Solved papers for JEE Main & Advanced JEE Main Solved Paper-2014

4) 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

B)

0.05 mA

C)

0.2 mA

D)

0.02 mA

View Answer

5) 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

B)

6 cm

C)

16 cm

D)

22 cm

View Answer

6) 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)

B)

(a) - (i) (b) - (i) (c) - (iii) (d) - (iv)

C)

(a) - (iv) (b) - (iii) (c) - (ii) (d) - (i)

D)

(a) - (i) (b) - (ii) (c) - (iv) (d) - (iii)

View Answer

7) 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)

\[3\times {{10}^{4}}C/{{m}^{2}}\]

B)

\[6\times {{10}^{4}}C/{{m}^{2}}\]

C)

\[6\times {{10}^{-7}}C/{{m}^{2}}\]

D)

\[3\times {{10}^{-7}}C/{{m}^{2}}\]

View Answer

8) 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.

B)

A screw gauge having 50 divisions in the circular scale and pitch as 1 mm.

C)

A meter scale.

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.

View Answer

9) 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)

\[\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}\]

B)

\[\frac{1}{2}\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}\]

C)

\[\sqrt{\frac{GM}{R}}\]

D)

\[\sqrt{2\sqrt{2}\frac{GM}{R}}\]

View Answer

10) 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

B)

14 A

C)

8 A

D)

10 A

View Answer

11) 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

B)

time period of oscillations is \[6\tau \]

C)

amplitude of motion is 3a

D)

time period of oscillations is \[8\tau \]

View Answer

12) 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

B)

6 A

C)

30 mA

D)

60 mA

View Answer

13) The forward biased diode connection is : JEE Main Solved Paper-2014

A)

B)

C)

D)

View Answer

14) 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.

B)

Both electric and magnetic energy densities are zero.

C)

Electric energy density is double of the magnetic energy density.

D)

Electric energy density is half of the magnetic density.

View Answer

15) 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

B)

\[\frac{1-e}{e}\]

C)

\[\frac{e}{1-e}\]

D)

1

View Answer

16) 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)

\[\frac{5g}{6}\]

B)

g

C)

\[\frac{2g}{3}\]

D)

\[\frac{g}{2}\]

View Answer

17) 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.

B)

The change in internal energy in the process BC is − 500 R.

C)

The change in internal energy in whole cyclic process is 250 R.

D)

The change in internal energy in the process CA is 700 R.

View Answer

18) 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)

\[2gH=n{{u}^{2}}(n-2)\]

B)

\[gH=(n-2){{u}^{2}}\]

C)

\[2gH={{n}^{2}}{{u}^{2}}\]

D)

\[gH={{(n-2)}^{2}}{{u}^{2}}\]

View Answer

19) 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

B)

\[{{f}_{1}}\]and\[{{f}_{2}}\] both become negative

C)

\[{{f}_{1}}={{f}_{2}}<f\]

D)

\[{{f}_{1}}>f\]and\[{{f}_{2}}\]becomes negative

View Answer

20) 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

B)

6.0 cal/s

C)

1.2 cal/s

D)

2.4 cal/s

View Answer

21) 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

B)

4

C)

12

D)

8

View Answer

22) 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)

\[\frac{1+\tan \alpha }{1-\tan \alpha }\]

B)

\[\frac{1+\sin \alpha }{1-\cos \alpha }\]

C)

\[\frac{1+\sin \alpha }{1-\sin \alpha }\]

D)

\[\frac{1+\cos \alpha }{1-\cos \alpha }\]

View Answer

23) 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.

B)

The entire spectrum of visible light will come out of the water at various angles to the normal.

C)

The entire spectrum of visible light will come out of the water at an angle of \[90{}^\circ\] to the normal.

D)

The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.

View Answer

24) 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)

\[{{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}\]

B)

\[{{\lambda }_{1}}=2{{\lambda }_{2}}=3{{\lambda }_{3}}=4{{\lambda }_{4}}\]

C)

\[4{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]

D)

\[{{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}\]

View Answer

25) 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

B)

1.6 eV

C)

1.8 eV

D)

1.1 eV

View Answer

26) 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)

\[\frac{1}{3}m\]

B)

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

C)

\[\frac{1}{6}m\]

D)

\[\frac{2}{3}m\]

View Answer

27) 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)

\[\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}\]

B)

\[\frac{1}{2}\left[ \frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3} \right]\]

C)

\[a{{L}^{2}}+b{{L}^{3}}\]

D)

\[\frac{1}{2}(a{{L}^{2}}+b{{L}^{3}})\]

View Answer

28) 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)

