Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

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.

5201.

A prism of refractive index \[\mu \] and angle A is placed in the minimum deviation position. If the angle of minimum deviation is A, then the value of A in terms of\[\mu \] is

A. \[{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]       
B. \[{{\sin }^{-1}}\sqrt{\frac{\mu -1}{2}}\]
C. \[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]     
D. \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
Answer» D. \[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
5202.

Two convex lenses placed in contact form the image of a distant object at P. If lens  is moved to the right, the image will

A. Move to the left
B. Move to the right
C. Remain at P
D. Move either to the left or right, depending upon focal lengths of the lenses.
Answer» C. Remain at P
5203.

A convex lens of focal length 1.0 m and a concave lens of focal length 0.25 m are 0.75 m apart. A parallel beam of light is incident on the convex lens. The beam emerging after refraction from both lenses is

A. Parallel to the principal axis
B. Convergent
C. Divergent
D. None of the above
Answer» B. Convergent
5204.

A light ray is incident by grazing one of the face of a prism and after refraction ray does not emerge out, what should be the angle of prism while critical angle is C?

A. Equal to 2C      
B. Less than 1C
C. More than 2C
D. None of the above
Answer» D. None of the above
5205.

A point object is placed at a distance of 25 cm from a convex lens of focal length 20 cm. If a glass slab of thickness t and refractive index 1.5 is inserted between the lens and the object, the image is formed at infinity. The thickness t is

A. 10 cm  
B. 5 cm
C. 20 cm  
D. 15 cm
Answer» E.
5206.

A positively charged particle moving along \[x\]-axis with a certain velocity enters a uniform electric field directed along positives\[y\]-axis. Its

A. Vertical velocity changes but horizontal velocity remains constant
B. Horizontal velocity changes but vertical velocity remains constant
C. Both vertical and horizontal velocities change
D. Neither vertical nor horizontal velocity changes
Answer» B. Horizontal velocity changes but vertical velocity remains constant
5207.

A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring is q, and the linear charge density on the straight wire is\[\lambda \]. The interaction force between the ring and the wire is

A. \[\frac{\lambda q}{4\pi {{\varepsilon }_{0}}r}\]  
B. \[\frac{\lambda q}{2\sqrt{2}\pi {{\varepsilon }_{0}}r}\]
C. \[\frac{2\sqrt{2}\lambda q}{\pi {{\varepsilon }_{0}}r}\]   
D. \[\frac{4\lambda q}{\pi {{\varepsilon }_{0}}r}\]
Answer» B. \[\frac{\lambda q}{2\sqrt{2}\pi {{\varepsilon }_{0}}r}\]
5208.

Two semicircular rings lying in the same plane of uniform linear charge density \[\lambda \] have radii r and 2r. They are joined using two straight uniformly charged wires of linear charge density \[\lambda \] and length r as shown in the figure. The magnitude of electric field at common centre of semi-circular rings is

A. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3\lambda }{2r}\]                      
B. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\lambda }{2r}\]
C. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2\lambda }{r}\]
D. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\lambda }{r}\]
Answer» E.
5209.

Two identical thin rings each of radius \[R\] meters are coaxially placed at a distance R meters apart. If \[{{Q}_{1}}\] coulomb and \[{{Q}_{2}}\] coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge\[q\] from the centre of one ring to that of other is

A. Zero                 
B. \[\frac{q({{Q}_{2}}-{{Q}_{1}})(\sqrt{2}-1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\]
C. \[\frac{q\sqrt{2}({{Q}_{1}}+{{Q}_{2}})}{4\pi {{\varepsilon }_{0}}R}\] 
D. \[\frac{q({{Q}_{1}}+{{Q}_{2}})(\sqrt{2}+1)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\]
Answer» C. \[\frac{q\sqrt{2}({{Q}_{1}}+{{Q}_{2}})}{4\pi {{\varepsilon }_{0}}R}\] 
5210.

In the given figure two tiny conducting balls of identical mass \[m\] and identical charge \[q\] hang from non-conducting threads of equal length\[L\]. Assume that \[\theta \] is so small that\[\tan \theta \]\[\approx \]\[\sin \theta \], then for equilibrium \[x\] is equal to

A. \[{{\left( \frac{{{q}^{2}}L}{2\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]       
B. \[{{\left( \frac{{{q}^{{}}}{{L}^{2}}}{2\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]
C. \[{{\left( \frac{{{q}^{2}}{{L}^{2}}}{4\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]    
D. \[{{\left( \frac{{{q}^{2}}{{L}^{{}}}}{4\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]
Answer» B. \[{{\left( \frac{{{q}^{{}}}{{L}^{2}}}{2\pi {{\varepsilon }_{0}}mg} \right)}^{\frac{1}{3}}}\]
5211.

