MCQOPTIONS
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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.
| 5301. |
Two particles \[A\] and \[B\] start moving due to their mutual interaction only. If at any time\[t\], \[{{\vec{a}}_{A}}and\,{{\vec{a}}_{B}}\] are their respective accelerations, \[{{\vec{v}}_{A}}\,and\,{{\vec{v}}_{B}}\] are their respective velocities, and up to that time \[{{W}_{A\,}}and\,{{W}_{B}}\] are the work done on \[A\] and \[B\] respectively by the mutual force, \[{{m}_{A\,}}and\,{{m}_{B}}\] are their masses respectively, then which of the following is always correct? |
| A. | \[{{\vec{v}}_{A}}\,+\,{{\vec{v}}_{B}}=0\] |
| B. | \[{{m}_{A\,}}{{\vec{v}}_{A}}+\,{{m}_{B}}{{\vec{v}}_{B}}=0\] |
| C. | \[{{W}_{A}}\,+\,{{W}_{B}}=0\] |
| D. | \[{{\vec{a}}_{A}}+{{\vec{a}}_{B}}=0\] |
| Answer» C. \[{{W}_{A}}\,+\,{{W}_{B}}=0\] | |
| 5302. |
Three particles of masses 1 kg, 2 kg and 3 kg are situated at the comers of an equilateral triangle move at speed \[6\,m{{s}^{-1}}\], \[3\,m{{s}^{-1}}\] and \[2\,m{{s}^{-1}}\] respectively. Each particle maintains a direction towards the particle at the next comer symmetrically. Find velocity of CM of the system at this 2kg 4 instant |
| A. | \[3\,m{{s}^{-1}}\] |
| B. | \[5\,m{{s}^{-1}}\] |
| C. | \[6\,m{{s}^{-1}}\] |
| D. | Zero |
| Answer» E. | |
| 5303. |
A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass |
| A. | of the box remains constant |
| B. | of the (box + ball), system remains constant |
| C. | of the ball remains constant |
| D. | of the ball relative to the box remains constant |
| Answer» C. of the ball remains constant | |
| 5304. |
A free body of mass 8 kg is travelling at 2 meter per second in a straight line. At a certain instant, the body splits into two equal parts due to internal explosion which releases 16 joules of energy. Neither part leaves the original line of motion finally |
| A. | Both parts continue to move in the same direction as that of the original body |
| B. | One part comes to rest and the other moves in the same direction as that of the original body |
| C. | One part comes to rest and the other moves in the direction opposite to that of the original body |
| D. | One part moves in the same direction and the other in the direction opposite to that of the original body |
| Answer» C. One part comes to rest and the other moves in the direction opposite to that of the original body | |
| 5305. |
A mass m is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now if the mass starts moving the position of C.M. of mass of system will |
| A. | remains unchanged |
| B. | change along the horizontal |
| C. | will move up in the vertical direction |
| D. | will move down in the vertical direction and changes along the horizontal |
| Answer» D. will move down in the vertical direction and changes along the horizontal | |
| 5306. |
A machinist starts with three identical square plates but cuts one comer from one of them, two comers from the second and three comers from the third. Rank the three according to the x-coordinate of their centre of mass, from smallest to largest. |
| A. | 3, 1, 2 |
| B. | 1, 3, 2 |
| C. | 3, 2, 1 |
| D. | 1 and 3 tie, then 2 |
| Answer» C. 3, 2, 1 | |
| 5307. |
A ball collides with a fixed inclined plane of inclination \[\theta \]after falling through a distance\[h\]? If it moves horizontally just after the impact, the coefficient of restitution is |
| A. | \[\tan \,\theta \] |
| B. | \[{{\tan }^{2}}\,\theta \] |
| C. | \[{{\cot }^{{}}}\,\theta \] |
| D. | \[{{\cot }^{2}}\,\theta \] |
| Answer» C. \[{{\cot }^{{}}}\,\theta \] | |
| 5308. |
