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question_answer1) A uniform tube of length 60.5 cm is held vertically with its lower end dipped in water. A sound source of frequency 500 Hz sends sound waves into the tube. When the length of tube above water is 16 cm and again when it is 50 cm, the tube resonates with the source of sound. Two lowest frequencies (in Hz), to which tube will resonate when it is taken out of water, are (approximately).
JEE Main Online Paper (Held On 19 May 2012)
A)
281,562
done
clear
B)
281,843
done
clear
C)
276,552
done
clear
D)
272,544
done
clear
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question_answer2) Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of 3 \[\text{m}{{\text{s}}^{\text{-1}}}\]will be
JEE Main Online Paper (Held On 19 May 2012)
A)
12N
done
clear
B)
6N
done
clear
C)
zero
done
clear
D)
18N
done
clear
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question_answer3) A block of weight crests on a horizontal floor with coefficient of static friction \[\mu .\]It is desired to make the block move by applying minimum amount of force. The angle \[\theta \] from the horizontal at which the force should be applied and magnitude of the force F are respectively.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\theta ={{\tan }^{-1}}\left( \mu \right),F=\frac{\mu W}{\sqrt{1+{{\mu }^{2}}}}\]
done
clear
B)
\[\theta ={{\tan }^{-1}}\left( \frac{1}{\mu } \right),F=\frac{\mu W}{\sqrt{1+{{\mu }^{2}}}}\]
done
clear
C)
\[\theta =0,F=\mu W\]
done
clear
D)
\[\theta ={{\tan }^{-1}}\left( \frac{\mu }{1+\mu } \right),F=\frac{\mu W}{1+\mu }\]
done
clear
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question_answer4)
A coil of self inductance L is connected at one end of two rails as shown in figure. A connector of length l, mass m can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction B going into the page. At an instant t = 0 an initial velocity Vg is imparted to it and as a result of that it starts moving along x-axis. The displacement of the connector is represented by the figure. 
JEE Main Online Paper (Held On 19 May 2012)
A)
done
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B)
done
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C)
done
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D)
done
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question_answer5) A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An Engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is (T = surface tension, \[\rho \] = density)
JEE Main Online Paper (Held On 19 May 2012)
A)
\[{{\left[ \frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]
done
clear
B)
\[{{\left[ \frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]
done
clear
C)
\[{{\left[ \frac{3T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]
done
clear
D)
\[{{\left[ \frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]
done
clear
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question_answer6) The amount of heat produced in an electric circuit depends upon the current (t), resistance (R) and time (I). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be
JEE Main Online Paper (Held On 19 May 2012)
A)
1%
done
clear
B)
2%
done
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C)
6%
done
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D)
3%
done
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question_answer7) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: An inventor claims to have constructed an engine that has an efficiency of 30% when operated between the boiling and freezing points of water. This is not possible. Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures.
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
done
clear
B)
Statement 1 is true. Statement 2 is false.
done
clear
C)
Statement 1 is false, Statement 2 is true.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
done
clear
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question_answer8) The displacement \[y(t)=A\sin (\omega t+\phi )\]of a pendulum for \[\phi =\frac{2\pi }{3}\] is correctly represented by
JEE Main Online Paper (Held On 19 May 2012)
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
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question_answer9) A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length \[\left( \frac{L}{2} \right)\]each. The rods are completely In sulated from the surroundings. If the free end If copper rod is maintained at \[100{}^\circ C\] and that of steel at \[0{}^\circ C\] then the temperature of junction is Thermal conductivity of copper is 9 times that if steel)
JEE Main Online Paper (Held On 19 May 2012)
A)
\[90{}^\circ C\]
done
clear
B)
\[50{}^\circ C\]
done
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C)
\[10{}^\circ C\]
done
clear
D)
\[67{}^\circ C\]
done
clear
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question_answer10) Two point masses of mass \[{{m}_{1}}=fM\]and \[{{m}_{2}}=(1-f)M(f<1)\]are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities \[{{\omega }_{1}}\]) for\[{{m}_{1}}\]and \[{{\omega }_{2}}\]for\[{{m}_{2}}\]. In that case
JEE Main Online Paper (Held On 19 May 2012)
A)
\[(1-f){{\omega }_{1}}=f\omega \]
done
clear
B)
\[{{\omega }_{1}}={{\omega }_{2}}\]and independent of f
done
clear
C)
\[f{{\omega }_{1}}=(1-f){{\omega }_{2}}\]
done
clear
D)
\[{{\omega }_{1}}={{\omega }_{2}}\] and depend on f
done
clear
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question_answer11) Which one of the following is the Boolean expression for NOR gate?
JEE Main Online Paper (Held On 19 May 2012)
A)
\[Y=\overline{A+B}\]
done
clear
B)
\[Y=\overline{A.B}\]
done
clear
C)
\[Y=A.B\]
done
clear
D)
\[Y=\overline{A}\]
done
clear
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question_answer12) Two coherent plane light waves of equal amplitude makes a small angle a (« 1) with each other. They fall almost normally on a screen. If \[\lambda \] the wavelength of light waves, the fringe width \[\Delta x\]of interference patterns of the two sets of waves on the screen is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{2\lambda }{\alpha }\]
done
clear
B)
\[\frac{\lambda }{\alpha }\]
done
clear
C)
\[\frac{\lambda }{\left( 2\alpha \right)}\]
done
clear
D)
\[\frac{\lambda }{\sqrt{\alpha }}\]
done
clear
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question_answer13) lonisation energy of Li (Lithium) atom in ground state is 5.4 eV. Binding energy of an electron in \[L{{i}^{+}}\]ion in ground state is 75.6 eV. Energy required to remove all three electrons of Lithium (Li) atom is
JEE Main Online Paper (Held On 19 May 2012)
A)
81.0 eV
done
clear
B)
135.4eV
done
clear
C)
203.4eV
done
clear
D)
156.6eV
done
clear
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question_answer14) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Self inductance of a long solenoid of length L, total number of turns N and radius r is less than \[\frac{\pi {{\mu }_{0}}{{N}^{2}}{{r}^{2}}}{L}.\] Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current I is \[\frac{{{\mu }_{0}}NI}{L}\]in the middle of the solenoid but becomes less as we move towards its ends.
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is true. Statement 2 is false.
done
clear
B)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
done
clear
C)
Statement 1 is false. Statement 2 is true.
done
clear
D)
Statement 1 is true. Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
done
clear
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question_answer15) A charge of total amount Q is distributed over two concentric hollow spheres of radii r and R (R > r) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]
done
clear
B)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{2\left( {{R}^{2}}+{{r}^{2}} \right)}\]
done
clear
C)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]
done
clear
D)
\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]
done
clear
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question_answer16) N divisions on the main scale of a vernier caliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is 'a' units then the least count of the instrument is
JEE Main Online Paper (Held On 19 May 2012)
A)
a
done
clear
B)
\[\frac{a}{N}\]
done
clear
C)
\[\frac{N}{N+1}\times a\]
done
clear
D)
\[\frac{a}{N+1}\]
done
clear
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question_answer17) The decay constants of a radioactive substance for \[\alpha \] and \[\beta \] emission are \[{{\lambda }_{\alpha }}\]and \[{{\lambda }_{\beta }}\] respectively. If the substance emits \[\alpha \] and \[\beta \] simultaneously, then the average half life of the material will be
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{2{{T}_{\alpha }}{{T}_{\beta }}}{{{T}_{\alpha }}+{{T}_{\beta }}}\]
done
clear
B)
\[{{T}_{\alpha }}+{{T}_{\beta }}\]
done
clear
C)
\[\frac{{{T}_{\alpha }}{{T}_{\beta }}}{{{T}_{\alpha }}+{{T}_{\beta }}}\]
done
clear
D)
\[\frac{1}{2}\left( {{T}_{\alpha }}+{{T}_{\beta }} \right)\]
done
clear
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question_answer18) A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to
JEE Main Online Paper (Held On 19 May 2012)
A)
33%
done
clear
B)
67%
done
clear
C)
90%
done
clear
D)
(d) 10%
done
clear
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question_answer19) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A metallic surface is irradiated by a monochromatic light of frequency \[\upsilon >{{\upsilon }_{0}}\] (the threshold frequency). If the incident frequency is now doubled, the photocurrent and the maximum kinetic energy are also doubled. Statement 2: The maximum kinetic energy of photoelectrons emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends only on the intensity of the incident light.
JEE Main Online Paper (Held On 19 May 2012)
A)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
done
clear
B)
Statement 1 is false. Statement 2 is true.
done
clear
C)
Statement 1 is true, Statement 2 is false.
