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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.
| 12001. |
A Hydrogen atom and a \[L{{i}^{++}}\] ion are both in the second excited state. If \[{{l}_{H}}\] and \[{{l}_{Li}}\] are their respective electronic angular momenta, and \[{{E}_{H}}\] and \[{{E}_{Li}}\] their respective energies, then [IIT-JEE (Screening) 2002] |
| A. | \[{{l}_{H}}>{{l}_{Li}}\,\text{ and }|{{E}_{H}}|>|{{E}_{Li}}|\] |
| B. | \[{{l}_{H}}={{l}_{Li}}\text{ and }|{{E}_{H}}|<|{{E}_{Li}}|\] |
| C. | \[{{l}_{H}}={{l}_{Li}}\text{ and }|{{E}_{H}}|>|{{E}_{Li}}|\] |
| D. | \[{{l}_{H}}<{{l}_{Li}}\text{ and }|{{E}_{H}}|<|{{E}_{Li}}|\] |
| Answer» C. \[{{l}_{H}}={{l}_{Li}}\text{ and }|{{E}_{H}}|>|{{E}_{Li}}|\] | |
| 12002. |
Assertion : Electrons in the atom are held due to coulomb forces. Reason : The atom is stable only because the centripetal force due to Coulomb?s law is balanced by the centrifugal force. |
| A. | If both assertion and reason are true and the reason is the correct explanation of the assertion. |
| B. | If both assertion and reason are true but reason is not the correct explanation of the assertion. |
| C. | If assertion is true but reason is false. |
| D. | If the assertion and reason both are false. |
| Answer» D. If the assertion and reason both are false. | |
| 12003. |
Half-life of a radioactive substance is 20 minutes. Difference between points of time when it is 33% disintegrated and 67% disintegrated is approximately [AIIMS 2000] |
| A. | 10 min |
| B. | 20 min |
| C. | 30 min |
| D. | 40 min |
| Answer» C. 30 min | |
| 12004. |
If \[F=20\text{ }N,\] with how much force does block A presses the block B - |
| A. | 10 N |
| B. | 20 N |
| C. | 30 N |
| D. | Zero |
| Answer» E. | |
| 12005. |
Two blocks of masses \[{{m}_{1}}\] and\[{{m}_{2}}\] are placed in contact with each other on a horizontal platform. The coefficient of friction between the platform and the two blocks is the same. The platform moves with an acceleration. The force of interaction between the blocks is |
| A. | zero, only if \[{{m}_{1}}={{m}_{2}}\] |
| B. | non-zero, when \[{{m}_{1}}>{{m}_{2}}\] |
| C. | non-zero, when \[{{m}_{1}}<{{m}_{2}}\] |
| D. | zero in all cases |
| Answer» E. | |
| 12006. |
A toy train consists of three identical compartment A, B and C. It is being pulled by a constant force F along C. The ratio of the tensions in the string connecting AB and BC is: |
| A. | 0.0840277777777778 |
| B. | 0.04375 |
| C. | 0.0423611111111111 |
| D. | 0.0430555555555556 |
| Answer» E. | |
| 12007. |
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is |
| A. | \[\frac{PM}{M+m}\] |
| B. | \[\frac{Pm}{M+m}\] |
| C. | \[\frac{Pm}{M-m}\] |
| D. | P |
| Answer» B. \[\frac{Pm}{M+m}\] | |
| 12008. |
Two masses\[{{\text{m}}_{1}}\]and\[{{\text{m}}_{\text{2}}}\]are attached to the ends of a massless string which passes over a frictionless pulley attached to the top of an inclined plane. The angle of inclination of the plane is \[\theta \]. Take \[g=10m{{s}^{-2}}\] If \[{{m}_{1}}=10\,kg,\,\,{{m}_{2}}=5\,kg,\] \[\theta ={{30}^{o}},\] what is the acceleration of mass \[{{m}_{2}}\]? |
| A. | zero |
| B. | \[(2/3)\text{ }m{{s}^{-2}}\] |