A block of mass \[m\] starts from rest and slides down a frictionless semi-circular track from a height h as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty. also having mass m. If the block and the putty stick together and continue to slide, the maximum height that the block-putty system could reach is |
| A. | \[h\]/4 |
| B. | \[h\]/2 |
| C. | \[h\] |
| D. | independent of \[h\] |
| Answer» C. \[h\] | |
| 5309. |
Three blocks are initially placed as shown in the figure. Block \[A\] has mass m and initial velocity \[v\] to the right. Block \[B\] with mass and block C with mass \[4m\] are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of blocks \[A\] is |
| A. | 0.6\[v\]to the left |
| B. | 1.4\[v\]to the left |
| C. | \[v\] to the left |
| D. | 0.4 \[v\] to the right |
| Answer» B. 1.4\[v\]to the left | |
| 5310. |
Two objects that are moving along an \[xy\]-plane on a frictionless floor collide. Assume that they form a closed, isolated system. The following table gives some of the momentum components (in kilogram meters per second) before and after the collision. Before collision After collision Before collisionAfter collisionObject \[{{p}_{x}}\] \[{{p}_{Y}}\] \[{{p}_{x}}\] \[{{p}_{Y}}\]A-453ABb-242What are the missing values (a, b)? |
| A. | 10, 11 |
| B. | 1, 11 |
| C. | 5, 7 |
| D. | 6, 4 |
| Answer» C. 5, 7 | |
| 5311. |
Distance of the centre of mass of a solid uniform cone from its vertex is \[{{z}_{0}}\]. If the radius of its base is R and its height is h then \[{{z}_{0}}\] is equal to |
| A. | \[\frac{{{h}^{2}}}{4R}\] |
| B. | \[\frac{3{{h}^{{}}}}{4}\] |
| C. | \[\frac{5{{h}^{{}}}}{8}\] |
| D. | \[\frac{3{{h}^{2}}}{8R}\] |
| Answer» C. \[\frac{5{{h}^{{}}}}{8}\] | |
| 5312. |
An object of mass 3m splits into three equal fragments. Two fragments have velocities \[v\hat{j}\,and\,v\hat{i}\]. The velocity of the third fragment is |
| A. | \[v(\hat{j}-\hat{i})\] |
| B. | \[v(\hat{i}-\hat{j})\] |
| C. | \[-v(\hat{i}+\hat{j})\] |
| D. | \[\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}\] |
| Answer» D. \[\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}\] | |
| 5313. |
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor |
| A. | Decreases |
| B. | Remains unchanged |
| C. | Becomes infinite |
| D. | Increases |
| Answer» C. Becomes infinite | |
| 5314. |
Two capacitors \[{{C}_{1}}\] and \[{{C}_{2}}\] are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then |
| A. | \[3{{C}_{1}}\,=\,5{{C}_{2}}\] |
| B. | \[3{{C}_{1}}\,+\,5{{C}_{2}}=0\] |
| C. | \[9{{C}_{1}}\,=\,4{{C}_{2}}\] |
| D. | \[5{{C}_{1}}\,=\,3{{C}_{2}}\] |
| Answer» B. \[3{{C}_{1}}\,+\,5{{C}_{2}}=0\] | |
| 5315. |
If there are \[n\] capacitors in parallel connected to a\[V\] volt source, then the energy stored is equal to |
| A. | \[CV\] |
| B. | \[\frac{1}{2}nC{{V}^{2}}\] |
| C. | \[C{{V}^{2}}\] |
| D. | \[\frac{1}{2n}C{{V}^{2}}\] |
| Answer» C. \[C{{V}^{2}}\] | |
| 5316. |
4. In the figure, a capacitor is filled with dielectrics. The dii resultant capacitance is |
| A. | \[\frac{2{{\varepsilon }_{0}}A}{d}\left[ \frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}+\frac{1}{{{K}_{3}}} \right]\] |
| B. | \[\frac{{{\varepsilon }_{0}}A}{d}\left[ \frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}+\frac{1}{{{K}_{3}}} \right]\] |
| C. | \[\frac{2{{\varepsilon }_{0}}A}{d}\left[ {{K}_{1}}+{{K}_{2}}+{{K}_{3}} \right]\] |
| D. | None of these |
| Answer» E. | |
| 5317. |
In the circuit shown, the effective capacitance between points\[X\] and \[Y\]is |
| A. | \[3.33\mu F\] |
| B. | \[1\,\mu F\] |
| C. | \[0.44\,\mu F\] |
| D. | None of these |
| Answer» C. \[0.44\,\mu F\] | |
| 5318. |
An uncharged capacitor is connected to a battery. On charging the capacitor |
| A. | All the energy supplied is siorea m me capacnor |
| B. | Half the energy supplied is stored in the capacitor |
