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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 5151. |
An infinitely long current carrying wire carries current i. A charge of mass m and charge q is projected with speed v parallel to the direction of current at a distance r from it. Then, the radius of curvature at the point of projection is |
| A. | \[\frac{2rmv}{q{{\mu }_{0}}i}\] |
| B. | \[\frac{2\pi rmv}{q{{\mu }_{0}}i}\] |
| C. | r |
| D. | Cannot be determined |
| Answer» C. r | |
| 5152. |
Two wires AO and OC carry equal currents i as shown in figure. One end of both the wires extends to infinity. Angle AOC is\[\alpha \]. The magnitude of magnetic field at point P on the bisector of these two wires at a distance r from point O is |
| A. | \[\frac{{{\mu }_{0}}}{2\pi }\frac{i}{r}\cot \left( \frac{\alpha }{2} \right)\] |
| B. | \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}\cot \left( \frac{\alpha }{2} \right)\] |
| C. | \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}\frac{\left( 1+\cos \frac{\alpha }{2} \right)}{\sin \left( \frac{\alpha }{2} \right)}\] |
| D. | \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}\left( \frac{\alpha }{2} \right)\] |
| Answer» D. \[\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}\left( \frac{\alpha }{2} \right)\] | |
| 5153. |
A ring of radius 5 m is lying in the x-y plane and is carrying current of 1 A in anti-clockwise sense. If a uniform magnetic field \[\vec{B}=3\hat{i}+4\hat{j}\] is switched on, then the co-ordinates of point about which the loop will lift up is |
| A. | (3, 4) |
| B. | (4, 3) |
| C. | (3, 0) |
| D. | (0, 3) |
| Answer» B. (4, 3) | |
| 5154. |
An electron is launched with velocity \[\vec{v}\] in a uniform magnetic field\[\vec{B}\]. The angle \[\theta \] between \[\vec{v}\] and \[\vec{B}\] lies between 0 and\[\pi /2\]. Its velocity vector \[\vec{v}\] returns to its initial value in a time interval of |
| A. | \[\frac{2\pi m}{eB}\] |
| B. | \[\frac{2\times 2\pi m}{eB}\] |
| C. | \[\frac{\pi m}{eB}\] |
| D. | Depends upon angle between \[\vec{v}\] and \[\vec{B}\] |
| Answer» B. \[\frac{2\times 2\pi m}{eB}\] | |
| 5155. |
Two identical particles having the same mass m and charges \[+q\] and \[-q\] separated by a distance d enter a uni-form magnetic field B directed perpendicular to paper inwards with speeds \[{{v}_{1}}\] and \[{{v}_{2}}\] as shown in figure. The particles will not collide if |
| A. | \[d>\frac{m}{Bq}({{v}_{1}}+{{v}_{2}})\] |
| B. | \[d<\frac{m}{Bq}({{v}_{1}}+{{v}_{2}})\] |
| C. | \[d>\frac{2m}{Bq}({{v}_{1}}+{{v}_{2}})\] |
| D. | \[{{v}_{1}}={{v}_{2}}\] |
| Answer» D. \[{{v}_{1}}={{v}_{2}}\] | |
| 5156. |
A loop of flexible conducting wire of length \[l\] lies in magnetic field B which is normal to the plane of loop. A current is passed through the loop. The tension I developed in the wire to open up is |
| A. | \[\frac{\pi }{2}BIl\] |
| B. | \[\frac{BIl}{2}\] |
| C. | \[\frac{BIl}{2\pi }\] |
| D. | \[BIl\] |
| Answer» D. \[BIl\] | |
| 5157. |
A charged particle moves through a magnetic field perpendicular to its direction. Then |
| A. | Both momentum and kinetic energy of the particle are not constant. |
| B. | Both momentum and kinetic energy of the particle are constant. |
| C. | Kinetic energy changes but the momentum remains constant. |
| D. | The momentum changes but kinetic energy remains constant. |
| Answer» E. | |
| 5158. |
A thin bar magnet of length 2 L is bent at the mid-point so that the angle between them is\[60{}^\circ \]. The new length of the magnet is |
