Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11 April 2014)

1) In terms of resistance R and time T, the dimensions of ratio\[\frac{\mu }{\varepsilon }\]of the permeability \[\mu \] and permittivity \[\varepsilon \] is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[[R{{T}^{-2}}]\]

B)

\[[{{R}^{2}}{{T}^{-1}}]\]

C)

\[[{{R}^{2}}]\]

D)

\[[{{R}^{2}}{{T}^{2}}]\]

View Answer

2) The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target ? [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

1.0m

B)

4.2 m

C)

6.1 m

D)

9.8 m

View Answer

3) A body of mass 5 kg under the action of constant force \[\overset{\to }{\mathop{F}}\,={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}\]has velocity at\[t=0s\]as\[\overset{\to }{\mathop{v}}\,=\left( 6\hat{i}-2\hat{j} \right)m/s\]and at t = 10s as \[\overset{\to }{\mathop{v}}\,=+6\hat{j}\,m/s.\] The force \[\overset{\to }{\mathop{F}}\,\]is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\left( -3\hat{j}+4\hat{j} \right)N\]

B)

\[\left( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} \right)N\]

C)

\[\left( 3\hat{i}-4\hat{j} \right)N\]

D)

\[\left( \frac{3}{5}\hat{i}-\frac{4}{5}\hat{j} \right)N\]

View Answer

4) A small ball of mass m starts at a point A with speed \[{{v}_{0}}\] and moves along a frictionless track AB as shown. The track BC has coefficient of friction m. The ball comes to stop at C after travelling a distance L which is:

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{2h}{\mu }+\frac{v_{o}^{2}}{2\mu g}\]

B)

\[\frac{h}{\mu }+\frac{v_{o}^{2}}{2\mu g}\]

C)

\[\frac{h}{2\mu }+\frac{v_{o}^{2}}{\mu g}\]

D)

\[\frac{h}{2\mu }+\frac{v_{o}^{2}}{2\mu g}\]

View Answer

5) The average mass of rain drops is \[3.0\times {{10}^{-5}}\]kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year. [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[3.0\times {{10}^{5}}J\]

B)

\[4.05\times {{10}^{4}}J\]

C)

\[3.0\times {{10}^{5}}J\]

D)

\[9.0\times {{10}^{4}}J\]

View Answer

6) A thin bar of length L has a mass per unit length \[\lambda \], that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is \[{{\lambda }_{O}},\] then the distance of the centre of mass from the lighter end is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{L}{2}-\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]

B)

\[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{8M}\]

C)

\[\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}\]

D)

\[\frac{2L}{3}-\frac{{{\lambda }_{o}}{{L}^{2}}}{6M}\]

View Answer

7) From a sphere of mass M and radius R, a smaller sphere of radius\[\frac{R}{2}\]is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{41G{{M}^{2}}}{3600{{R}^{2}}}\]

B)

\[\frac{41G{{M}^{2}}}{450{{R}^{2}}}\]

C)

\[\frac{59\,G{{M}^{2}}}{450{{R}^{2}}}\]

D)

\[\frac{\,G{{M}^{2}}}{225{{R}^{2}}}\]

View Answer

8) The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of \[{{10}^{9}}N{{m}^{-2}}.\]For a given value of pressure, the fractional compression in volume is \[\frac{\Delta V}{V}.\]Which of the following statements about \[\frac{\Delta V}{V}\]for these three liquids is correct? [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

Ethanol > Water > Mercury

B)

Water > Ethanol > Mercury

C)

Mercury > Ethanol > Water

D)

Ethanol > Mercury > Water

View Answer

9) A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 ms? 2 and density of water \[={{10}^{3}}kg\,{{m}^{-3}}\]) [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[10.7m{{s}^{-1}}\]

B)

\[9.6m{{s}^{-1}}\]

C)

\[8.5m{{s}^{-1}}\]

D)

\[7.6m{{s}^{-1}}\]

View Answer

10) An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density \[{{10}^{3}}kg/{{m}^{3}}.\] The pressure inside the bubble is \[1100N{{m}^{-2}}\] greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? \[(g=9.8m{{s}^{-2}})\] [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

0.1m

B)

0.15m

C)

0.20m

D)

0.25m

View Answer

11) A hot body, obeying Newton's law of cooling is cooling down from its peak value \[80{}^\circ C\] to an ambient temperature of \[30{}^\circ C\]. It takes 5 minutes in cooling down from \[80{}^\circ C\] to \[40{}^\circ C\]. How much time will it take to cool down from \[42{}^\circ C\] to \[32{}^\circ C\]? (Given In 2 = 0.693, In 5 = 1.609) [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

3.75 minutes

B)

8.6 minutes

C)

9.6 minutes

D)

6.5 minutes

View Answer

12) During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: \[(R=8.3J{{K}^{-1}}mo{{l}^{-1}})\] [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

40 K

B)

33 K

C)

20 K

D)

E)

14 K

View Answer

13) An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \[8.0\times {{10}^{-3}}{{m}^{2}}.\]Initially the gas is at 300 K and occupies a volume of \[2.4\times {{10}^{-3}}{{m}^{3}}\] and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is \[1.0\times {{10}^{5}}N/{{m}^{2}}.\] The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible).