| C. | \[5\text{ }m{{s}^{-2}}\] |
| D. | \[10/3\text{ }m{{s}^{-2}}\] |
| Answer» B. \[(2/3)\text{ }m{{s}^{-2}}\] | |
| 12009. |
A particle moves in the \[x-y\] plane under the action of a force \[\overrightarrow{F}\] such that the value of its linear momentum \[\overrightarrow{P}\] at any time \[t\] is \[{{P}_{x}}=2\,\cos t,\] \[{{P}_{y}}=2\sin t\]. The angle \[\theta \] between \[\overrightarrow{F}\] and \[\overrightarrow{P}\] at a given time t will be |
| A. | \[90{}^\circ \] |
| B. | \[0{}^\circ \] |
| C. | \[180{}^\circ \] |
| D. | \[30{}^\circ \] |
| Answer» B. \[0{}^\circ \] | |
| 12010. |
In the system shown in figure \[{{m}_{A}}=4m,\,\,{{m}_{B}}=3m\] and \[{{m}_{C}}=8m\]. Friction is absent everywhere. String is light and inextensible. If the system is released from rest find the acceleration of block B |
| A. | \[\frac{g}{8}\] |
| B. | \[\frac{g}{2}\] |
| C. | \[\frac{g}{4}\] |
| D. | g |
| Answer» C. \[\frac{g}{4}\] | |
| 12011. |
An explosion blows a rock into three parts. Two parts go off at right angles of each other. These two are 1 kg first part moving with a velocity of \[12\,m{{s}^{-1}}\] and 2 kg second part moving with a velocity of \[8\,m{{s}^{-1}}\]. If the third part files off with a velocity of \[4\,m{{s}^{-1}},\] its mass would be : |
| A. | 5 kg |
| B. | 7 kg |
| C. | 17 kg |
| D. | 3 kg |
| Answer» B. 7 kg | |
| 12012. |
A sphere of mass m is held between two smooth inclined walls. For sin \[37{}^\circ =3/5,\] the normal reaction of the wall (2) is equal to : |
| A. | mg |
| B. | \[mg\sin {{74}^{o}}\] |
| C. | \[mg\cos {{74}^{o}}\] |
| D. | none of the above |
| Answer» B. \[mg\sin {{74}^{o}}\] | |
| 12013. |
Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the left is 10 m/s. What is the speed of B when angle \[\theta ={{45}^{o}}?\] |
| A. | 5 m/s |
| B. | (b)\[5\sqrt{2}m/s\] |
| C. | 10 m/s |
| D. | 7.5 m/s |
| Answer» D. 7.5 m/s | |
| 12014. |
The system shown in figure 18 is in equilibrium. The maximum value of W, so that the maximum value of static frictional force on 100 kg body is 450 N, will be |
| A. | 100 N |
| B. | 250 N |
| C. | 450 N |
| D. | 1000 N |
| Answer» D. 1000 N | |
| 12015. |
A man stands on a weighing machine kept inside a lift. Initially the lift is ascending with the acceleration 'a' due to which the reading is W. Now the lift decends with the same acceleration and reading is 10% of initial. Find the acceleration of lift? |
| A. | \[\frac{g}{19}\,m/{{\sec }^{2}}\] |
| B. | \[\frac{9g}{11}\,m/{{\sec }^{2}}\] |
| C. | \[0\,/{{\sec }^{2}}\] |
| D. | \[g\,m/{{\sec }^{2}}\] |
| Answer» C. \[0\,/{{\sec }^{2}}\] | |
| 12016. |
A body of mass 50 kg resting on a smooth inclined plane is connected by a massless inextensible string passing over a smooth pulley, at the top of the inclined plane have another mass of 40 kg as shown in the figure. The distance through which 50 kg mass fall in 4 sec will be -(The angle of the inclined plane is \[{{30}^{o}}\]) |
| A. | 13.04 m |
| B. | 1.63 m |
| C. | 1.304 m |
| D. | 16.3 m |
| Answer» B. 1.63 m | |
| 12017. |
A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in figure. Which of following statements are correct: |
| A. | \[\overrightarrow{N}+\overrightarrow{T}+\overrightarrow{W}=0\] |