| C. | The energy stored depends upon the capacity of the capacitor only |
| D. | The energy stored depends upon the time for which the capacitor is charged |
| Answer» C. The energy stored depends upon the capacity of the capacitor only | |
| 5319. |
In the figure initial status of capacitor and their connection is shown. Which of the following is incorrect about this circuit? |
| A. | Final charge on each capacitor will be zero |
| B. | Final total electrical energy of the capacitors will be zero |
| C. | Total charge flown from A to D is \[30\mu C\] |
| D. | Total charge flown from A to D is -\[30\mu C\] |
| Answer» D. Total charge flown from A to D is -\[30\mu C\] | |
| 5320. |
A parallel plate capacitor has capacitance C when no dielectric between the plates. Now a slab of dielectric constant K, having same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be |
| A. | \[(K+1)\frac{C}{4}\] |
| B. | \[(K+2)\frac{C}{4}\] |
| C. | \[(K+3)\frac{C}{4}\] |
| D. | \[\frac{KC}{4}\] |
| Answer» D. \[\frac{KC}{4}\] | |
| 5321. |
Three plates of common surface area \[A\] are connected as shown. The effective capacitance will be |
| A. | \[\frac{{{\varepsilon }_{0}}A}{d}\] |
| B. | \[\frac{3{{\varepsilon }_{0}}A}{d}\] |
| C. | \[\frac{3}{2}\frac{{{\varepsilon }_{0}}A}{d}\] |
| D. | \[\frac{2{{\varepsilon }_{0}}A}{d}\] |
| Answer» E. | |
| 5322. |
Two identical capacitors, have the same capacitance\[C\]. One of them is charged to potential \[{{V}_{1}}\] and the other to \[{{V}_{2}}\] the negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is |
| A. | \[\frac{1}{4}C({{V}^{2}}_{{{1}^{{}}}}-{{V}^{2}}_{2})\] |
| B. | \[\frac{1}{4}C({{V}^{2}}_{1}+{{V}^{2}}_{2})\] |
| C. | \[\frac{1}{4}C{{({{V}_{1}}-{{V}_{2}})}^{2}}\] |
| D. | \[\frac{1}{4}C{{({{V}_{1}}+{{V}_{2}})}^{2}}\] |
| Answer» D. \[\frac{1}{4}C{{({{V}_{1}}+{{V}_{2}})}^{2}}\] | |
| 5323. |
The capacity of a parallel plate capacitor with no dielectric substance but with a separation of 0.4 cm is\[2\mu F\]. The separation is reduced to half and it is filled with a dielectric substance of value 2.8. The final capacity of the capacitor is |
| A. | \[11.2\mu F\] |
| B. | \[15.6\mu F\] |
| C. | \[19.2\mu F\] |
| D. | \[22.4\mu F\] |
| Answer» B. \[15.6\mu F\] | |
| 5324. |
A parallel plate capacitor of plate area A and plate separation d is charged to potential V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitors so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and work done on the system in question in the process of inserting the slab, then state incorrect relation from the following |
| A. | \[Q=\frac{{{\varepsilon }_{0}}AV}{d}\] |
| B. | \[W=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2Kd}\] |
| C. | \[E=\frac{{{V}^{{}}}}{Kd}\] |
| D. | \[W=\frac{{{\varepsilon }_{0}}A{{V}^{2}}}{2d}\left( 1-\frac{1}{K} \right)\] |
| Answer» E. | |
| 5325. |
A parallel plate capacitor has plates of area \[A\] and separation \[d\] and is charged to a potential difference\[V\]. The charging battery is then disconnected and the plates are pulled apart until their separation is 2\[d\]. What is the work required to separate the plates? |
| A. | \[2{{\varepsilon }_{0}}A{{V}^{2}}/d\] |
| B. | \[{{\varepsilon }_{0}}A{{V}^{2}}/d\] |
| C. | \[3{{\varepsilon }_{0}}A{{V}^{2}}/d\] |
| D. | \[{{\varepsilon }_{0}}A{{V}^{2}}/2d\] |
| Answer» E. | |
| 5326. |
Four lenses of focal length + 15 cm, + 20cm, + 150cm and + 250 cm are available for making an astronomical telescope. To produce the largest magnification, the focal length of the eye-piece should be [CPMT 2001; AIIMS 2001] |
| A. | + 15 cm |
| B. | + 20 cm |
| C. | +150 cm |
| D. | + 250 cm |
| Answer» B. + 20 cm | |
| 5327. |
The resolving power of a telescope depends on [MP PET 2000, 01; DCE 2003] |