| A. | \[\sqrt{2}\,L\] |
| B. | \[\sqrt{3}\,L\] |
| C. | \[2\,L\] |
| D. | \[L\] |
| Answer» E. | |
| 5159. |
An electron is revolving in a circular orbit of radius r in a hydrogen atom. The angular momentum of the electron is The dipole moment associated with it is |
| A. | \[(2e/m)\,l\] |
| B. | \[(e/2m)\,l\] |
| C. | \[(e/m)\,l\] |
| D. | \[(2m\text{/}e)\,l\] |
| Answer» C. \[(e/m)\,l\] | |
| 5160. |
A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a plane where dip angle is \[30{}^\circ \] and 15 oscillations per minute at a place where dip angle is \[60{}^\circ \]. The ratio of earth's magnetic field at two places is |
| A. | \[3\sqrt{3:}8\] |
| B. | \[16:9\sqrt{3}\] |
| C. | \[4:9\] |
| D. | \[2\sqrt{2}:3\] |
| Answer» C. \[4:9\] | |
| 5161. |
A small rod of bismuth is suspended freely between the poles of a strong electromagnet. It is found to arrange itself at right angles to the magnetic field. This observation establishes that bismuth is |
| A. | Diamagnetic |
| B. | Paramagnetic |
| C. | Fern-magnetic |
| D. | Antiferro-magnetic |
| Answer» B. Paramagnetic | |
| 5162. |
In the following figure a wire bent in the form of a regular polygon of n sides is inscribed in a circle of radius\[a\]. Net magnetic field at centre will be |
| A. | \[\frac{{{\mu }_{0}}i}{2\pi a}\tan \frac{\pi }{n}\] |
| B. | \[\frac{{{\mu }_{0}}ni}{2\pi a}\tan \frac{\pi }{n}\] |
| C. | \[\frac{2}{\pi }\frac{ni}{a}{{\mu }_{0}}\tan \frac{\pi }{n}\] |
| D. | \[\frac{ni}{2a}{{\mu }_{0}}\tan \frac{\pi }{n}\] |
| Answer» C. \[\frac{2}{\pi }\frac{ni}{a}{{\mu }_{0}}\tan \frac{\pi }{n}\] | |
| 5163. |
Heat energy absorbed by a system in going through a cyclic process shown in figure is |
| A. | \[{{10}^{7}}\pi J\] |
| B. | \[{{10}^{4}}\pi J\] |
| C. | \[{{10}^{2}}\pi J\] |
| D. | \[{{10}^{-3}}\pi J\] |
| Answer» D. \[{{10}^{-3}}\pi J\] | |
| 5164. |
The specific heat at constant volume for the monatomic argon is 0.075 kcal/kg-K, whereas its gram molecular specific heat is\[{{C}_{v}}=2.98\,cal/mol/k\]. The mass of the argon atom is (Avogadro's number \[=6.02\times {{10}^{23}}\] molecules/mol) |
| A. | \[6.60\times {{10}^{-23}}g\] |
| B. | \[3.30\times {{10}^{-23}}g\] |
| C. | \[2.20\times {{10}^{-23}}g\] |
| D. | \[13.20\times {{10}^{-23}}g\] |
| Answer» B. \[3.30\times {{10}^{-23}}g\] | |
| 5165. |
The molecules of a given mass of a gas have root mean square speeds of \[100\,m{{s}^{-1}}\] at \[27{}^\circ C\] and 1.00 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at \[127{}^\circ C\] and 2.0 atmospheric pressure? |
| A. | \[\frac{150}{\sqrt{3}}m/s\] |
| B. | \[\frac{125}{\sqrt{3}}m/s\] |
| C. | \[\frac{200}{\sqrt{3}}m/s\] |
| D. | \[100\sqrt{3}m/s\] |
| Answer» D. \[100\sqrt{3}m/s\] | |
| 5166. |
A certain mass of an ideal diatomic gas contained in a closed vessel is heated; it is observed that the temperature remains constant; however, half the amount of gas gets dissociated; the ratio of the heat supplied to the gas initial internal energy of the gas will be |
| A. | 1:2 |
| B. | 0.0444444444444444 |
| C. | 1 :5 |
| D. | 0.0486111111111111 |
| Answer» E. | |
| 5167. |
Energy of all molecules of a monatomic gas having a volume \[F\] and pressure \[p\] is 3/2\[P\]\[V\]. The total translational kinetic energy of all molecules of a diatomic gas at the same volume and pressure is |
| A. | \[1/2\,PV\] |
| B. | \[3/2\,PV\] |
| C. | \[5/2\,PV\] |
| D. | \[3\,PV\] |
