5 V.
Question: When a diode is forward biased, it has a voltage drop of $0.5 \mathrm{~V}$. The safe limit of current through the diode is $10 \mathrm{~mA}$. If a battery of emf $1.5 \mathrm{~V}$ is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is :$100 \Omega$$50 \Omega$$300 \Omega$$200 \Omega$Correct Option: 1 Solution: $1.5-0.5-\mathrm{R} \times 10 \times 10^{-3}=0$ $\therefore \mathrm{R}=100 \Omega$...
Read More →Solve this following
Question: The specific heat of water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ and the latent heat of ice $=3.4 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1}$. 100 grams of ice at $0^{\circ} \mathrm{C}$ is placed in $200 \mathrm{~g}$ of water at $25^{\circ} \mathrm{C}$. The amount of ice that will melt as the temperature of water reaches $0^{\circ} \mathrm{C}$ is close to (in grams): $61.7$$63.8$$69.3$$64.6$Correct Option: 1 Solution: Here the water will provide heat for ice to melt t...
Read More →An elliptical loop having resistance
Question: An elliptical loop having resistance $\mathrm{R}$, of semi major axis a, and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$, the average power loss in the loop due to Joule heating is : $\frac{\pi^{2} \mathrm{a}^{2} \mathrm{~b}^{2} \mathrm{~B}^{2} \omega^{2}}{2 \mathrm{R}}$Zero$\frac{\pi^{2} \mathrm{a}^{2} \mathrm{~b}^{2} \mathrm{~B}^{2} \omega^{2}}{\mathrm{R}}$$\frac{\pi \mathrm{abB} \om...
Read More →In a resonance tube experiment when the tube is filled with water up to height
Question: In a resonance tube experiment when the tube is filled with water up to height of $17.0 \mathrm{~cm}$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5 \mathrm{~cm}$. If the velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$, the tuning fork frequency is:$1100 \mathrm{~Hz}$$3300 \mathrm{~Hz}$$2200 \mathrm{~Hz}$$550 \mathrm{~Hz}$Correct Option: , 3 Solution: $\Rightarrow \la...
Read More →A balloon is moving up in air vertically above a point A on the ground.
Question: A balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $\mathrm{h}_{1}$, a girl standing at a distance $\mathrm{d}$ (point $\mathrm{B}$ ) from A (see figure) sees it at an angle $45^{\circ}$ with respect to the vertical. When the balloon climbs up a further height $\mathrm{h}_{2}$, it is seen at an angle $60^{\circ}$ with respect to the vertical if the girl moves further by a distance $2.464 \mathrm{~d}$ (point C). Then the height $\mathrm{h}_{...
Read More →Solve this following
Question: Blocks of masses $\mathrm{m}, 2 \mathrm{~m}, 4 \mathrm{~m}$ and $8 \mathrm{~m}$ are arranged in a line on a frictionless floor. Another block of mass $m$, moving with speed $v$ along the same line (see figure) collides with mass $\mathrm{m}$ in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass $8 \mathrm{~m}$ starts moving the total energy loss is $\mathrm{p} \%$ of the original energy. Value of ' $p$ ' is close t...
Read More →Solve this following
Question: A battery of $3.0 \mathrm{~V}$ is connected to a resistor dissipating $0.5 \mathrm{~W}$ of power. If the terminal voltage of the battery is $2.5 \mathrm{~V}$, the power dissipated within the internal resistance is : $0.50 \mathrm{~W}$$0.125 \mathrm{~W}$$0.072 \mathrm{~W}$$0.10 \mathrm{~W}$Correct Option: , 4 Solution: $P_{R}=0.5 W$ $\Rightarrow \mathrm{i}^{2} \mathrm{R}=0.5 \mathrm{~W}$ Also, $\mathrm{V}=\mathrm{E}-\mathrm{ir}$ $2.5=3-\mathrm{ir}$ $\Rightarrow$ ir $=0.5$ Power dissipat...
Read More →A small bar magnet is moved through a coil at constant speed from one end to the other
Question: A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations wil be seen on the galvanometer $\mathrm{G}$ attached across the coil ? Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit. Correct Option: , 3 Solution: When bar magnet is entering with constant speed, flux will change and an e.m.f. is induced, so galvanometer will deflect in positive direction. ...