| B. | \[{{T}^{2}}+{{N}^{2}}+{{W}^{2}}=0\] |
| C. | \[T=N+W\] |
| D. | \[N=W\sin \theta \] |
| Answer» B. \[{{T}^{2}}+{{N}^{2}}+{{W}^{2}}=0\] | |
| 12018. |
A light spring of length I and spring constant k is placed vertically on a table. A small ball of mass m falls on it. The height h from the surface of the table at which the ball will have the maximum velocity is |
| A. | \[\frac{l}{k}\] |
| B. | \[l-\frac{mg}{k}\] |
| C. | \[l+\frac{k}{mg}\] |
| D. | \[l-kg\] |
| Answer» C. \[l+\frac{k}{mg}\] | |
| 12019. |
In the arrangement shown in figure the ends P and Q of an stretchable string move downwards with a uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed of |
| A. | \[2U\cos \theta \] |
| B. | \[U\cos \theta \] |
| C. | \[2U/\cos \theta \] |
| D. | \[U/\cos \theta \] |
| Answer» E. | |
| 12020. |
A perfectly straight portion of a uniform rope has mass M and length L. At end A of the segment, the tension in the rope is \[{{T}_{A}}\] and at end B it is \[{{T}_{B}}({{T}_{B}}>{{T}_{A}})\]. Neglect effect of gravity and no contact force acts on the rope in between points A and B. The tension in the rope at a distance L/5 from end A is |
| A. | \[{{T}_{B}}-{{T}_{A}}\] |
| B. | \[({{T}_{A}}+{{T}_{B}})/5\] |
| C. | \[(4{{T}_{A}}+{{T}_{B}})/5\] |
| D. | \[({{T}_{A}}-{{T}_{B}})/5\] |
| Answer» D. \[({{T}_{A}}-{{T}_{B}})/5\] | |
| 12021. |
Two trains A and B are running in the same direction on parallel tracks such that A is faster than B. If packets of equal weight are exchanged between the two, then |
| A. | A will be retarded but B will be accelerated |
| B. | A will be accelerated but B will be retarded |
| C. | there will be no change in velocity of A but B will be accelerated |
| D. | there will be no change in velocity of B, but A will be accelerated |
| Answer» B. A will be accelerated but B will be retarded | |
| 12022. |
Two solid rubber balls A and B having masses 200 and 400 gm respectively are moving in opposite directions with velocity of A equal to 0.3 m/s. After collision the two balls come to rest, then the velocity of B is: |
| A. | 0.15 m/s |
| B. | 1.5 m/s |
| C. | - 0.15 m/s |
| D. | None of the above |
| Answer» D. None of the above | |
| 12023. |
A body of mass m released from a height h on a smooth inclined plane that is shown in the figure. The following can be true about the velocity of the block knowing that the wedge is fixed. |
| A. | v is maximum when it just touches the spring |
| B. | v is maximum when it compresses the spring by some amount |
| C. | v is maximum when the spring comes back to natural position |
| D. | none of these |
| Answer» C. v is maximum when the spring comes back to natural position | |
| 12024. |
Two men of masses m and m/2 starts climbing up on two massless strings fixed at the ceiling with acceleration g and g/2 respectively. The ratio of tensions in the two strings will be: |
| A. | 0.0840277777777778 |
| B. | 0.167361111111111 |
| C. | 0.16875 |
| D. | 0.335416666666667 |
| Answer» E. | |
| 12025. |
A truck moving on a smooth horizontal surface with a uniform speed u is carrying dust. If a mass \[\Delta m\] of the dust leaks from the truck in vertical downward direction in time \[\Delta t,\] the force needed to keep the truck moving at its constant speed is |