\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{T}}\]

B)

\[{{R}^{2}}\sqrt{\frac{3{{\rho }_{w}}g}{T}}\]

C)

\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{3T}}\]

D)

\[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{6T}}\]

View Answer

29) 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

B)

\[\frac{1}{3}\]

C)

3

D)

\[\frac{3}{2}\]

E)

View Answer

30) 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

B)

80 J

C)

120 J

D)

−120 J

View Answer

31) Which one of the following properties is not shown by NO? JEE Main Solved Paper-2014

A)

It combines with oxygen to form nitrogen dioxide

B)

It is bond order is 2.5

C)

It is diamagnetic in gaseous state

D)

It is a neutral oxide

View Answer

32) If Z is a compressibility factor, van der Waals equation at low pressure can be written as : JEE Main Solved Paper-2014

A)

\[Z=1-\frac{Pb}{RT}\]

B)

\[Z=1+\frac{Pb}{RT}\]

C)

\[Z=1+\frac{RT}{Pb}\]

D)

\[Z=1-\frac{a}{VRT}\]

View Answer

33) 63. The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is : JEE Main Solved Paper-2014

A)

Cu

B)

Cr

C)

Ag

D)

Ca

View Answer

34) Resistance of 0.2 M solution of an electrolyte is \[50\Omega .\]The specific conductance of the solution is\[\text{S}{{\text{m}}^{\text{-1}}}\]. The resistance of 0.5 M solution of the same electrolyte is \[280\Omega .\]The molarconductivity of 0.5 M solution of the electrolyte in \[\text{S}\,{{\text{m}}^{\text{2}}}\,\text{mo}{{\text{l}}^{-1}}\] is : JEE Main Solved Paper-2014

A)

\[5\times {{10}^{3}}\]

B)

\[5\times {{10}^{2}}\]

C)

\[5\times {{10}^{-4}}\]

D)

\[5\times {{10}^{-3}}\]

View Answer

35) CsCl crystallises in body centred cubic lattice. If ?a? is its edge length then which of thefollowing expressions is correct ? JEE Main Solved Paper-2014

A)

\[{{r}_{Cs}}+{{r}_{Cl-}}=\frac{\sqrt{3}}{2}a\]

B)

\[{{r}_{Cs}}{{+}_{C{{l}^{-}}}}=\sqrt{3}a\]

C)

\[{{r}_{Cs}}_{+}{{+}_{C{{l}^{-}}}}=3a\]

D)

\[{{r}_{Cs}}_{+}+{{r}_{C{{l}^{-}}}}=\frac{3a}{2}\]

View Answer

36) Consider separate solutions of \[0.500M{{C}_{2}}{{H}_{5}}OH(aq),\] \[0.100M\,M{{g}_{3}}{{(P{{O}_{4}})}_{2}}(aq),0.250\,MKBr(aq)\]and \[0.125MN{{a}_{3}}P{{O}_{4}}(aq)\]at \[25{}^\circ C\]. Which statement is true about these solutions, assuming allsalts to be strong electrolytes ? JEE Main Solved Paper-2014

A)

\[0.125MN{{a}_{3}}P{{O}_{4}}(aq)\]has the highest osmotic pressure.

B)

\[0.500M{{C}_{2}}{{H}_{5}}OH(aq)\]has the highest osmotic pressure.

C)

They all have the same osmotic pressure.

D)

\[0.100MM{{g}_{3}}{{(P{{O}_{4}})}_{2}}(aq)\]has the highest osmotic pressure.

View Answer

37) In which of the following reactions \[{{H}_{2}}{{O}_{2}}\]acts as a reducing agent ?

(A)\[{{H}_{2}}{{O}_{2}}+2{{H}^{+}}+2{{e}^{-}}\to 2{{H}_{2}}O\]

(B)\[{{H}_{2}}{{O}_{2}}-2{{e}^{-}}\to {{O}_{2}}+2{{H}^{+}}\]

(C)\[{{H}_{2}}{{O}_{2}}+2{{e}^{-}}\to 2O{{H}^{-}}\]

(D)\[{{H}_{2}}{{O}_{2}}+2O{{H}^{-}}-2{{e}^{-}}\to {{O}_{2}}+2{{H}_{2}}O\]

JEE Main Solved Paper-2014

A)

\[(a), (c)\]

B)

\[(b), (d)\]

C)

\[(a), (b)\]

D)

\[(c), (d)\]

View Answer

38) In \[{{S}_{N}}2\]reactions, the correct order of reactivity for the following compounds : \[C{{H}_{3}}Cl,C{{H}_{3}}C{{H}_{2}}Cl,{{(C{{H}_{3}})}_{2}}CHCl\]and\[{{(C{{H}_{3}})}_{3}}CCl\]is: JEE Main Solved Paper-2014