done
clear
D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
done
clear
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question_answer20) A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\sqrt{2}R\]
done
clear
B)
\[\frac{R}{\sqrt{2}}\]
done
clear
C)
\[\frac{R}{2}\]
done
clear
D)
R
done
clear
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question_answer21)
A glass prism of refractive index 1.5 is immersed in water (refractive index \[\frac{4}{3}\]) as shown in figure. A light beam incident normally on the face AB is totally reflected to reach the face BC, if 
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\sin \theta >\frac{5}{9}\]
done
clear
B)
\[\sin \theta >\frac{2}{3}\]
done
clear
C)
\[\sin \theta >\frac{8}{9}\]
done
clear
D)
\[\sin \theta >\frac{1}{3}\]
done
clear
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question_answer22) An electromagnetic wave with frequency co and wavelength \[\lambda \]travels in the + y direction. Its magnetic field is along + x-axis. The vector equation for the associated electric field (of amplitude \[{{E}_{0}}\]) is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{x}\]
done
clear
B)
\[\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{x}\]
done
clear
C)
\[\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{z}\]
done
clear
D)
\[\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{z}\]
done
clear
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question_answer23)
A 6.0 volt battery is connected to two light bulbs as shown in figure. Light bulb 1 has resistance 3 ohm while light bulb 2 has resistance 6 ohm. Battery has negligible internal resistance. Which bulb will glow brighter? 
JEE Main Online Paper (Held On 19 May 2012)
A)
Bulb 1 will glow more first and then its brightness will become less than bulb 2
done
clear
B)
Bulbl
done
clear
C)
Bulb2
done
clear
D)
Both glow equally
done
clear
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question_answer24) A generator has armature resistance of \[0.1\Omega \]and develops an induced emf of 120 F when driven at its rated speed. Its terminal voltage when a current of 50 A is being drawn is
JEE Main Online Paper (Held On 19 May 2012)
A)
120 V
done
clear
B)
5V
done
clear
C)
115 V
done
clear
D)
70 V
done
clear
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question_answer25) A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity.
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{u+v}{2}\]
done
clear
B)
\[\frac{1}{2}\sqrt{{{u}^{2}}+{{v}^{2}}}\]
done
clear
C)
\[\sqrt{uv}\]
done
clear
D)
\[\sqrt{\left( \frac{{{u}^{2}}+{{v}^{2}}}{2} \right)}\]
done
clear
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question_answer26)
A ring is suspended from a point S on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take \[g={{\pi }^{2}}\]) 
JEE Main Online Paper (Held On 19 May 2012)
A)
0.15m
done
clear
B)
1.5m
done
clear
C)
1.0m
done
clear
D)
0.5m
done
clear
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question_answer27)
The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric field E is applied at an angle\[\frac{\pi }{4}\]with the vertical direction. The electric flux through the curved surface of the hemisphere is 
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\pi {{a}^{2}}E\]
done
clear
B)
\[\frac{\pi {{a}^{2}}E}{\sqrt{2}}\]
done
clear
C)
\[\frac{\pi {{a}^{2}}E}{2\sqrt{2}}\]
done
clear
D)
\[\frac{\left( \pi +2 \right)\pi {{a}^{2}}E}{{{\left( 2\sqrt{2} \right)}^{2}}}\]
done
clear
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question_answer28) A steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of
JEE Main Online Paper (Held On 19 May 2012)
A)
50kg
done
clear
B)
400kg
done
clear
C)
100kg
done
clear
D)
200kg
done
clear
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question_answer29) Given the electric field of a complete amplitude modulated wave as\[\overset{_{\to }}{\mathop{E}}\,=\hat{i}{{E}_{C}}\left( 1+\frac{{{E}_{m}}}{{{E}_{C}}}\cos {{\omega }_{m}}t \right)\cos {{\omega }_{C}}t.\] Where the subscript c stands for the carrier wave and m for the modulating signal. The frequencies present in the modulated wave are
JEE Main Online Paper (Held On 19 May 2012)
A)
\[{{\omega }_{C}}\]and\[\sqrt{\omega _{c}^{2}+\omega _{m}^{2}}\]
done
clear
B)
\[{{\omega }_{c}},{{\omega }_{c}}+{{\omega }_{m}}\] and\[{{\omega }_{c}}-{{\omega }_{m}}\]
done
clear
C)
\[{{\omega }_{c}}\]and\[{{\omega }_{m}}\]
done
clear
D)
\[{{\omega }_{c}}\]and\[\sqrt{{{\omega }_{c}}{{\omega }_{m}}}\]
done
clear
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question_answer30) The pressure of an ideal gas varies with volume as \[P=\alpha V,\] where a is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes 'm times its initial volume. The work done by the gas in the process is
JEE Main Online Paper (Held On 19 May 2012)
A)
\[\frac{\alpha V}{2}\left( {{m}^{2}}-1 \right)\]
done
clear
B)
\[\frac{{{\alpha }^{2}}{{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]
done
clear
C)
\[\frac{\alpha }{2}\left( {{m}^{2}}-1 \right)\]
done
clear
D)
\[\frac{\alpha {{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]
done
clear
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