| A. | Zero |
| B. | \[\frac{u\,\Delta m}{\Delta t}\] |
| C. | \[\Delta m\times \frac{du}{dt}\] |
| D. | \[u\frac{\Delta m}{\Delta t}+\Delta m\times \frac{du}{dt}\] |
| Answer» B. \[\frac{u\,\Delta m}{\Delta t}\] | |
| 12026. |
Three blocks are placed at rest on a smooth inclined plane with force acting on \[{{m}_{1}}\] parallel to the inclined plane. Find the contact force between \[{{m}_{2}}\] and \[{{m}_{3}}\]: |
| A. | \[\frac{({{m}_{1}}+{{m}_{2}}+{{m}_{3}})F}{{{m}_{3}}}\] |
| B. | \[\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] |
| C. | \[F-({{m}_{1}}+{{m}_{2}})g\] |
| D. | F |
| Answer» C. \[F-({{m}_{1}}+{{m}_{2}})g\] | |
| 12027. |
If M is mass of rocket, r is rate of ejection of gases with respect to rocket, then acceleration of the rocket \[\frac{dv}{dt}\] is equal to |
| A. | \[\frac{ru}{(m-rt)}\] |
| B. | \[\frac{(m-rt)}{ru}\] |
| C. | \[\frac{ru}{(m+rt)}\] |
| D. | \[\frac{ru}{m}\] |
| Answer» B. \[\frac{(m-rt)}{ru}\] | |
| 12028. |
A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25 then the maximum fraction of length of chain that can hang over on edge of table is |
| A. | 0.2 |
| B. | 0.35 |
| C. | 0.25 |
| D. | 0.15 |
| Answer» B. 0.35 | |
| 12029. |
The time taken by a body in sliding down a rough inclined plane of angle of inclination \[45{}^\circ \] is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be |
| A. | \[1/(1-{{n}^{2}})\] |
| B. | \[1-(1/{{n}^{2}})\] |
| C. | Ö\[\left\{ 1-(1/{{n}^{2}}) \right\}\] |
| D. | Ö\[\left\{ 1/(1-{{n}^{2}}) \right\}\] |
| Answer» C. Ö\[\left\{ 1-(1/{{n}^{2}}) \right\}\] | |
| 12030. |
Let \[\frac{1}{2\sqrt{3}}\sec \] be the coefficient of friction between blocks of mass m and M. The pulleys are frictionless and strings are massless. Acceleration of mass m is |
| A. | \[\frac{\sqrt{5}\,mg}{M+\sqrt{5}\,m\,+2\,\mu \,m}\] |
| B. | \[\frac{2\,mg}{m+5\,M\,+2\,\mu \,m}\] |
| C. | \[\frac{2\sqrt{5}\,mg}{M+5\,M\,+2\,\mu \,m}\] |
| D. | \[\frac{5\sqrt{2}\,mg}{M+\sqrt{5}\,m\,+\sqrt{2}\,\mu \,m}\] |
| Answer» D. \[\frac{5\sqrt{2}\,mg}{M+\sqrt{5}\,m\,+\sqrt{2}\,\mu \,m}\] | |
| 12031. |
Two blocks (m and M) are arranged as shown in Fig. 21. If there is friction between ground and M only and other surfaces are frictionless. The coefficient of friction between ground and M is \[\mu =0.75\] . The maximum ratio of m and M (m/M) so that the system remains at rest is |
| A. | \[1/4\] |
| B. | 3 |
| C. | \[1/3\] |
| D. | None of these |
| Answer» C. \[1/3\] | |
| 12032. |
The member OA rotates about a horizontal axis through O with a constant counter clockwise velocity \[\omega =3\] \[\text{rad}/\text{sec}\]. As it passes the position\[\theta ={{0}^{o}}\], a small mass m is placed upon it at a radial distance r = 0.5 m. If the mass is observed to slip at \[\theta ={{37}^{o}}\], the coefficient of friction between the mass & the member is: |
| A. | \[\frac{3}{16}\] |
| B. | \[\frac{9}{16}\] |
| C. | \[\frac{4}{9}\] |
| D. | \[\frac{5}{9}\] |
| Answer» B. \[\frac{9}{16}\] | |
| 12033. |