A)

\[C{{H}_{3}}C{{H}_{2}}Cl>C{{H}_{3}}Cl>{{(C{{H}_{3}})}_{2}}CHCl>{{(C{{H}_{3}})}_{3}}CCl\]

B)

\[{{(C{{H}_{3}})}_{2}}CHCl>C{{H}_{3}}C{{H}_{2}}Cl>C{{H}_{3}}Cl>{{(C{{H}_{3}})}_{3}}CCl\]

C)

\[C{{H}_{3}}Cl>{{(C{{H}_{3}})}_{2}}CHCl>C{{H}_{2}}C{{H}_{2}}Cl>{{(C{{H}_{3}})}_{3}}CCl\]

D)

\[C{{H}_{3}}Cl>C{{H}_{3}}C{{H}_{2}}Cl>{{(C{{H}_{3}})}_{2}}CHCl>{{(C{{H}_{3}})}_{3}}CCl\]

View Answer

39) The octahedral complex of a metal ion \[{{M}^{3+}}\] with four monodentate ligands \[{{L}_{1}},{{L}_{2}},{{L}_{3}}\]and \[{{L}_{4}}\]absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasingorder of ligand strength of the four ligands is : JEE Main Solved Paper-2014

A)

\[{{L}_{3}}<{{L}_{2}}<{{L}_{4}}<{{L}_{1}}\]

B)

\[{{L}_{1}}<{{L}_{2}}<{{L}_{4}}<{{L}_{3}}\]

C)

\[{{L}_{4}}<{{L}_{3}}<{{L}_{2}}<{{L}_{1}}\]

D)

\[{{L}_{1}}<{{L}_{3}}<{{L}_{2}}<{{L}_{4}}\]

View Answer

40) For the estimation of nitrogen, 1.4 g of an organic compound was digested by Kjeldahl methodand the evolved ammonia was absorbed in 60 mL of\[\frac{M}{10}\]sulphuric acid. The unreacted acid required 20 mL of \[\frac{M}{10}\]sodium hydroxide for complete neutralization. The percentage of nitrogenin the compound is : JEE Main Solved Paper-2014

A)

3 %

B)

5 %

C)

6 %

D)

10 %

View Answer

41) The equivalent conductance of NaCl at concentration C and at infinite dilution are \[{{\lambda }_{C}}\] and \[{{\lambda }_{\infty }}\]respectively. The correct relationship between \[{{\lambda }_{C}}\] and \[{{\lambda }_{\infty }}\]is given as : (where the constant B is positive) JEE Main Solved Paper-2014

A)

\[{{\lambda }_{C}}={{\lambda }_{\infty }}-(B)\sqrt{C}\]

B)

\[{{\lambda }_{C}}={{\lambda }_{\infty }}+(B)\sqrt{C}\]

C)

\[{{\lambda }_{C}}={{\lambda }_{\infty }}+(B)C\]

D)

\[{{\lambda }_{C}}={{\lambda }_{\infty }}-(B)C\]

View Answer

42) For the reaction \[S{{O}_{2}}_{(g)}+\frac{1}{2}{{O}_{2(g)}}S{{O}_{3(g)}}\]if \[{{K}_{P}}={{K}_{C}}{{(RT)}^{x}}\] where the symbols have usual meaning then the value of x is : (assuming ideality) JEE Main Solved Paper-2014

A)

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

B)

1

C)

-1

D)

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

View Answer

43) In the reaction, \[C{{H}_{3}}COOH\xrightarrow[{}]{LiAl{{H}_{4}}}A\xrightarrow[{}]{PC{{l}_{5}}}B\xrightarrow[{}]{Alc.KOH}C,\]the product C is : JEE Main Solved Paper-2014

A)

Ethylene

B)

Acetyl chloride

C)

Acetaldehyde

D)

Acetylene

View Answer

44) Sodium phenoxide when heated with \[C{{O}_{2}}\]under pressure at \[125{}^\circ C\] yields a product which on acetylation produces C.

The major product C would be : JEE Main Solved Paper-2014

A)

B)

C)

D)

View Answer

45) On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, theorganic compound formed is : JEE Main Solved Paper-2014

A)

an alkyl cyanide

B)

an alkyl isocyanide

C)

analkanol

D)

analkanediol

View Answer

46) The correct statement for the molecule, \[Cs{{I}_{3}},\]is : JEE Main Solved Paper-2014

A)

it contains \[C{{s}^{3+}}\]and \[{{I}^{-}}\] ions.

