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question_answer1) From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\frac{ch}{2\pi \varepsilon _{o}^{2}}\]
done
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B)
\[\frac{{{e}^{2}}}{2\pi \varepsilon _{o}^{{}}Gm_{e}^{2}}\](\[{{m}_{e}}=\] mass of electron)
done
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C)
\[\frac{{{\mu }_{o}}{{\varepsilon }_{o}}}{{{c}^{2}}}\frac{G}{h{{e}^{2}}}\]
done
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D)
\[\frac{2\pi \sqrt{{{\mu }_{o}}{{\varepsilon }_{o}}}}{c{{e}^{2}}}\frac{h}{G}\]
done
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question_answer2) A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator?
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
37 s
done
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B)
27 s
done
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C)
24 s
done
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D)
45 s
done
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question_answer3)
Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: 
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\frac{u}{12}\left( \hat{i}+\sqrt{3}\hat{j} \right)\]
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B)
\[\frac{u}{12}\left( \hat{i}-\sqrt{3}\hat{j} \right)\]
done
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C)
\[\frac{u}{12}\left( -\hat{i}+\sqrt{3}\hat{j} \right)\]
done
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D)
\[\frac{u}{12}\left( -\hat{i}-\sqrt{3}\hat{j} \right)\]
done
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question_answer4) A bullet of mass 4g is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately?
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
0.19 m
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B)
0.379 m
done
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C)
0.569 m
done
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D)
0.758 m
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question_answer5) A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\frac{1}{2}m{{v}^{2}}\]
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B)
\[m{{v}^{2}}\]
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C)
\[\frac{1}{3}m{{v}^{2}}\]
done
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D)
\[\frac{1}{6}m{{v}^{2}}\]
done
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question_answer6)
A particle is moving in a circular path of radius a, with a constant velocity v as shown in the figure. The centre of circle is marked by 'C'. The angular momentum from the origin O can be written as: 
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[va(1+cos2\theta )\]
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B)
\[va(1+cos\theta )\]
done
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C)
\[vacos2\theta \]
done
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D)
\[va\]
done
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question_answer7)
Two hypothetical planets of masses m1 and m2 are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ?d?? (Speed of \[{{m}_{1}}\] is \[{{v}_{1}}\] and that of \[{{m}_{2}}\] is \[{{v}_{2}}\])
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[{{v}_{1}}={{v}_{2}}\]
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B)
\[{{v}_{1}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\] \[{{v}_{2}}={{m}_{1}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]
done
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C)
\[{{v}_{1}}={{m}_{1}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]\[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{d\left( {{m}_{1}}+{{m}_{2}} \right)}}\]
done
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D)
\[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{1}}}}\] \[{{v}_{2}}={{m}_{2}}\sqrt{\frac{2G}{{{m}_{2}}}}\]
done
clear
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question_answer8) Steel ruptures when a shear of \[3.5\times {{10}^{8}}N{{m}^{-2}}\]is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[1.4\times {{10}^{4}}N\]
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B)
\[2.7\times {{10}^{4}}N\]
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C)
\[3.3\times {{10}^{4}}N\]
done
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D)
\[1.1\times {{10}^{4}}N\]
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question_answer9) A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius 'a'. The time in which it will be emptied is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\frac{2A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]
done
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B)
\[\frac{\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]
done
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C)
\[\frac{2\sqrt{2}A}{\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]
done
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D)
\[\frac{A}{\sqrt{2}\pi {{a}^{2}}}\sqrt{\frac{h}{g}}\]
done
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question_answer10) Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct?