Two infinitely long parallel wires having linear charge densities \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] respectively are placed at a distance of \[R\] metres. The force per unit length on either wire will be \[\left( k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)\]

A. \[k\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{2}}}\]    
B. \[k\frac{2{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{{}}}}\]
C. \[k\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{2}}}\]      
D. \[k\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{R}\]
Answer» C. \[k\frac{{{\lambda }_{1}}{{\lambda }_{2}}}{{{R}^{2}}}\]      
5212.

The maximum electric field at a point on the axis of a uniformly charged ring is \[{{E}_{0}}\]. At how any points on the axis will the magnitude of the electric field be\[{{E}_{0}}/2\].

A. 1                     
B. 2
C. 3                     
D. 4
Answer» E.
5213.

The electric flux from a cube of edge \[l\] is\[\phi \]. If an edge of the cube is made \[2l\] and the charge enclosed is halved, its value will be

A. \[4\phi \]                       
B. \[2\phi \]
C. \[\phi /2\]                      
D. \[\phi \]
Answer» D. \[\phi \]
5214.

It is required to hold equal charges \[q\] in equilibrium at the comers of a square. What charge when placed at the center of the square will do this?

A. \[-\frac{q}{2}(1+2\sqrt{2})\]      
B. \[\frac{q}{2}(1+2\sqrt{2})\]
C. \[\frac{q}{4}(1+2\sqrt{2})\]       
D. \[-\frac{q}{4}(1+2\sqrt{2})\]
Answer» E.
5215.

A charged oil drop is suspended in a uniform field of \[3\times {{10}^{4}}V/m\] so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge as \[9.9\times {{10}^{-15}}kg\,and\,g\,as\,10m/{{s}^{2}}\]

A. \[3.3\times {{10}^{-18}}C\]     
B. \[3.2\times {{10}^{-18}}C\]
C. \[1.6\times {{10}^{-18}}C\]     
D. \[4.8\times {{10}^{-18}}C\]
Answer» B. \[3.2\times {{10}^{-18}}C\]
5216.

Variation of electrostatic potential along the \[x\]-direction is shown in figure. The correct statement about electric field is

A. \[x\]-component at point B is maximum
B. \[x\]-component at point A is toward positive \[x\]-axis
C. \[x\]-component at point C is along negative \[x\]-axis
D. \[x\]-component at point C is along positive \[x\]- axis
Answer» E.
5217.

At a point in space, the electric field points toward north. In the region surrounding this point, the rate of change of potential will be zero along

A. North   
B. South
C. North-south       
D. East-west
Answer» E.
5218.

A small conducting sphere of radius\[a\], carrying a charge\[+Q\], is placed inside an equal and oppositely charged conducting shell of radius b such that their centers coincide. Determine the potential at a point which is at a distance c from center such that a < c < b.

A. \[k(Q/c+Q/b)\]
B. \[k(Q/a+Q/b)\]
C. \[k(Q/a-Q/b)\]
D. \[k(Q/c-Q/b)\]
Answer» E.
5219.

A uniform electric field pointing in positive \[x\]-direction exists in a region. Let \[A\] be the origin, \[B\] be the point on the \[x\]-axis at \[x=+1\] cm and \[C\] be the point on the \[y\]-axis at \[y=+1\]cm. Then the potentials at the points \[A\], \[B\] and \[C\] satisfy

A. \[{{V}_{A}}<{{V}_{B}}\]
B. \[{{V}_{A}}>{{V}_{B}}\]
C. \[{{V}_{A}}<{{V}_{C}}\]       
D. \[{{V}_{A}}>{{V}_{C}}\]  
Answer» C. \[{{V}_{A}}<{{V}_{C}}\]       
5220.

A soap bubble (surface tension =\[T\]) is charged to a maximum surface density of charge =\[\sigma \]. When it is just going to burst? Its radius R is given by

A. \[R=\frac{{{\sigma }^{2}}}{8{{\varepsilon }_{0}}T}\]  
B. \[R=8{{\varepsilon }_{0}}\frac{T}{{{\sigma }^{2}}}\]
C. \[R=\frac{{{\sigma }^{{}}}}{\sqrt{8{{\varepsilon }_{0}}T}}\]   
D. \[R=\frac{{{\sqrt{8{{\varepsilon }_{0}}T}}^{{}}}}{\sigma }\]
Answer» C. \[R=\frac{{{\sigma }^{{}}}}{\sqrt{8{{\varepsilon }_{0}}T}}\]   
5221.