A particle is projected on a rough horizontal ground along positive x-axis from x = 0, with an initial speed of \[{{\text{V}}_{\text{0}}}\] The friction coefficient to the ground varies with x as Here K is a positive constant. The particle comes to rest at x equal |
| A. | \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{\text{Kg}}}\] |
| B. | \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{Kg}\] |
| C. | \[\frac{{{\text{v}}_{\text{0}}}}{\sqrt{2Kg}}\] |
| D. | \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{\sqrt{Kg}}\] |
| Answer» B. \[\frac{\text{2}{{\text{v}}_{\text{0}}}}{Kg}\] | |
| 12034. |
A block of mass m is attached with massless spring of force constant k. The block is placed over a fixed rough inclined surface for which the coefficient of friction is \[\mu =3/4.\] The block of mass m is initially at rest. The block of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the block up the plane is (neglect mass of string and pulley and friction in pulley.) |
| A. | \[\frac{3}{5}m\] |
| B. | \[\frac{4}{5}m\] |
| C. | \[\frac{6}{5}m\] |
| D. | \[\frac{3}{2}m\] |
| Answer» B. \[\frac{4}{5}m\] | |
| 12035. |
A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of friction between the block and the surface is 0.4. if the acceleration of the truck is 5\[m\text{/}{{s}^{2}}\]. Find the frictional force acting on the block? |
| A. | 2 N |
| B. | 55 M |
| C. | 4 N |
| D. | 10 N |
| Answer» D. 10 N | |
| 12036. |
With reference to the figure shown, if the coefficient of friction at the surfaces is 0.42, then the force F required to pull out the 6.0 kg block with an acceleration of 1.50\[m\text{/}{{s}^{2}}\] will be: |
| A. | 36 N |
| B. | 24 N |
| C. | 84 N |
| D. | 51 N |
| Answer» E. | |
| 12037. |
A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is\[{{x}^{2}}=ay\]. If the coefficient of friction is \[{{M}_{1}}\] the highest distance above the x-axis at which the particle will be in equilibrium is |
| A. | \[\mu a\] |
| B. | \[{{\mu }^{2}}a\] |
| C. | \[\frac{1}{4}{{\mu }^{2}}a\] |
| D. | \[\frac{1}{2}\mu a\] |
| Answer» D. \[\frac{1}{2}\mu a\] | |
| 12038. |
If the coefficient of friction between A and B is \[{{m}_{2}}\], the maximum horizontal acceleration of the wedge A for which B will remain at rest with respect to the wedge is: |
| A. | \[{{m}_{1}}={{m}_{2}}\] |
| B. | \[{{m}_{2}}\] |
| C. | \[{{m}_{1}}={{m}_{2}}\] |
| D. | \[{{m}_{2}}\] |
| Answer» C. \[{{m}_{1}}={{m}_{2}}\] | |
| 12039. |
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient or friction between the block and the wall is 0.2. The weight of the block is : \[\left( g=10\text{ }m/{{s}^{2}} \right)\] |
| A. | 20 N |
| B. | 50 N |
| C. | 100 N |
| D. | 2 N |
| Answer» E. | |
| 12040. |
A cannon after firing recoils due to [EAMCET 1980] |
| A. | Conservation of energy |
| B. | Backward thrust of gases produced |
| C. | Newton's third law of motion |
| D. | Newton's first law of motion |
| Answer» D. Newton's first law of motion | |
| 12041. |
A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore [J&K CET 2005] |
| A. | By throwing his shirt in vertically upward direction |
| B. | By spitting horizontally |
| C. | He will wait for the ice to melt in pond |
| D. | Unable to get at the shore |
| Answer» C. He will wait for the ice to melt in pond | |
| 12042. |
A book is lying on the table. What is the angle between the action of the book on the table and the reaction of the table on the book [Kerala PMT 2005] |
| A. | \[0{}^\circ \] |
| B. | \[30{}^\circ \] |
| C. | \[45{}^\circ \] |
| D. | \[180{}^\circ \] |
| Answer» E. | |
| 12043. |
Action and reaction forces act on |
| A. | The same body |
| B. | The different bodies |
| C. | The horizontal surface |
| D. | Nothing can be said |
| Answer» C. The horizontal surface | |
| 12044. |
In the figure shown, a block of weight 10 N resting on a horizontal surface. The coefficient of static friction between the block and the surface \[{{\mu }_{s}}=0.4\]. A force of 3.5 N will keep the block in uniform motion, once it has been set in motion. A horizontal force of 3 N is applied to the block, then the block will [MP PET 1993] |
| A. | Move over the surface with constant velocity |
| B. | Move having accelerated motion over the surface |
| C. | Not move |
| D. | First it will move with a constant velocity for some time and then will have accelerated motion |
| Answer» D. First it will move with a constant velocity for some time and then will have accelerated motion | |
| 12045. |
A body of mass 2 kg is kept by pressing to a vertical wall by a force of 100 N. The coefficient of friction between wall and body is 0.3. Then the frictional force is equal to [Orissa JEE 2003] |
| A. | 6 N |
| B. | 20 N |
| C. | 600 N |
| D. | 700 N |
| Answer» C. 600 N | |
| 12046. |
A force of 98 N is required to just start moving a body of mass 100 kg over ice. The coefficient of static friction is |
| A. | 0.6 |
| B. | 0.4 |
| C. | 0.2 |
| D. | 0.1 |
| Answer» E. | |
| 12047. |
When two surfaces are coated with a lubricant, then they [AFMC 1998, 99; AIIMS 2001] |
| A. | Stick to each other |
| B. | Slide upon each other |
| C. | Roll upon each other |
| D. | None of these |
| Answer» C. Roll upon each other | |
| 12048. |
A block of 1 kg is stopped against a wall by applying a force F perpendicular to the wall. If \[\mu =0.2\] then minimum value of F will be [MP PMT 2003] |
| A. | 980 N |
| B. | 49 N |
| C. | 98 N |
| D. | 490 N |
| Answer» C. 98 N | |
| 12049. |
A particle is moving along a circular path in the xy plane (see figure). When it crosses the x-axis, it has an acceleration along the path of\[1.5\text{ }m/{{s}^{2}}\], and is moving with a speed of 10 m/s in the negatives-direction. The total acceleration of the particle is: |
| A. | \[50\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] |
| B. | \[-50\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] |
| C. | \[10\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] |
| D. | \[1.5\hat{i}-50\hat{j}\text{ m/}{{\text{s}}^{2}}\] |
| Answer» C. \[10\hat{i}-1.5\hat{j}\text{ m/}{{\text{s}}^{2}}\] | |
| 12050. |
A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration a directed horizontally as shown in figure. Other end of the string is pulled with constant acceleration a vertically. The tension in the string is equal to |
| A. | \[m\sqrt{{{g}^{2}}+{{a}^{2}}}\] |
| B. | \[m\sqrt{{{g}^{2}}+{{a}^{2}}}-ma\] |
| C. | \[m\sqrt{{{g}^{2}}+{{a}^{2}}}+ma\] |
| D. | \[m\left( g+a \right)\] |
| Answer» D. \[m\left( g+a \right)\] | |