A swimmer can swim with velocity of 12km /h in still water.
Question: A swimmer can swim with velocity of $12 \mathrm{~km} / \mathrm{h}$ in still water. Water flowing in a river has velocity $6 \mathrm{~km} / \mathrm{h}$. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is___________. (Round off to the Nearest Integer) (find the angle in degree) Solution: Ans. (12) $12 \sin \theta=\mathrm{v}_{\mathrm{r}}$ $\sin \theta=\frac{1}{2}$ $\sin \the...
Read More →A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
Question: A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :hyperbolaparabola in the direction of motion of planestraight line vertically down the planeparabola in a direction opposite to the motion of planeCorrect Option: , 3 Solution: $\mathrm{v}_{\mathrm{B}}=\mathrm{u}_{0} \hat{\mathrm{i}}-\mathrm{gt} \hat{\mathrm{j}}$ $\overrightarrow{\mathrm{v}}_{\mathrm{B} / \mathrm{P}}=\overrightarrow{\mathrm{v}}_{\mathrm{B}}-\ove...
Read More →For full scale deflection
Question: For full scale deflection of total 50 divisions, $50 \mathrm{mV}$ voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is $2 \mathrm{div} / \mathrm{mA}$ will be :$1 \Omega$$5 \Omega$$4 \Omega$$2 \Omega$Correct Option: , 4 Solution: $\mathrm{I}_{\max }=\frac{50}{2}=25 \mathrm{~mA}$ $\mathbf{R}=\frac{\mathrm{V}}{\mathrm{I}}=\frac{50 \mathrm{mV}}{25 \mathrm{~mA}}=2 \Omega$...
Read More →A body of mass 2kg moves under a force
Question: A body of mass $2 \mathrm{~kg}$ moves under a force of $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. It starts from rest and was at the origin initially. After $4 \mathrm{~s}$, its new coordinates are $(8, b, 20)$. The value of $b$ is_________ (Round off to the Nearest Integer) Solution: Ans. (12) $\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\frac{2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{2}$ $=\hat{\mathrm{i}}+1...
Read More →A mass of
Question: A mass of $50 \mathrm{~kg}$ is placed at the centre of a uniform spherical shell of mass $100 \mathrm{~kg}$ and radius $50 \mathrm{~m}$. If the gravitational potential at a point, $25 \mathrm{~m}$ from the centre is $\mathrm{V} \mathrm{kg} / \mathrm{m}$. The value of $\mathrm{V}$ is :$-60 \mathrm{G}$$+2 G$$-20 \mathrm{G}$$-4 \mathrm{G}$Correct Option: , 4 Solution: $\mathrm{V}_{\mathrm{A}}=\left[-\frac{\mathrm{GM}_{1}}{\mathrm{r}}-\frac{\mathrm{GM}_{2}}{\mathrm{R}}\right]$ $=\left[-\fr...
Read More →A parallel - plate capacitor with plate area A has separation
Question: A parallel - plate capacitor with plate area A has separation $\mathrm{d}$ between the plates. Two dielectric slabs of dielectric constant $K_{1}$ and $K_{2}$ of same area $\mathrm{A} / 2$ and thickness $\mathrm{d} / 2$ are inserted in the space between the plates. The capacitance of the capacitor will be given by : $\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}\left(\frac{1}{2}+\frac{\mathrm{K}_{1} \mathrm{~K}_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}\right)$$\frac{\varepsilon_{0} \mathr...
Read More →A constant magnetic field
Question: A constant magnetic field of $1 \mathrm{~T}$ is applied in the $x0$ region. A metallic circular ring of radius $1 \mathrm{~m}$ is moving with a constant velocity of $1 \mathrm{~m} / \mathrm{s}$ along the $\mathrm{x}$-axis. At $\mathrm{t}=0 \mathrm{~s}$, the centre of $\mathrm{O}$ of the ring is at $\mathrm{x}=-1 \mathrm{~m} .$ What will be the value of the induced emf in the ring at $\mathrm{t}=1 \mathrm{~s}$ ? (Assume the velocity of the ring does not change.) $1 \mathrm{~V}$$2 \pi V$...
Read More →A deviation of
Question: A deviation of $2^{\circ}$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are $0.02$ and $0.03$ respectively and refractive index for yellow light for these glasses are $1.5$ and $1.6$ respectively. The refracting angles for crown glass prism will be ____________${ }^{\circ}$ (in degree) (Round off to the Nearest Integer) Solution: Ans. (12) $\omega_{1}=0.02 ; \mu_{1}=1.5 ; \omega_{2}=0.03...
Read More →The solid cylinder of length
Question: The solid cylinder of length $80 \mathrm{~cm}$ and mass $M$ has a radius of $20 \mathrm{~cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to $\mathrm{AB}$ as shown in figure is $2.7 \mathrm{~kg} \mathrm{~m}^{2}$. $14.9 \mathrm{~kg} / \mathrm{m}^{3}$$7.5 \times 10^{1} \mathrm{~kg} / \mathrm{m}^{3}$$7.5 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$$1.49 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$Correct Option: , 4 Soluti...
Read More →If the rms speed of oxygen
Question: If the rms speed of oxygen molecules at $0^{\circ} \mathrm{C}$ is $160 \mathrm{~m} / \mathrm{s}$, find the rms speed of hydrogen molecules at $0^{\circ} \mathrm{C}$.$640 \mathrm{~m} / \mathrm{s}$$40 \mathrm{~m} / \mathrm{s}$$80 \mathrm{~m} / \mathrm{s}$$332 \mathrm{~m} / \mathrm{s}$Correct Option: 1 Solution: $\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{KT}}{\mathrm{M}}}$ $\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{H}_{2}}}{\mathrm{M}_{\...
Read More →If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied
Question: If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5} \frac{G^{2}}{R}$ where $x$ is (Round off to the Nearest Integer) ( $M$ is the mass of earth, R is the radius of earth, $\mathrm{G}$ is the gravitational constant) Solution: Ans. (3) Energy given $=\mathrm{U}_{\mathrm{f}}-\mathrm{U}_{\mathrm{i}}$ $=0-\left(-\frac{3}{5} \frac{\mathrm{GM}^{2}}{\mathrm{R}}\right)$ $=\frac{3}{5}...
Read More →An antenna is mounted
Question: An antenna is mounted on a $400 \mathrm{~m}$ tall building. What will be the wavelength of signal of signal that can be radiated effectively by the transmission tower upto a range of $44 \mathrm{~km}$ ?$37.8 \mathrm{~m}$$605 \mathrm{~m}$$75.6 \mathrm{~m}$$302 \mathrm{~m}$Correct Option: , 2 Solution: $\mathrm{h}$ : height of antenna $\lambda$ : wavelength of signal $\mathrm{h}\lambda$ $\lambda\mathrm{h}$ $\lambda400 \mathrm{~m}$...
Read More →The colour coding
Question: The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is : $(5700 \pm 285) \Omega$$(7500 \pm 750) \Omega$$(5700 \pm 375) \Omega$$(7500 \pm 375) \Omega$Correct Option: , 4 Solution: $R=75 \times 10^{2} \pm 5 \%$ of 7500 $R=(7500 \pm 375) \Omega$...
Read More →In the following logic circuit the sequence
Question: In the following logic circuit the sequence of the inputs $\mathrm{A}, \mathrm{B}$ are $(0,0),(0,1),(1,0)$ and $(1,1)$. The output $\mathrm{Y}$ for this sequence will be : $1,0,1,0$$0,1,0,1$$1,1,1,0$$0,0,1,1$Correct Option: , 3 Solution: $\mathrm{Y}=\overline{(\mathrm{A} \cdot \mathrm{B}) \cdot(\mathrm{A}+\mathrm{B})}$ $Y)_{(0,0)}=1$ $\mathrm{Y})_{(0,1)}=1$ $\mathbf{Y})_{(1,0)}=1$ $Y)_{(1,1)}=0$ Option (3) is correct...
Read More →If you are provided a set of resistances
Question: If you are provided a set of resistances $2 \Omega, 4 \Omega$, $6 \Omega$ and $8 \Omega$. Connect these resistances so as to obtain an equivalent resistance of $\frac{46}{3} \Omega$.$4 \Omega$ and $6 \Omega$ are in parallel with $2 \Omega$ and $8 \Omega$ in series$6 \Omega$ and $8 \Omega$ are in parallel with $2 \Omega$ and $4 \Omega$ in series$2 \Omega$ and $6 \Omega$ are in parallel with $4 \Omega$ and $8 \Omega$ in series$2 \Omega$ and $4 \Omega$ are in parallel with $6 \Omega$ and ...
Read More →solve this
Question: A force $\overrightarrow{\mathrm{F}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ is applied on an intersection point of $x=2$ plane and $x$-axis. The magnitude of torque of this force about a point $(2,3,4)$ is . (Round off to the Nearest Integer) Solution: Ans. $(20)$ $\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}$ $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}})-(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})=-3 \hat{\mathrm{j}}-4...
Read More →The two thin coaxial rings, each of radius '
Question: The two thin coaxial rings, each of radius ' $a$ ' and having charges $+Q$ and $-Q$ respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :$\frac{\mathrm{Q}}{2 \pi \varepsilon_{0}}\left[\frac{1}{\mathrm{a}}+\frac{1}{\sqrt{\mathrm{s}^{2}+\mathrm{a}^{2}}}\right]$$\frac{Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{a}+\frac{1}{\sqrt{s^{2}+a^{2}}}\right]$$\frac{Q}{4 \pi \varepsilon_{0}}\left[\frac{1}{a}-\frac{1}{\sqrt{s^{2}+a^{2}}}\righ...
Read More →In a parallel plate capacitor set up,
Question: In a parallel plate capacitor set up, the plate area of capacitor is $2 \mathrm{~m}^{2}$ and the plates are separated by $1 \mathrm{~m}$. If the space between the plates are filled with a dielectric material of thickness $0.5 \mathrm{~m}$ and area $2 \mathrm{~m}^{2}$ (see fig.) the capacitance of the set-up will be_________$\varepsilon_{0}$ (Dielectric constant of the material $=3.2$ ) (Round off to the Nearest Integer) Solution: Ans. (3) $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{...