Assume that the silicon diode in the circuit requires a minimum current of 1 m A to be above the knee point (0.7 V) of I-V characteristics. Also assume that the voltage across the diode is independent of current above the knee point. If \[{{V}_{B}}\]= 5 V, then the maximum value of R so that the voltage is above the knee point is

A. \[4.3k\Omega \] 
B. \[2\,k\Omega \]
C. \[1\,\Omega \]               
D. 0
Answer» B. \[2\,k\Omega \]
5222.

Consider an optical communication system operating at \[\lambda \approx 800\] nm. Suppose, only 1% of the optical source frequency is the available channel bandwidth for optical communication. How many channels can be accommodated for transmitting audio signals requiring a bandwidth of 8 kHz?

A. \[4.8\times {{10}^{8}}\]          
B. 48
C. \[6.2\times {{10}^{8}}\]          
D. \[4.8\times {{10}^{5}}\]
Answer» B. 48
5223.

In the following circuit of PN junction diodes\[{{D}_{1}}\], \[{{D}_{2}}\] and \[{{D}_{3}}\] are ideal then I is

A. \[E/R\]  
B. \[E/2R\]
C. \[2E/3R\]           
D. Zero
Answer» B. \[E/2R\]
5224.

In the given detector circuit, the suitable value of carrier frequency is

A. \[<<{{10}^{9}}Hz\]   
B. \[<<{{10}^{5}}Hz\]
C. \[>>{{10}^{9}}Hz\]   
D. None of these
Answer» B. \[<<{{10}^{5}}Hz\]
5225.

The transfer ratio of a transistor is 50. The input resistant of the transistor when used in the common-emittej configuration is 1 k\[\Omega \]. The peak value for an AC input voltage of 0.01 V peak is

A. \[100\mu A\]     
B. \[0.01mA\]
C. \[0.25mA\]        
D. \[500\mu A\]  
Answer» E.
5226.

A telephone link operating at a central frequency of 10 GHz is established. If 1% of this is available then how many telephone channel can be simultaneously give (when each telephone covering a band width of 5 kHz?

A. \[2\times {{10}^{4}}\] 
B. \[2\times {{10}^{6}}\]
C. \[5\times {{10}^{4}}\] 
D. \[5\times {{10}^{6}}\]
Answer» B. \[2\times {{10}^{6}}\]
5227.

The dominant mechanisms for motion of charge carriel in forward and reverse biased silicon P-N junctions are

A. Drift in forward bias, diffusion in reverse bias
B. Diffusion in forward bias, drift in reverse bias
C. Diffusion in both forward and reverse bias
D. Drift in both forward and reverse bias
Answer» C. Diffusion in both forward and reverse bias
5228.

If the area to be covered for TV telecast is doubled then height of transmitting antenna (TV tower) will have to be

A. Doubled
B. Halved
C. Quadrupled       
D. Kept unchanged
Answer» B. Halved
5229.

A TV tower has a height of 100 m. How much population is covered by the TV broadcast if the average population density around the tower is\[1000\,k{{m}^{-2}}\]? (Radius of the earth\[=6.37\times {{10}^{6}}m\])

A. 4 lakh   
B. 4 billion
C. 40,000 
D. 40 lakh
Answer» E.
5230.

In the circuit given below, V(t) is the sinusoidal voltage source, voltage drop \[{{V}_{AB}}(t)\] across the resistance R

A. Is half wave rectified
B. Is full wave rectified
C. Has the same peak value in the positive and negative half cycles
D. Has different peak values during positive and negative half cycle
Answer» E.
5231.

How many photons of a radiation of wavelength \[\lambda =5\times {{10}^{-7}}m\] must fall per second on a blackened plate in order to produce a force of \[6.62\times {{10}^{-5}}\]N?

A. \[3\times {{10}^{19}}\]
B. \[5\times {{10}^{22}}\]
C. \[2\times {{10}^{22}}\]
D. \[1.67\times {{10}^{18}}\]
Answer» B. \[5\times {{10}^{22}}\]
5232.

Television signals on earth cannot be received at distances greater than 100 km from the transmission station. Thereason behind this is that

A. The receiver antenna is unable to detect the signal at a distance greater than 100 km
B. The TV programme consists of both audio and video signals.
C. The TV signals are less powerful than radi signals
D. The surface of earth is curved like a sphere
Answer» E.
5233.

When a silicon PN junction is in forward biased condition with series resistance, it has knee voltage of 0.6 V. Current flow in it is 5 mA, when PN junction is connected with 2.6 V battery, the value of series resistance is

A. \[100\Omega \]  
B. \[200\Omega \]
C. \[400\Omega \]
D. \[500\Omega \]
Answer» D. \[500\Omega \]
5234.

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line whose slope

A. Depends on the nature of the metal used
B. Depends on the intensity of the radiation
C. Depends both on the intensity of the radiation and the metal used
D. Is the same for all metals and independent of the intensity of the radiation?
Answer» E.
5235.

The ratio of de Broglie wavelength of a a-particle to that of a proton being subjected to the same magnetic field so that the radii of their paths are equal to each other assuming the field induction vector \[\vec{B}\] is perpendicular to the velocity vectors of the a-particle and the proton is

A. 1                     
B. \[\frac{1}{4}\]
C. \[\frac{1}{2}\]  
D. \[2\]
Answer» D. \[2\]
5236.

The potential energy of a particle of mass m is given by \[U(x)=\left\{ \begin{matrix}    {{E}_{0}};  \\    0;  \\ \end{matrix}\begin{matrix}    0\le x\le 1  \\    x>1  \\ \end{matrix} \right.\] \[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\] are the de Broglie wavelengths of the particle, when \[0\le x\le 1\]and \[x>1\] respectively. If the total energy of particle is 2\[{{E}_{0}}\], the ratio \[\frac{{{\lambda }_{0}}}{{{\lambda }_{2}}}\] will be

A. 2                     
B. 1         
C. \[\sqrt{2}\]        
D. \[\frac{1}{\sqrt{2}}\]
Answer» D. \[\frac{1}{\sqrt{2}}\]
5237.

A plane electromagnetic wave \[{{E}_{z}}=100\cos (6\times {{10}^{8}}t+4x)V/m\] propagates in a medium of dielectric constant

A. 1.5
B.  2.0
C. 2.4                   
D. 4
Answer» C. 2.4                   
5238.

Light from a hydrogen discharge tube is incident on the cathode of a photoelectric cell. The work function of the cathode surface is 4.2 eV. In order to reduce the photo- current to zero the voltage of the anode relative to the cathode must be made

A. -4.2V   
B. -9.4V
C. -17.8V  
D. +9.4 V
Answer» C. -17.8V  
5239.

The transmitting antenna of a radio-station is mounted vertically. At a point 10 km due north of the transmitter the peak electric field is\[{{10}^{-3}}\,V\text{/}m.\] The amplitude of the radiated magnetic field is

A. \[3.33\times {{10}^{-10}}T\]    
B. \[3.33\times {{10}^{-12}}T\]
C. \[{{10}^{-13}}T\]       
D. \[3\times {{10}^{5}}T\]
Answer» C. \[{{10}^{-13}}T\]       
5240.

In the experiment on photoelectric effect, the graph between \[{{E}_{K}}_{(max)}\] is found to be a straight line as shown in figure. The threshold frequency and Planck's constant according to this graph are

A. \[3.33\times {{10}^{18}}{{s}^{-1}},\,\,6\times {{10}^{-34}}J\text{-}s\]
B. \[6\times {{10}^{18}}{{s}^{-1}},6\times {{10}^{-34}}J\text{-}s\]
C. \[2.66\times {{10}^{18}}{{s}^{-1}},\,\,4\times {{10}^{-34}}J\text{-}s\]
D. \[4\times {{10}^{18}}{{s}^{-1}},\,\,3\times {{10}^{-34}}J\text{-}s\]  
Answer» B. \[6\times {{10}^{18}}{{s}^{-1}},6\times {{10}^{-34}}J\text{-}s\]
5241.

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of \[2.5\times {{10}^{10}}Hz\] and amplitude 480 V/m. The amplitude of the oscillating magnetic field will be

A. \[1.52\times {{10}^{-8}}Wb/{{m}^{2}}\]        
B. \[1.52\times {{10}^{-7}}Wb/{{m}^{2}}\]
C. \[1.6\times {{10}^{-6}}Wb/{{m}^{2}}\]
D. \[1.6\times {{10}^{-7}}Wb/{{m}^{2}}\]
Answer» D. \[1.6\times {{10}^{-7}}Wb/{{m}^{2}}\]
5242.