| A. | Focal length of eye lens |
| B. | Focal length of objective lens |
| C. | Length of the telescope |
| D. | Diameter of the objective lens |
| Answer» E. | |
| 5328. |
The diameter of the objective of a telescope is a, its magnifying power is m and wavelength of light is \[\lambda .\]The resolving power of the telescope is [MP PMT 2000] |
| A. | \[(1.22\,\lambda )/a\] |
| B. | \[(1.22\,a)/\lambda \] |
| C. | \[\lambda m/(1.22a)\] |
| D. | \[a/(1.22\lambda \,)\] |
| Answer» E. | |
| 5329. |
The focal lengths of the objective and eye-piece of a telescope are respectively 100 cm and 2 cm. The moon subtends an angle of \[{{0.5}^{o}}\,\]at the eye. If it is looked through the telescope, the angle subtended by the moon's image will be [MP PMT 2000; DCE 2003] |
| A. | \[{{100}^{o}}\] |
| B. | \[{{50}^{o}}\] |
| C. | \[{{25}^{o}}\] |
| D. | \[{{10}^{o}}\] |
| Answer» D. \[{{10}^{o}}\] | |
| 5330. |
The number of lenses in a terrestrial telescope is [KCET 1999; MH CET 2003] |
| A. | Two |
| B. | Three |
| C. | Four |
| D. | Six |
| Answer» C. Four | |
| 5331. |
An astronomical telescope of ten-fold angular magnification has a length of 44 cm. The focal length of the objective is [CBSE PMT 1997] |
| A. | 4 cm |
| B. | 40 cm |
| C. | 44 cm |
| D. | 440 cm |
| Answer» C. 44 cm | |
| 5332. |
The length of a telescope is 36 cm. The focal lengths of its lenses can be [Bihar MEE 1995] |
| A. | 30 cm, 6 cm |
| B. | ? 30 cm, ? 6 cm |
| C. | 30 cm, ? 6 cm |
| D. | ? 30 cm, 6 cm |
| Answer» B. ? 30 cm, ? 6 cm | |
| 5333. |
If tube length of astronomical telescope is 105 cm and magnifying power is 20 for normal setting, calculate the focal length of objective [AFMC 1994] |
| A. | 100 cm |
| B. | 10 cm |
| C. | 20 cm |
| D. | 25 cm |
| Answer» B. 10 cm | |
| 5334. |
A planet is observed by an astronomical refracting telescope having an objective of focal length 16 m and an eye-piece of focal length 2 cm [IIT-JEE 1992; Roorkee 2000] |
| A. | The distance between the objective and the eye-piece is 16.02 m |
| B. | The angular magnification of the planet is 800 |
| C. | The image of the planet is inverted |
| D. | The objective is larger than the eye-piece |
| Answer» B. The angular magnification of the planet is 800 | |
| 5335. |
The focal length of objective and eye-piece of a telescope are 100 cm and 5 cm respectively. Final image is formed at least distance of distinct vision. The magnification of telescope is [RPET 1997] |
| A. | 20 |
| B. | 24 |
| C. | 30 |
| D. | 36 |
| Answer» C. 30 | |
| 5336. |
The minimum magnifying power of a telescope is M, If the focal length of its eye lens is halved, the magnifying power will become [MP PMT/PET 1998] |
| A. | M / 2 |
| B. | 2 M |
| C. | 3 M |
| D. | 4 M |
| Answer» C. 3 M | |
| 5337. |
The focal lengths of the objective and eye lenses of a telescope are respectively 200 cm and 5 cm. The maximum magnifying power of the telescope will be [MP PMT/PET 1998; JIPMER 2001, 02] |
| A. | ? 40 |
| B. | ? 48 |
| C. | ? 60 |
| D. | ? 100 |
| Answer» C. ? 60 | |
| 5338. |
When diameter of the aperture of the objective of an astronomical telescope is increased, its [MP PMT 1997] |
| A. | Magnifying power is increased and resolving power is decreased |
| B. | Magnifying power and resolving power both are increased |
| C. | Magnifying power remains the same but resolving power is increased |
| D. | Magnifying power and resolving power both are decreased |
| Answer» D. Magnifying power and resolving power both are decreased | |
| 5339. |
In an astronomical telescope, the focal length of the objective lens is 100 cm and of eye-piece is 2 cm. The magnifying power of the telescope for the normal eye is [MP PET 1997] |
| A. | 50 |
| B. | 10 |
| C. | 100 |