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

300 K

B)

800 K

C)

500 K

D)

1000 K

View Answer

14) The angular frequency of the damped oscillator is given by,\[\omega =\sqrt{\left( \frac{k}{m}-\frac{{{r}^{2}}}{4{{m}^{2}}} \right)}\]where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio\[\frac{{{r}^{2}}}{mk}\]is 8%, the change in time period compared to the undamped oscillator is approximately as follows: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

increases by 1%

B)

increases by 8%

C)

decreases by 1%

D)

decreases by 8%

View Answer

15) Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

2

B)

4

C)

8

D)

10

View Answer

16) A cone of base radius R and height h is located in a uniform electric field \[\overset{\to }{\mathop{E}}\,\] parallel to its base. The electric flux entering the cone is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{1}{2}EhR\]

B)

her

C)

2 E h R

D)

4 E h R

View Answer

17) A parallel plate capacitor is made of two plates of length l, width w and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force\[F=-\frac{\partial U}{\partial x}\]where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is:

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{{{Q}^{2}}d}{2\omega {{1}^{2}}{{\varepsilon }_{o}}}K\]

B)

\[\frac{{{Q}^{2}}\omega }{2d{{1}^{2}}{{\varepsilon }_{o}}}\left( K-1 \right)\]

C)

\[\frac{{{Q}^{2}}d}{2w{{1}^{2}}{{\varepsilon }_{o}}}\left( K-1 \right)\]

D)

\[\frac{{{Q}^{2}}w}{2d{{1}^{2}}{{\varepsilon }_{o}}}K\]

View Answer

18) In the circuit shown, current (in A) through 50 V and 30 V batteries are, respectively:

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

2.5 and 3

B)

3.5 and 2

C)

4.5 and 1

D)

3 and 2.5

View Answer

19) Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[3\times {{10}^{-4}}N\] toward right

B)

\[6\times {{10}^{-4}}N\] toward right

C)

\[9\times {{10}^{-4}}N\]toward right

D)

Zero

View Answer

20) Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows:

Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P): [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[A\leftrightarrow D,B\leftrightarrow P,C\leftrightarrow F\]

B)

\[A\leftrightarrow F,B\leftrightarrow D,C\leftrightarrow P\]

C)

\[A\leftrightarrow P,B\leftrightarrow F,C\leftrightarrow D\]

D)

\[A\leftrightarrow F,B\leftrightarrow P,C\leftrightarrow D\]

View Answer

21) A coil of circular cross-section having 1000 turns and \[4c{{m}^{2}}\]face area is placed with its axis parallel to a magnetic field which decreases by \[{{10}^{-2}}\] Wb \[{{m}^{-2}}\] in 0.01 s. The e.m.f. induced in the coil is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

400 mV

B)

200 mV

C)

4 mV

D)

0.4 mV

View Answer

22) An electromagnetic wave of frequency \[1\times {{10}^{14}}\]hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If \[{{\varepsilon }_{0}}=8.8\times {{10}^{-12}}{{C}^{2}}/N-{{m}^{2}},\]then average energy density of electric field will be: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[35.2\times {{10}^{-10}}J/{{m}^{3}}\]

B)

\[35.2\times {{10}^{-11}}J/{{m}^{3}}\]

C)

\[35.2\times {{10}^{-12}}J/{{m}^{3}}\]

D)

\[35.2\times {{10}^{-13}}J/{{m}^{3}}\]

View Answer

23) An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 3. What is the distance between the screen and the object? [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

124.5 cm

B)

144.5 cm

C)

65.0 cm

D)

99.0 cm

View Answer

24) Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

\[\frac{16}{9}\]

B)

\[\frac{4}{3}\]

C)

\[\frac{7}{1}\]

D)

\[\frac{49}{1}\]

View Answer

25) In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

200

B)

100

C)

400

D)

150

View Answer

26) A photon of wavelength l is scattered from an electron, which was at rest. The wavelength shift \[\Delta \lambda \] is three times of \[\lambda \] and the angle of scattering \[\theta \] is \[60{}^\circ \]. The angle at which the electron recoiled is \[\phi .\] The value of tan \[\phi \] is : (electron speed is much smaller than the speed of light) [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

0.16

B)

0.22

C)

0.25

D)

0.28

View Answer

27) A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t = 0 there were no nuclei, the time when there are 50 nuclei is: [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

1s

B)

\[2\ln \left( \frac{4}{3} \right)s\]

C)

\[\ln 2s\]

D)

\[\ln \left( \frac{4}{3} \right)s\]

View Answer

28) Zener diode is connected to a battery and a load as show below:

The currents, \[I,{{I}_{Z}}\] and \[{{I}_{L}}\] are respectively. [JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

15 mA, 5 mA, 10 mA

B)

15 mA, 7.5 mA, 7.5 mA

C)

12.5 mA, 5 mA, 7.5 mA

D)

12.5 mA, 7.5 mA, 5 mA

View Answer

29) Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II (Part of electromagnetic spectrum) and select the correct code from the choices given below this lists:

(I) Doublet of sodium	(a) Visible radiation
(II) Wavelength corresponding to temperature associated with the isotropic radiation filling all space	(b) Microwave
(III) Wavelength emitted by Atomic hydrogen in Interstellar space	(c) Short radio wave
(IV) Wavelength of radiation arising from two close energy levels in hydrogen	(d) X-rays

[JEE Main Online Paper ( Held On 11 Apirl 2014 )

A)

(I)-(A), (II)-(B), (III)-(B), (IV)-(C)

B)

(I)-(A), (II)-(B), (III)-(C), (IV)-(C)

C)

(I)-(D), (II)-(C), (III)-(A), (IV)-(B)

D)

(I)-(B), (II)-(A), (III)-(D), (IV)-(A)

View Answer

30) In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as: