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question_answer1) The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by \[100{}^\circ C\] is : (For steel Young?s modulus is \[2\times {{10}^{11}}N{{m}^{-2}}\]and coefficient of thermal expansion is \[1.1\times {{10}^{-5}}{{K}^{-1}}\])
JEE Main Solved Paper-2014
A)
\[2.2\times {{10}^{7}}Pa\]
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B)
\[2.2\times {{10}^{6}}Pa\]
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C)
\[2.2\times {{10}^{8}}Pa\]
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D)
\[2.2\times {{10}^{9}}Pa\]
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question_answer2)
A conductor lies along the z-axis at \[-1.5\le z<1.5m\]and carries a fixed current of 10.0 A in \[-{{\hat{a}}_{z}}\]direction (see figure). For a field \[\vec{B}=3.0\times {{10}^{-4}}{{e}^{-0.2x}}{{\hat{a}}_{y}}T,\]find the power required to move the conductorat constant speed to \[x=2.0m,y=0m\]in \[5\times {{10}^{-3}}s.\] Assume parallel motion along the x-axis. 
JEE Main Solved Paper-2014
A)
14.85 W
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B)
29.7 W
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C)
1.57 W
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D)
2.97 W
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question_answer3)
- A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \[\omega \]rad/s about the vertical. About the point of suspension:
JEE Main Solved Paper-2014
A)
angular momentum changes in direction but not in magnitude.
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B)
angular momentum changes both in direction and magnitude.
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C)
angular momentum is conserved.
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D)
angular momentum changes in magnitude but not in direction.
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question_answer4) 2. The current voltage relation of diode is given by \[I=\left( {{e}^{1000V/T}}-1 \right)mA,\]where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ± 0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
JEE Main Solved Paper-2014
A)
0.5 mA
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B)
0.05 mA
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C)
0.2 mA
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D)
0.02 mA
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question_answer5) 3. An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)
JEE Main Solved Paper-2014
A)
38 cm
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B)
6 cm
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C)
16 cm
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D)
22 cm
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question_answer6)
Match List - I (Electromagnetic wave type) with List - II (Its association/application) and select thecorrect option from the choices given below the lists :
| List - I |
List - II |
| (a) Infrared waves |
(i) To treat muscular strain |
| (b) Radio waves |
(ii) For broadcasting |
| (c) X-rays |
(iii) To detect fracture of bones |
| (d) Ultraviolet rays |
(iv) Absorbed by the ozone layer of the atmosphere |
JEE Main Solved Paper-2014
A)
(a) - (iii) (b) - (ii) (c) - (i) (d) - (iv)
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B)
(a) - (i) (b) - (i) (c) - (iii) (d) - (iv)
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C)
(a) - (iv) (b) - (iii) (c) - (ii) (d) - (i)
done
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D)
(a) - (i) (b) - (ii) (c) - (iv) (d) - (iii)
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question_answer7) A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with adielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is\[3\times {{10}^{4}}V/m,\]the charge density of the positive plate will be close to :
JEE Main Solved Paper-2014
A)
\[3\times {{10}^{4}}C/{{m}^{2}}\]
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B)
\[6\times {{10}^{4}}C/{{m}^{2}}\]
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C)
\[6\times {{10}^{-7}}C/{{m}^{2}}\]
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D)
\[3\times {{10}^{-7}}C/{{m}^{2}}\]
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question_answer8) 5. A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it ?
JEE Main Solved Paper-2014
A)
A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.
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B)
A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.
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C)
A meter scale.
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D)
A verniercalliper where the 10 divisions in vernier scale matches with 9 division in main scale &main scale has 10 divisions in 1 cm.