| D. | \[\frac{1}{50}\] |
| Answer» B. 10 | |
| 5340. |
A Gallilean telescope has objective and eye-piece of focal lengths 200 cm and 2 cm respectively. The magnifying power of the telescope for normal vision is [MP PMT 1996] |
| A. | 90 |
| B. | 100 |
| C. | 108 |
| D. | 198 |
| Answer» C. 108 | |
| 5341. |
The length of an astronomical telescope for normal vision (relaxed eye) (fo = focal length of objective lens and fe = focal length of eye lens) is [EAMCET (Med.) 1995; CPMT 1999; BVP 2003] |
| A. | \[{{f}_{o}}\times {{f}_{e}}\] |
| B. | \[\frac{{{f}_{o}}}{{{f}_{e}}}\] |
| C. | \[{{f}_{o}}+{{f}_{e}}\] |
| D. | \[{{f}_{o}}-{{f}_{e}}\] |
| Answer» D. \[{{f}_{o}}-{{f}_{e}}\] | |
| 5342. |
A terrestrial telescope is made by introducing an erecting lens of focal length f between the objective and eye piece lenses of an astronomical telescope. This causes the length of the telescope tube to increase by an amount equal to [KCEE 1996] |
| A. | f |
| B. | 2f |
| C. | 3f |
| D. | 4f |
| Answer» E. | |
| 5343. |
All of the following statements are correct except [Manipal MEE 1995] |
| A. | The total length of an astronomical telescope is the sum of the focal lengths of its two lenses |
| B. | The image formed by the astronomical telescope is always erect because the effect of the combination of the two lenses is divergent |
| C. | The magnification of an astronomical telescope can be increased by decreasing the focal length of the eye-piece |
| D. | The magnifying power of the refracting type of astronomical telescope is the ratio of the focal length of the objective to that of the eye-piece |
| Answer» C. The magnification of an astronomical telescope can be increased by decreasing the focal length of the eye-piece | |
| 5344. |
The diameter of the objective lens of a telescope is 5.0 m and wavelength of light is 6000 Å. The limit of resolution of this telescope will be [MP PMT 1994] |
| A. | 0.03 sec |
| B. | 3.03 sec |
| C. | 0.06 sec |
| D. | 0.15 sec |
| Answer» B. 3.03 sec | |
| 5345. |
Two convex lenses of focal lengths 0.3 m and 0.05 m are used to make a telescope. The distance kept between the two is [MNR 1994] |
| A. | 0.35 m |
| B. | 0.25 m |
| C. | 0.175 m |
| D. | 0.15 m |
| Answer» B. 0.25 m | |
| 5346. |
Large aperture of telescope are used for [CPMT 1981; MP PMT 1995; AFMC 2000] |
| A. | Large image |
| B. | Greater resolution |
| C. | Reducing lens aberration |
| D. | Ease of manufacture |
| Answer» C. Reducing lens aberration | |
| 5347. |
On which of the following does the magnifying power of a telescope depends [MP PET 1992] |
| A. | The focal length of the objective only |
| B. | The diameter of aperture of the objective only |
| C. | The focal length of the objective and that of the eye piece |
| D. | The diameter of aperture of the objective and that of the eye piece |
| Answer» D. The diameter of aperture of the objective and that of the eye piece | |
| 5348. |
The length of the compound microscope is 14 cm. The magnifying power for relaxed eye is 25. If the focal length of eye lens is 5 cm, then the object distance for objective lens will be [Pb. PMT 2002] |
| A. | 1.8 cm |
| B. | 1.5 cm |
| C. | 2.1 cm |
| D. | 2.4 cm |
| Answer» B. 1.5 cm | |
| 5349. |
The aperture of the objective lens of a telescope is made large so as to [AIEEE 2003; KCET 2003] |
| A. | Increase the magnifying power of the telescope |
| B. | Increase the resolving power of the telescope |
| C. | Make image aberration less |
| D. | Focus on distant objects |
| Answer» C. Make image aberration less | |
| 5350. |
A reflecting telescope utilizes [CPMT 1983] |
| A. | A concave mirror |
| B. | A convex mirror |
| C. | A prism |
| D. | A plano-convex lens |
| Answer» B. A convex mirror | |