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
4PV + 3ST = 0
done
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B)
3PV + 4ST = 0
done
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C)
2PV + 3ST = 0
done
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D)
3PV + 2ST = 0
done
clear
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question_answer11) Hot water cools from \[60{}^\circ C\] to \[50{}^\circ C\] in the first 10 minutes and to \[42{}^\circ C\] in the next 10 minutes. The temperature of the surroundings is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[25{}^\circ C\]
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B)
\[10{}^\circ C\]
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C)
\[15{}^\circ C\]
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D)
\[20{}^\circ C\]
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question_answer12) A Carnot engine absorbs 1000 J of heat energy from a reservoir at \[127{}^\circ C\] and rejects 600 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[20%\text{ }and\,\,-43{}^\circ C\]
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B)
\[40%\text{ }and\,\,-33{}^\circ C\]
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C)
\[50%\text{ }and\,\,-20{}^\circ C\]
done
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D)
\[70%\text{ }and\,\,-10{}^\circ C\]
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question_answer13) At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 \[\text{m}{{\text{s}}^{\text{-1}}}\]. The gas is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[{{H}_{2}}\]
done
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B)
\[C{{l}_{2}}\]
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C)
\[{{O}_{2}}\]
done
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D)
\[{{F}_{2}}\]
done
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question_answer14) Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a, b, c are positive constants?
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[a+bx-c{{x}^{2}}\]
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B)
\[b{{x}^{2}}\]
done
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C)
\[a-bx+c{{x}^{2}}\]
done
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D)
\[-bx\]
done
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question_answer15) A source of sound A emitting waves of frequency 1800 Hz is falling towards ground with a terminal speed v. The observer B on the ground directly beneath the source receives waves of frequency 2150 Hz. The source A receives waves, reflected from ground of frequency nearly: (Speed of sound = 343 m/s)
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
2150 Hz
done
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B)
2500 Hz
done
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C)
1800 Hz
done
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D)
2400 Hz
done
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question_answer16) A spherically symmetric charge distribution is characterized by a charge density having the following variations: \[\rho (r)={{\rho }_{o}}\left( 1-\frac{r}{R} \right)\]for r < R\[\rho (r)=0\]for \[r\ge R\] Where r is the distance from the centre of the charge distribution \[{{\rho }_{o}}\]is a constant. The electric field at an internal point (r < R) is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\frac{{{\rho }_{o}}}{4{{\varepsilon }_{0}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]
done
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B)
\[\frac{{{\rho }_{o}}}{{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]
done
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C)
\[\frac{{{\rho }_{o}}}{3{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]
done
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D)
\[\frac{{{\rho }_{o}}}{12{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)\]
done
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question_answer17) The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \[K(x)={{K}_{o}}+\lambda x\] (\[\lambda =\] a constant) The capacitance C, of the capacitor, would be related to its vacuum capacitance Co for the relation :
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[C=\frac{\lambda d}{\ln (1+{{K}_{o}}\lambda d)}{{C}_{o}}\]
done
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B)
\[C=\frac{\lambda }{d.ln(1+{{K}_{o}}\lambda d)}{{C}_{o}}\]
done
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C)
\[C=\frac{\lambda d}{ln(1+\lambda d/{{K}_{o}})}{{C}_{o}}\]
done
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D)
\[C=\frac{\lambda }{d.ln(1+{{K}_{o}}/\lambda d)}{{C}_{o}}\]
done
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question_answer18)
The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors \[3\Omega ,9\Omega \]and \[9\Omega \] and a capacitor of 5.0 \[\mu F.\] 
How much is the current I in the circuit in steady state?