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question_answer9) 9. Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :
JEE Main Solved Paper-2014
A)
\[\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}\]
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B)
\[\frac{1}{2}\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}\]
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C)
\[\sqrt{\frac{GM}{R}}\]
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D)
\[\sqrt{2\sqrt{2}\frac{GM}{R}}\]
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question_answer10) 10. In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :
JEE Main Solved Paper-2014
A)
12 A
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B)
14 A
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C)
8 A
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D)
10 A
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question_answer11) 11. A particle moves with simple harmonic motion in a straight line. In first \[\tau s\], after starting from rest it travels a distance a, and in next \[\tau s\] it travels 2a, in same direction, then :
JEE Main Solved Paper-2014
A)
amplitude of motion is 4a
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B)
time period of oscillations is \[6\tau \]
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C)
amplitude of motion is 3a
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D)
time period of oscillations is \[8\tau \]
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question_answer12) The coercivity of a small magnet where the Ferro magnet gets demagnetized is \[3\times {{10}^{3}}A\,{{m}^{-1}}.\]The currentrequired to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet getsdemagnetized when inside the solenoid, is :
JEE Main Solved Paper-2014
A)
3 A
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B)
6 A
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C)
30 mA
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D)
60 mA
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question_answer13) The forward biased diode connection is :
JEE Main Solved Paper-2014
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_answer14) During the propagation of electromagnetic waves in a medium :
JEE Main Solved Paper-2014
A)
Electric energy density is equal to the magnetic energy density.
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B)
Both electric and magnetic energy densities are zero.
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C)
Electric energy density is double of the magnetic energy density.
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D)
Electric energy density is half of the magnetic density.
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question_answer15)
In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to : 
JEE Main Solved Paper-2014
A)
−1
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B)
\[\frac{1-e}{e}\]
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C)
\[\frac{e}{1-e}\]
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D)
1
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question_answer16)
A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m andradius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? 
JEE Main Solved Paper-2014
A)
\[\frac{5g}{6}\]
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B)
g
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C)
\[\frac{2g}{3}\]
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D)
\[\frac{g}{2}\]
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question_answer17)
One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement : 
JEE Main Solved Paper-2014
A)
The change in internal energy in the process AB is − 350 R.
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B)
The change in internal energy in the process BC is − 500 R.
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C)
The change in internal energy in whole cyclic process is 250 R.
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D)
The change in internal energy in the process CA is 700 R.
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question_answer18) From a tower of height H, a particle is thrown vertically upwards with a speed U. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is :
JEE Main Solved Paper-2014
A)
\[2gH=n{{u}^{2}}(n-2)\]
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B)
\[gH=(n-2){{u}^{2}}\]
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C)
\[2gH={{n}^{2}}{{u}^{2}}\]
done
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D)
\[gH={{(n-2)}^{2}}{{u}^{2}}\]
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question_answer19) A thin convex lens made from crown glass\[\left[ \mu =\frac{3}{2} \right]\]has focal length f. When it is measured in two different liquids having refractive indices\[\frac{4}{3}\]and\[\frac{5}{3},\]it has the focal lengths f1 and f2 respectively. The correct relation between the focal lengths is :
JEE Main Solved Paper-2014
A)
\[{{f}_{2}}>f\]and\[{{f}_{1}}\] becomes negative
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B)
\[{{f}_{1}}\]and\[{{f}_{2}}\] both become negative
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C)
\[{{f}_{1}}={{f}_{2}}<f\]
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D)
\[{{f}_{1}}>f\]and\[{{f}_{2}}\]becomes negative
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question_answer20) Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of crosssection of each rod \[=4c{{m}^{2}}.\]End of copper rod is maintained at \[100{}^\circ C\] where as ends of brass and steel are kept at \[0{}^\circ C\]. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :
JEE Main Solved Paper-2014
A)
4.8 cal/s
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B)
6.0 cal/s
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C)
1.2 cal/s
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D)
2.4 cal/s
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question_answer21) A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of aircolumn in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
JEE Main Solved Paper-2014
A)
6
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B)
4
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C)
12
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D)
8
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question_answer22)
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities \[{{d}_{1}}\] and \[{{d}_{2}}\]are filled in the tube. Each liquid subtends \[90{}^\circ\]angle at centre. Radius joining their interface makes an angle \[\alpha \] with vertical. Ratio \[\frac{{{d}_{1}}}{{{d}_{2}}}\]is 
JEE Main Solved Paper-2014
A)
\[\frac{1+\tan \alpha }{1-\tan \alpha }\]
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B)
\[\frac{1+\sin \alpha }{1-\cos \alpha }\]
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C)
\[\frac{1+\sin \alpha }{1-\sin \alpha }\]
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D)
\[\frac{1+\cos \alpha }{1-\cos \alpha }\]
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question_answer23) A green light is incident from the water to the air - water interface at the critical angle (θ). Select the correct statement.