Read More →A helicopter is flying horizontally with a speed ' v '
Question: A helicopter is flying horizontally with a speed ' $v$ ' at an altitude 'h' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?$\sqrt{\frac{2 g h v^{2}+1}{h^{2}}}$$\sqrt{2 \mathrm{ghv}^{2}+\mathrm{h}^{2}}$$\sqrt{\frac{2 v^{2} h}{g}+h^{2}}$$\sqrt{\frac{2 g h}{v^{2}}}+h^{2}$Correct Option: , 3 Solution: $R=\sqrt{\frac{2 h}{g}} \cdot v$ $\mathrm{D}=\sqrt{\mathrm{R}^{2}+\mathrm{h}^{2}}$ $=\sqrt{\left(\sqrt{\fra...
Read More →A light beam is described by
Question: A light beam is described by $E=800 \sin \omega\left(t-\frac{x}{c}\right)$ . An electron is allowed to move normal to the propagation of light beam with a speed of $3 \times 10^{7}$ $\mathrm{ms}^{-1}$. What is the maximum magnetic force exerted on the electron? $1.28 \times 10^{-18} \mathrm{~N}$$1.28 \times 10^{-21} \mathrm{~N}$$12.8 \times 10^{-17} \mathrm{~N}$$12.8 \times 10^{-18} \mathrm{~N}$Correct Option: , 4 Solution: $\frac{\mathrm{E}_{0}}{\mathrm{C}}=\mathrm{B}_{0}$ $\mathrm{F}...
Read More →The energy dissipated by a resistor is 10 mJ in 1 s when an electric current of 2 mA flows through it.
Question: The energy dissipated by a resistor is $10 \mathrm{~mJ}$ in $1 \mathrm{~s}$ when an electric current of $2 \mathrm{~mA}$ flows through it. The resistance is $\Omega$ (Round off to the Nearest Integer) Solution: Ans. $(2500)$ $Q=i^{2} R T$ $R=\frac{Q}{i^{2} t}=\frac{10 \times 10^{-3}}{4 \times 10^{-6} \times 1}=2500 \Omega$...
Read More →Solve this following
Question: The angle between vector $(\overrightarrow{\mathrm{A}})$ and $(\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}})$ is : $\tan ^{-1}\left(\frac{-\frac{B}{2}}{A-B \frac{\sqrt{3}}{2}}\right)$$\tan ^{-1}\left(\frac{A}{0.7 B}\right)$$\tan ^{-1}\left(\frac{\sqrt{3} B}{2 A-B}\right)$$\tan ^{-1}\left(\frac{\mathrm{B} \cos \theta}{\mathrm{A}-\mathrm{B} \sin \theta}\right)$Correct Option: , 3 Solution: Angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}, \theta=60^...
Read More →A cylindrical container of volume
Question: A cylindrical container of volume $4.0 \times 10^{-3} \mathrm{~m}^{3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400 \mathrm{~K}$. The pressure of the mixture of gases is : [Take gas constant as $8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ ] $249 \times 10^{1} \mathrm{~Pa}$$24.9 \times 10^{3} \mathrm{~Pa}$$24.9 \times 10^{5} \mathrm{~Pa}$$24.9 \mathrm{~Pa}$Correct Option: , 3 Solution: $\mathrm{V}=4 \times 10^{-3} ...
Read More →Three capacitors
Question: Three capacitors $\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=6 \mu \mathrm{F}$ and $\mathrm{C}_{3}=12 \mu \mathrm{F}$ are connected as shown in figure. Find the ratio of the charges on capacitors $C_{1}, C_{2}$ and $C_{3}$ respectively : $2: 1: 1$$2: 3: 3$$1: 2: 2$$3: 4: 4$Correct Option: , 3 Solution: $\left(V_{D}-V\right) C_{2}+\left(V_{D}-0\right) C_{3}=0$ $\left(V_{D}-V\right) 6+\left(V_{D}-0\right) 12=0$ $V_{D}-V+2 V_{D}=0$ $V_{D}=\frac{V}{3}$ $\mathrm{q}_{2}=\left(\mathrm{V}...
Read More →A galaxy is moving away from the earth at a speed
Question: A galaxy is moving away from the earth at a speed of $286 \mathrm{kms}^{-1}$. The shift in the wavelength of a red line at $630 \mathrm{~nm}$ is $x \times 10^{-10} \mathrm{~m}$. The value of $x$, to the nearest integer, is_______. [Take the value of speed of light c, as $3 \times 10^{8}$ $\mathrm{ms}^{-1}$ ] Solution: $\frac{\Delta \lambda}{\lambda} \mathrm{c}=\mathrm{v}$ $\Delta \lambda=\frac{\mathrm{v}}{\mathrm{c}} \times \lambda=\frac{286}{3 \times 10^{5}} \times 630 \times 10^{-9}=...
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