Read More →In the circuit shown in the figure,
Question: In the circuit shown in the figure, the total charge in $750 \mu \mathrm{C}$ and the voltage across capacitor $\mathrm{C}_{2}$ is $20 \mathrm{~V}$. Then the charge on capacitor $\mathrm{C}_{2}$ is : $590 \mu \mathrm{C}$$450 \mu \mathrm{C}$$650 \mu \mathrm{C}$$160 \mu \mathrm{C}$Correct Option: 1 Solution: $\mathrm{q}_{3}=20 \times 8=160 \mu \mathrm{C}$ $\therefore \mathrm{q}_{2}=750-160=590 \mu \mathrm{C}$...
Read More →Solve this following
Question: Particle $\mathrm{A}$ of mass $\mathrm{m}_{\mathrm{A}}=\frac{\mathrm{m}}{2}$ moving along the $x$-axis with velocity $v_{0}$ collides elastically with another particle $\mathrm{B}$ at rest having mass $\mathrm{m}_{\mathrm{B}}=\frac{\mathrm{m}}{3}$. If both particles move along the $x$-axis after the collision, the change $\Delta \lambda$ in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength $\left(\lambda_{0}\right)$ before collision is : $\Delta \lambda=4 \lamb...
Read More →A small bar magnet placed with its axis at
Question: A small bar magnet placed with its axis at $30^{\circ}$ with an external field of $0.06 \mathrm{~T}$ experiences a torque of $0.018 \mathrm{Nm}$. The minimum work required to rotate it from its stable to unstable equilibrium position is : $9.2 \times 10^{-3} \mathrm{~J}$$6.4 \times 10^{-2} \mathrm{~J}$$11.7 \times 10^{-3} \mathrm{~J}$$7.2 \times 10^{-2} \mathrm{~J}$Correct Option: , 4 Solution: Torque on a bar magnet : I = MB $\sin \theta$ Here, $\theta=30^{\circ}, \mathrm{I}=0.018 \ma...
Read More →For a transverse wave travelling along a straight line, the distance between two peaks
Question: For a transverse wave travelling along a straight line, the distance between two peaks (crests) is $5 \mathrm{~m}$, while the distance between one crest and one trough is $1.5 \mathrm{~m}$. The possible wavelengths (in $\mathrm{m}$ ) of the waves are : $1,2,3$,$\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \ldots$$1,3,5, \ldots \ldots$$\frac{1}{1}, \frac{1}{3}, \frac{1}{5}, \ldots$Correct Option: , 4 Solution: Given $\mathrm{T}$ to $\mathrm{C} 1.5 \mathrm{~m}$ $\mathrm{C}$ to $\mathrm{C} 5 \m...
Read More →Solve this following
Question: A wire A, bent in the shape of an arc of a circle, carrying a current of $2 \mathrm{~A}$ and having radius $2 \mathrm{~cm}$ and another wire B, also bent in the shape of arc of a circle, carrying a current of $3 \mathrm{~A}$ and having radius of $4 \mathrm{~cm}$, are placed as shown in the figure. The ratio of the magnetic fields due to the wires $\mathrm{A}$ and $\mathrm{B}$ at the common centre $\mathrm{O}$ is : $4: 6$$6: 4$$6: 5$$2: 5$Correct Option: , 3 Solution: Given $\mathrm{i}_...
Read More →Given figure shows few data points in a photo electric effect experiment for a certain metal.
Question: Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surfface is : (Plancks constant $\left.\mathrm{h}=6.62 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)$ $2.27 \mathrm{eV}$$2.59 \mathrm{eV}$$1.93 \mathrm{eV}$$2.10 \mathrm{eV}$Correct Option: 1 Solution: Graph of $\mathrm{V}_{\mathrm{s}}$ and f given (B $5.5,0$ ) $\mathrm{h} v=\phi+\mathrm{eV}_{\mathrm{s}}$ at $\mathrm{B} \mathrm{V}_{\mathrm...
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