A plane em wave of wave intensity of \[10\,W/{{m}^{2}}\] strikes a small mirror of area 20\[c{{m}^{2}}\], held perpendicular to the approaching wave. The radiation force on the mirror will be

A. \[6.6\times {{10}^{-11}}N\]     
B. \[1.33\times {{10}^{-11}}N\]
C. \[1.33\times {{10}^{-10}}N\]
D. \[6.6\times {{10}^{-10}}N\]
Answer» D. \[6.6\times {{10}^{-10}}N\]
5243.

Given that a photon of light of wavelength 10,000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\] has an energy equal to 1.23 eV. When light of wavelength 5000 \[\overset{\text{o}}{\mathop{\text{A}}}\,\] and intensity \[{{I}_{0}}\] falls on a photoelectric cell, the saturation current is \[0.40\times {{10}^{-6}}\]\[\overset{\text{o}}{\mathop{\text{A}}}\,\] and the stopping potential is 1.36 V; then the work function is

A. \[0.43\,eV\]       
B. \[1.10\,eV\]
C. \[1.36\,eV\]       
D. \[2.47\,eV\]
Answer» C. \[1.36\,eV\]       
5244.

A material particle with a rest mass \[{{m}_{0}}\] is moving with a velocity of light c. Then, the wavelength of the de Broglie wave associated with it is

A. \[(h/{{m}_{0}}c)\]        
B. Zero
C. \[\infty \]                       
D. \[({{m}_{0}}c/h)\]
Answer» C. \[\infty \]                       
5245.

If the intensity of radiation incident on a photocell be increased four times, then the number of photoelectrons and the energy of photoelectrons emitted respectively become

A. Four times, doubled
B. Doubled, remains unchanged
C. Remains unchanged, doubled
D. Four times, remains unchanged
Answer» E.
5246.

Two electrons are moving with same speed v. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field, then after some time de Broglie wavelengths of two are \[{{\lambda }_{1}}\] and\[{{\lambda }_{2}}\], respectively. Now,

A. \[{{\lambda }_{1}}={{\lambda }_{2}}\]
B. \[{{\lambda }_{1}}>{{\lambda }_{2}}\]
C. \[{{\lambda }_{1}}<{{\lambda }_{2}}\]
D. \[{{\lambda }_{1}}\]can be greater than or less than \[{{\lambda }_{2}}\]
Answer» E.
5247.

What is the de Broglie wavelength of the wave associated with an electron that has been accelerated through a potential difference of 50.0 V?

A. \[2.7\times {{10}^{-10}}\]        
B. \[1.74\times {{10}^{-10}}\]
C. \[3.6\times {{10}^{-9}}\]         
D. \[4.9\times {{10}^{-11}}\]
Answer» C. \[3.6\times {{10}^{-9}}\]         
5248.

Two resistors of 10\[\Omega \] and 20\[\Omega \] and an ideal inductor of 10 H are connected to a 2 V battery as shown in figure. Key K is inserted at time t = 0. The initial (t = 0) and final (\[t\to \infty \]) currents through the battery are

A. \[\frac{1}{15}A,\frac{1}{10}A\] 
B. \[\frac{1}{10}A,\frac{1}{15}A\]
C. \[\frac{2}{15}A,\frac{1}{10}A\] 
D. \[\frac{1}{15}A,\frac{2}{25}A\]
Answer» B. \[\frac{1}{10}A,\frac{1}{15}A\]
5249.

A conducting ring of radius r is rolling without slipping with a constant angular velocity \[\omega \](figure). If the magnetic field strength is B and is directed into the page then the emf induced across PQ is

A. \[B\omega {{r}^{2}}\] 
B. \[\frac{B\omega {{r}^{2}}}{2}\]
C. \[4B\omega {{r}^{2}}\]
D. \[\frac{{{\pi }^{2}}{{r}^{2}}B\omega }{8}\]
Answer» B. \[\frac{B\omega {{r}^{2}}}{2}\]
5250.

A conducting rod PQ of length \[l\] = 2 m is moving at a speed of \[2\,m{{s}^{-1}}\] making an angle of \[30{}^\circ \] with its length. A uniform magnetic field B = 2 T exists in a direction perpendicular to the plane of motion. Then

A. \[{{V}_{p}}-{{V}_{Q}}=8V\]
B. \[{{V}_{p}}-{{V}_{Q}}=4V\]
C. \[{{V}_{Q}}-{{V}_{P}}=8V\]
D. \[{{V}_{Q}}-{{V}_{P}}=4V\]
Answer» C. \[{{V}_{Q}}-{{V}_{P}}=8V\]