| Answer» C. \[5/2\,PV\] | |
| 5168. |
The air tight and smooth pistons of a cylindrical vessel are connected with a string, as shown. Initially,, pressure and temperature of the gas are \[{{p}_{0}}\] and \[{{T}_{0}}\]. The atmospheric pressure is also\[{{p}_{0}}\]. At a later time, tension in the string is \[\frac{3}{8}{{p}_{0}}A\] where A is the cross-sectional are of the cylinder. At this time, the temperature of the gas has become: |
| A. | \[\frac{3}{8}{{T}_{0}}\] |
| B. | \[\frac{3}{4}{{T}_{0}}\] |
| C. | \[\frac{11}{8}{{T}_{0}}\] |
| D. | \[\frac{13}{8}{{T}_{0}}\] |
| Answer» D. \[\frac{13}{8}{{T}_{0}}\] | |
| 5169. |
Three closed vessels\[A\], \[B\] and \[C\] are at the same temperature \[T\] and contain gases which obey the Maxwellian distribution of velocities. Vessel contains only\[{{O}_{2}}\], \[B\] only \[{{N}_{2}}\] and \[C\] a mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\] molecules in vessel A is \[{{V}_{2}}\] that of the \[{{N}_{3}}\] molecules in vessel B is \[{{V}_{2}}\], the average speed of the \[{{O}_{2}}\] molecules in vessel C is (where \[M\] is the mass of an oxygen molecule) |
| A. | \[({{V}_{2}}+{{V}_{2}})/2\] |
| B. | \[{{V}_{1}}\] |
| C. | \[{{({{V}_{1}}{{V}_{2}})}^{1/2}}\] |
| D. | \[\sqrt{3kT/M}\] |
| Answer» C. \[{{({{V}_{1}}{{V}_{2}})}^{1/2}}\] | |
| 5170. |
A light container having a diatomic gas enclosed within is moving with velocity\[v\]. Mass of the gas is \[M\] and number of mass of moles is n. The kinetic energy of gas w.r.t. ground is |
| A. | \[\frac{1}{2}M{{V}^{2}}+\frac{3}{2}nRT\] |
| B. | \[\frac{1}{2}M{{V}^{2}}\] |
| C. | \[\frac{1}{2}M{{V}^{2}}+\frac{5}{2}nRT\] |
| D. | \[\frac{5}{2}nRT\] |
| Answer» D. \[\frac{5}{2}nRT\] | |
| 5171. |
A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until the volume is doubled. The average molar heat capacity for the whole process is |
| A. | \[\frac{13R}{6}\] |
| B. | \[\frac{19R}{6}\] |
| C. | \[\frac{23R}{6}\] |
| D. | \[\frac{17R}{6}\] |
| Answer» C. \[\frac{23R}{6}\] | |
| 5172. |
The relation between internal energy \[U\], pressure \[P\] and volume \[V\] of a gas in an adiabatic process is \[U=a+bPV\] where a and b are constants. What is the effective value of adiabatic constant\[\gamma \]? |
| A. | \[\frac{a}{b}\] |
| B. | \[\frac{b+1}{b}\] |
| C. | \[\frac{a+1}{a}\] |
| D. | \[\frac{b}{a}\] |
| Answer» C. \[\frac{a+1}{a}\] | |
| 5173. |
A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by\[62{}^\circ C\], the efficiency of the engine is doubled. The temperatures of the source and sink are |
| A. | \[80{}^\circ C\], \[37{}^\circ C\] |
| B. | \[95{}^\circ C\], \[98{}^\circ C\] |
| C. | \[90{}^\circ C\], \[37{}^\circ C\] |
| D. | \[99{}^\circ C\], \[37{}^\circ C\] |
| Answer» E. | |
| 5174. |
One mole of an ideal monatomic gas requires 210 J heat to raise the temperature by 10 K, when heated at constant temperature. If the same gas is heated at constant volume to raise the temperature by 10 K then heat required is |
| A. | 238 J |
| B. | 126 J |
| C. | 210 J |
| D. | 350 J |
| Answer» C. 210 J | |
| 5175. |
Wires \[A\] and \[B\] are connected with blocks \[P\] and \[Q\], as shown. The ratio of lengths, radii and Young's modulus of wires \[A\] and \[B\] are \[r,\,2r\] and 3r respectively (\[r\] is a constant). Find the mass of block \[P\] if ratio of increase in their corresponding lengths is \[\frac{1}{6{{r}^{2}}}\]. The mass of the block \[Q\] is 3\[M\] |
| A. | \[M\] |
| B. | \[3M\] |
| C. | \[6M\] |
| D. | \[9M\] |
| Answer» D. \[9M\] | |
| 5176. |
If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity? |
| A. | Decreases by 19% |
| B. | Increases by 19% |
| C. | Decreases by more than 19% |
| D. | Increase by more than 19% |
| Answer» E. | |
| 5177. |
Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area \[A\] and wire 2 has cross-sectional area\[3A\]. If the length of wire 1 increases by Ax on applying a force \[F\], how much force is needed to stretch wire 2 by the same amount? |
| A. | \[F\] |
| B. | \[4F\] |
| C. | \[6F\] |
| D. | \[9F\] |
| Answer» E. | |
| 5178. |
As observed from the earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would |
| A. | be similarly true |
| B. | not be true because the force between the earth and mercury is not inverse square law |
| C. | not be true because the major gravitational force on mercury is due to the sun |
| D. | not be true because mercury is influenced by forces other than gravitational forces |
| Answer» D. not be true because mercury is influenced by forces other than gravitational forces | |
| 5179. |
A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The. amount of energy lost as heat per cycle per unit volume will be |
| A. | \[\left( \frac{\pi }{2}-1 \right)\times 16\times {{10}^{2}}J\] |
| B. | \[\left( \frac{\pi }{4}-1 \right)\times 8\times {{10}^{2}}J\] |
| C. | \[\left( \frac{\pi }{4}-1 \right)\times 32\times {{10}^{2}}J\] |
| D. | \[\left( \frac{\pi }{2}-1 \right)\times 32\times {{10}^{2}}J\] |
| Answer» E. | |
| 5180. |
The earth moves around the Sun in an elliptical orbit as shown Earth in the figure. The ratio\[OA/OB=x\]. The ratio of the speed of the earth at B to that at A is nearly |
| A. | \[\sqrt{x}\] |
| B. | \[x\] |
| C. | \[x\sqrt{x}\] |
| D. | \[{{x}^{2}}\] |
| Answer» C. \[x\sqrt{x}\] | |
| 5181. |
Suppose, the acceleration due to gravity at the Earth's surface is \[10\,m{{s}^{2}}\] and at the surface of Mars it is \[4.0\,m/{{s}^{2}}\].\[A\,60-kg\] passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time? |
| A. | A |
| B. | B |
| C. | C |
| D. | D |
| Answer» D. D | |
| 5182. |
Two bodies of masses \[{{M}_{1}}\] and \[{{M}_{2}}\] are placed at a distance \[R\]apart. Then at the position where the gravitational field due to them is zero, the gravitational potential is |
| A. | \[-G\frac{\sqrt{{{M}_{1}}}}{R}\] |
| B. | \[-G\frac{\sqrt{{{M}_{2}}}}{R}\] |
| C. | \[-{{(\sqrt{{{M}_{1}}}+\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] |
| D. | \[-{{(\sqrt{{{M}_{1}}}-\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] |
| Answer» D. \[-{{(\sqrt{{{M}_{1}}}-\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] | |
| 5183. |
Four particles, each of mass \[M\]and equidistant from each other, move along a circle of radius \[R\] under the action of their mutual gravitational attraction. The speed of each particle is |
| A. | \[\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] |
| B. | \[\frac{1}{2}\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] |
| C. | \[\sqrt{\frac{GM}{R}}\] |
| D. | \[\sqrt{2\sqrt{2}\frac{GM}{R}}\] |
| Answer» C. \[\sqrt{\frac{GM}{R}}\] | |
| 5184. |
A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (\[{{v}_{0}}\]). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If \[R\]= radius of the Earth and \[\omega \]) be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth. |
| A. | \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] |
| B. | \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\] |
| C. | \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\] |
| D. | \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] |
| Answer» D. \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] | |
| 5185. |
In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K'R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger of being thrown into space: |
| A. | \[{{\left[ \frac{2KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] |
| B. | \[{{\left[ \frac{KGM}{2g} \right]}^{1/2}}-\frac{1}{2}K'R\] |
| C. | \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] |
| D. | \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-K'R\] |
| Answer» E. | |
| 5186. |
The length of an elastic string is \[a\] metre when the longitudinal tension is 4 N and \[b\] metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is |
| A. | \[a-b\] |
| B. | \[5b-4a\] |
| C. | \[2a-\frac{1}{4}a\] |
| D. | \[4a-3b\] |
| Answer» C. \[2a-\frac{1}{4}a\] | |
| 5187. |
A uniform ring of mass \[m\] and radius r is placed directly above a uniform sphere of mass \[M\] and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\]\[r\] as shown in the figure. The gravitational force exerted by the sphere on the ring will be |
| A. | \[\frac{GMm}{8{{r}^{2}}}\] |
| B. | \[\frac{GMm}{4{{r}^{2}}}\] |
| C. | \[\sqrt{3}\frac{GMm}{8{{r}^{2}}}\] |
| D. | \[\frac{GMm}{8{{r}^{2}}\sqrt{3}}\] |
| Answer» D. \[\frac{GMm}{8{{r}^{2}}\sqrt{3}}\] | |
| 5188. |
A rectangular block of size \[10cm\times 8cm\times 5cm\] is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be |
| A. | Same in all the three cases |
| B. | Maximum in \[P\] position |
| C. | Maximum in \[Q\] position |
| D. | Maximum in \[R\] position |
| Answer» E. | |
| 5189. |
The ratio of diameters of two wires of same material is n: 1. The length of each wire is 4 m. On applying the same load, the increases in the length of the thin wire will be (n>\) |
| A. | \[{{n}^{2}}times\] |
| B. | \[{{n}^{{}}}times\] |
| C. | \[2{{n}^{{}}}times\] |
| D. | \[{{(2n+1)}^{{}}}times\] |
| Answer» B. \[{{n}^{{}}}times\] | |
| 5190. |
A ray of light is incident on a glass sphere of refractive index 3/2. What should be the angle of incidence so that the ray which enters the sphere does not come out of the sphere? |
| A. | \[te{{n}^{-1}}(2/3)\] |
| B. | \[{{60}^{0}}\] |
| C. | \[{{90}^{0}}\] |
| D. | \[{{30}^{0}}\] |
| Answer» D. \[{{30}^{0}}\] | |
| 5191. |
A lens forms a real image of an object. The distance from the object to the lens is x cm and that from the lens to the image is y cm. The graph (see figure) shows the variation of y with x. It can be deduced that the lens is |
| A. | Converging and of focal length 10 cm |
| B. | Converging and of focal length 20 cm |
| C. | Converging and of focal length 40 cm |
| D. | Diverging and of focal length 20 cm |
| Answer» B. Converging and of focal length 20 cm | |
| 5192. |
Critical angle of glass is\[{{\theta }_{1}}\]and that of water is\[{{\theta }_{2}}\]. The critical angle for water and glass surface would be \[({{\mu }_{g}}=3/2,{{\mu }_{w}}=4/3)\] |
| A. | Less than\[{{\theta }_{2}}\] |
| B. | Between \[{{\theta }_{1}}\] and\[{{\theta }_{2}}\] |
| C. | Greater than \[{{\theta }_{2}}\] |
| D. | Less than \[{{\theta }_{1}}\] |
| Answer» D. Less than \[{{\theta }_{1}}\] | |
| 5193. |
Consider the situation shown in figure. Water \[(\mu =4/3)\] is filled in a beaker upto a height of 10 cm. A plane mirror is fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object 0 at the bottom of the beaker is |