JEE Main Solved Paper-2014
A)
The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
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B)
The entire spectrum of visible light will come out of the water at various angles to the normal.
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C)
The entire spectrum of visible light will come out of the water at an angle of \[90{}^\circ\] to the normal.
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D)
The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
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question_answer24) Hydrogen \[{{(}_{1}}{{H}^{1}}),\]Deuterium\[{{(}_{1}}{{H}^{2}}),\] singly ionised Helium \[{{{{(}_{2}}H{{e}^{4}})}^{+}}\]and doubly ionised lithium \[{{{{(}_{3}}L{{i}^{6}})}^{++}}\]allhave one electron around the nucleus. Consider an electron transition from n = 2 ton = l. If the wave lengths of emitted radiation are \[{{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}}\]and \[{{\lambda }_{4}}\]respectively then approximately whichone of the following is correct ?
JEE Main Solved Paper-2014
A)
\[{{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\]
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B)
\[{{\lambda }_{1}}=2{{\lambda }_{2}}=3{{\lambda }_{3}}=4{{\lambda }_{4}}\]
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C)
\[4{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]
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D)
\[{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]
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question_answer25) The radiation corresponding to \[3\to 2\]transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \[3\times {{10}^{-4}}T.\]If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to:
JEE Main Solved Paper-2014
A)
0.8 eV
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B)
1.6 eV
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C)
1.8 eV
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D)
1.1 eV
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question_answer26) A block of mass m is placed on a surface with a vertical cross section given by \[y=\frac{{{x}^{3}}}{6}.\]If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :
JEE Main Solved Paper-2014
A)
\[\frac{1}{3}m\]
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B)
\[\frac{1}{2}m\]
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C)
\[\frac{1}{6}m\]
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D)
\[\frac{2}{3}m\]
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question_answer27) When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude\[F=ax+b{{x}^{2}}\]where a and b are constants. The work done in stretching the unstretched rubber-band by Lis :
JEE Main Solved Paper-2014
A)
\[\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}\]
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B)
\[\frac{1}{2}\left[ \frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3} \right]\]
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C)
\[a{{L}^{2}}+b{{L}^{3}}\]
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D)
\[\frac{1}{2}(a{{L}^{2}}+b{{L}^{3}})\]
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question_answer28)
On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius R and making a circularcontact of radius r with the bottom of the vessel. If r << R, and the surface tension of water is T, value of r just before bubblesdetatch is : (density of water is \[{{\rho }_{w}}\]) 
JEE Main Solved Paper-2014
A)
\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{T}}\]
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B)
\[{{R}^{2}}\sqrt{\frac{3{{\rho }_{w}}g}{T}}\]
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C)
\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{3T}}\]
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D)
\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{6T}}\]
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question_answer29) Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through 30° makes the two beams appear equally bright. If the initial intensities of the two beams are \[{{\text{I}}_{\text{A}}}\] and \[{{\text{I}}_{\text{B}}}\]respectively, then \[\frac{{{\text{I}}_{\text{A}}}}{{{\text{I}}_{\text{B}}}}\]equals :
JEE Main Solved Paper-2014
A)
1
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B)
\[\frac{1}{3}\]
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C)
3
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D)
\[\frac{3}{2}\]
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E)
done
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question_answer30) Assume that an electric field \[\vec{E}=30{{x}^{2}}\hat{i}\]exists in space. Then the potential difference \[{{V}_{A}}-{{V}_{O}},\]where\[{{\text{V}}_{\text{O}}}\]is the potential at the origin and \[{{\text{V}}_{\text{A}}}\] the potential at x = 2 m is :
JEE Main Solved Paper-2014
A)
80 J
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B)
80 J
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C)
120 J
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D)
−120 J
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