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
1.6 A
done
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B)
0.67 A
done
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C)
2.5 A
done
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D)
0.25 A
done
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question_answer19) A positive charge 'q' of mass 'm' is moving along the + x axis. We wish to apply a uniform magnetic field B for time \[\Delta t\]so that the charge reverses its direction crossing the y axis at a distance d. Then:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[B=\frac{mv}{qd}\]and\[\Delta t=\frac{\pi d}{v}\]
done
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B)
\[B=\frac{mv}{2qd}\]and\[\Delta t=\frac{\pi d}{2v}\]
done
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C)
\[B=\frac{2mv}{qd}\]and\[\Delta t=\frac{\pi d}{2v}\]
done
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D)
\[B=\frac{2mv}{qd}\]and\[\Delta t=\frac{\pi d}{v}\]
done
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question_answer20) Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field \[{{B}_{1}},\] at its centre when a current I passes through it. The ratio \[{{B}_{1}}:{{B}_{2}}\] is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
1 : 1
done
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B)
1 : 3
done
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C)
1 : 9
done
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D)
9 : 1
done
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question_answer21) A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L = 0.02 H. The current through the coil is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
10 cos (500 t)
done
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B)
- 10 cos (500t)
done
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C)
10 sin (500t)
done
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D)
- 10 sin (500t)
done
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question_answer22) A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
1.34 V/m
done
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B)
2.68 V/m
done
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C)
4.02 V/m
done
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D)
5.36 V/m
done
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question_answer23) The refractive index of the material of a concave lens is m. It is immersed in a medium of refractive index \[{{\mu }_{1}}.\] A parallel beam of light is incident on the lens. The path of the emergent rays when \[{{\mu }_{1}}>\mu \] is:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
done
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B)
done
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C)
done
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D)
done
clear
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question_answer24)
Interference pattern is observed at 'P' due to superimposition of two rays coming out from a source 'S' as shown in the figure. The value of 'l' for which maxima is obtained at 'P' is: (R is perfect reflecting surface) 
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[1=\frac{1n\lambda }{\sqrt{3}-1}\]
done
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B)
\[1=\frac{(2n-1)\lambda }{2\left( \sqrt{3}-1 \right)}\]
done
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C)
\[1=\frac{(2n-1)\lambda \sqrt{3}}{4\left( 2-\sqrt{3} \right)}\]
done
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D)
\[1=\frac{(2n-1)\lambda }{\sqrt{3}-1}\]
done
clear
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question_answer25) In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is \[\text{6600}\overset{\text{o}}{\mathop{\text{A}}}\,\], then wavelength of first maximum will be:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[\text{3300}\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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B)
\[\text{4400}\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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C)
\[\text{5500}\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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D)
\[\text{6600}\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
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question_answer26) A beam of light has two wavelengths of \[\text{497200}\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[\text{6216}\overset{\text{o}}{\mathop{\text{A}}}\,\] with a total intensity of \[3.6\times {{10}^{-3}}W{{m}^{-2}}\] equally distributed among the two wavelengths. The beam falls normally on an area of 1 \[c{{m}^{2}}\] of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2s is approximately:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
\[6\times {{10}^{11}}\]
done
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B)
\[9\times {{10}^{11}}\]
done
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C)
\[11\times {{10}^{11}}\]
done
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D)
\[15\times {{10}^{11}}\]
done
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question_answer27) A piece of bone of an animal from a ruin is found to have \[^{14}C\] activity of 12 disintegrations per minute per gm of its carbon content. The 14C activity of a living animal is 16 disintegrations per minute per gm. How long ago nearly did the animal die? (Given half life of 14C is t1/2 = 5760 years)
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
1672 years
done
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B)
2391 years
done
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C)
3291 years
done
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D)
4453 years
done
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question_answer28) For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
eV to 0.4 eV
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B)
0.5 eV to 0.8 eV
done
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C)
0.9 eV to 1.6 eV
done
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D)
1.7 eV to 3.0 eV
done
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question_answer29) For sky wave propagation, the radio waves must have a frequency range in between:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
MHz to 2 MHz
done
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B)
5 MHz to 25 MHz
done
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C)
35 MHz to 40 MHz
done
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D)
45 MHz to 50 MHz
done
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question_answer30) In the experiment of calibration of voltmeter, a standard cell of e.m.f. 1.1 volt is balanced against 440 cm of potential wire. The potential difference across the ends of resistance is found to balance against 220 cm of the wire. The corresponding reading of voltmeter is 0.5 volt. The error in the reading of volmeter will be:
[JEE Main Online Paper ( Held On 12 Apirl 2014 )
A)
0. 15 volt
done
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B)
0.15 volt
done
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C)
0.5 volt
done
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D)
? 0.05 volt
done
clear
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