| A. | 15 cm |
| B. | 12.5 cm |
| C. | 7.5 cm |
| D. | 10 cm |
| Answer» C. 7.5 cm | |
| 5194. |
A beam of light propagates through medium 1 and falls onto another medium 2, at an angle \[{{\alpha }_{1}}\] as shown in figure. After that, it propagates in Medium 2 at an angle \[{{\alpha }_{2}}\] as shown. The light's wavelength in medium 1 is \[{{\lambda }_{1}}\]. What is the wavelength of light in medium 2? |
| A. | \[\frac{\sin \,{{\alpha }_{1}}}{\sin {{\alpha }_{2}}}{{\lambda }_{1}}\] |
| B. | \[\frac{\sin \,{{\alpha }_{2}}}{\sin {{\alpha }_{1}}}{{\lambda }_{1}}\] |
| C. | \[\frac{\cos \,{{\alpha }_{1}}}{\cos {{\alpha }_{2}}}{{\lambda }_{1}}\] |
| D. | \[\frac{\cos \,{{\alpha }_{2}}}{\cos {{\alpha }_{1}}}{{\lambda }_{1}}\] |
| Answer» C. \[\frac{\cos \,{{\alpha }_{1}}}{\cos {{\alpha }_{2}}}{{\lambda }_{1}}\] | |
| 5195. |
The graph shows variation of v with change in u for a mirror. Points plotted above the P point on the curve are for values of v |
| A. | Smaller than\[f\] |
| B. | Smaller than\[2f\] |
| C. | Larger than \[2f\] |
| D. | Larger than\[f\] |
| Answer» D. Larger than\[f\] | |
| 5196. |
A point object is placed at a distance of 10 cm and its real image is formed at a distance of 20 cm from a concave mirror. If the object is moved by 0.1 cm towards the mirror, the image will shift by about |
| A. | 0.4 cm away from the mirror |
| B. | 0.4 cm towards the mirror |
| C. | 0.8 cm away from the mirror |
| D. | 0.8 cm towards the mirror |
| Answer» B. 0.4 cm towards the mirror | |
| 5197. |
A rectangular glass slab ABCD, of refractive index \[{{n}_{1}}\] is immersed in water of refractive index\[{{n}_{2}}({{n}_{1}}>{{n}_{2}})\]. A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence\[{{\alpha }_{\max }}\] such that the ray comes out only from the other surface CD is given by |
| A. | \[{{\sin }^{-1}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\frac{{{n}_{2}}}{{{n}_{1}}} \right) \right]\] |
| B. | \[{{\sin }^{-1}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\frac{1}{{{n}_{2}}} \right) \right]\] |
| C. | \[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{{{n}_{2}}} \right)\] |
| D. | \[{{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] |
| Answer» B. \[{{\sin }^{-1}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\frac{1}{{{n}_{2}}} \right) \right]\] | |
| 5198. |
Light is incident normally on face AB of a prism as shown in figure; A liquid of refractive index \[\mu \] is placed on face AC of the prism, the prism is made of glass of refractive index 3/2. The limits of \[\mu \] for which total internal reflection takes place on face AC is |
| A. | \[\mu >\frac{3}{4}\] |
| B. | \[\mu <\frac{3}{4}\] |
| C. | \[\mu >\sqrt{3}\] |
| D. | \[\mu <\frac{\sqrt{3}}{2}\] |
| Answer» D. \[\mu <\frac{\sqrt{3}}{2}\] | |
| 5199. |
A telescope of diameter 2 m uses light of wavelength 5000 A for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is |
| A. | \[4\times {{10}^{-4}}\]rad |
| B. | \[0.25\times {{10}^{-6}}\]rad |
| C. | \[0.31\times {{10}^{-6}}\]rad |
| D. | \[5.0\times {{10}^{-3}}\]rad |
| Answer» D. \[5.0\times {{10}^{-3}}\]rad | |
| 5200. |
The magnifying power of an astronomical telescope is 8 and the distance between the two lenses is 54 cm. The focal length of eye lens and objective lens will be respectively |
| A. | 6 cm and 48 cm |
| B. | 48 cm and 6 cm |
| C. | 8 cm and 64 cm |
| D. | 64 cm and 8 cm |
| Answer» B. 48 cm and 6 cm | |