B)

it contains \[C{{s}^{+}},{{I}^{-}}\]and lattice \[{{I}_{2}}\] molecule.

C)

it is a covalent molecule.

D)

it contains \[C{{s}^{+}}\]and \[I_{3}^{-}\]ions.

View Answer

47) The equation which is balanced and represents the correct product(s) is : JEE Main Solved Paper-2014

A)

\[{{[Mg{{({{H}_{2}}O)}_{6}}]}^{2+}}+{{(EDTA)}^{4-}}\xrightarrow[{}]{excessNaOH}{{[Mg(EDTA)]}^{2}}+6{{H}_{2}}O\]

B)

\[CuS{{O}_{4}}+4KCN\to {{K}_{2}}[Cu{{(CN)}_{4}}]+{{K}_{2}}S{{O}_{4}}\]

C)

\[L{{i}_{2}}+2KCl\to 2LiCl+{{K}_{2}}O\]

D)

\[[CoCl{{(N{{H}_{3}})}_{5}}]++5{{H}^{+}}\to C{{o}^{2+}}+5NH_{4}^{+}+C{{l}^{-}}\]

View Answer

48) For which of the following molecule significant \[\mu \ne 0?\] JEE Main Solved Paper-2014

(i)
(ii)
(iii)
(iv)

A)

\[Only (iii)\]

B)

\[(iii) and (iv)\]

C)

\[Only (i)\]

D)

\[(i) and (ii)\]

View Answer

49) For the non-stoichiometrereaction \[2A+B\to C+D,\]the following kinetic data were obtained inthree separate experiments, all at 298 K.

Initial concentration (A)	Initial Concentration (B)	Initial rate of formation of C \[(mol\,{{L}^{-}}{{S}^{-}})\]
\[0.1M\]	\[0.1M\]	\[1.2\times {{10}^{-3}}\]
\[0.1M\]	\[0.2M\]	\[1.2\times {{10}^{-3}}\]
\[0.2M\]	\[0.1M\]	\[2.4\times {{10}^{-3}}\]

The rate law for the formation of C is : JEE Main Solved Paper-2014

A)

\[\frac{dc}{dt}=k[A]{{[B]}^{2}}\]

B)

\[\frac{dc}{dt}=k[A]\]

C)

\[\frac{dc}{dt}=k[A][B]\]

D)

\[\frac{dc}{dt}=k{{[A]}^{2}}[B]\]

View Answer

50) Which series of reactions correctly represents chemical relations related to iron and itscompound? JEE Main Solved Paper-2014

A)

\[Fe\xrightarrow[{}]{C{{l}_{2}}.heat}FeC{{l}_{3}}\xrightarrow[{}]{heat,air}FeC{{l}_{2}}\xrightarrow[{}]{Zn}Fe\]

B)

\[Fe\xrightarrow[{}]{{{O}_{2}},heat}F{{e}_{3}}{{O}_{4}}\xrightarrow[{}]{CO,{{600}^{o}}C}FeO\xrightarrow[{}]{CO,{{700}^{o}}C}Fe\]

C)

\[Fe\xrightarrow[{}]{dil\,{{H}_{2}}S{{O}_{4}}}FeS{{O}_{4}}\xrightarrow[{}]{{{H}_{2}}S{{O}_{4}},{{O}_{2}}}F{{e}_{2}}{{(S{{O}_{4}})}_{3}}\xrightarrow[{}]{heat}Fe\]

D)

\[Fe\xrightarrow[{}]{{{O}_{2}},heat}FeO\xrightarrow[{}]{dil\,{{H}_{2}}S{{O}_{4}}}FeS{{O}_{4}}\xrightarrow[{}]{heat}Fe\]

E)

View Answer

51) Considering the basic strength of amines in aqueous solution, which one has the smallest \[\text{p}{{\text{K}}_{\text{b}}}\]value? JEE Main Solved Paper-2014

A)

\[{{(C{{H}_{3}})}_{3}}N\]

B)

\[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\]

C)

\[{{(C{{H}_{3}})}_{2}}NH\]

D)

\[C{{H}_{3}}N{{H}_{2}}\]

View Answer

52) Which one of the following bases is not present in DNA? JEE Main Solved Paper-2014

A)

Cytosine

B)

Thymine

C)

Quinoline

D)

Adenine

View Answer

53) The correct set of four quantum numbers for the valence electrons of rubidium atom (Z = 37) is : JEE Main Solved Paper-2014

A)

\[5,1,1,+\frac{1}{2}\]

B)

\[5,0,1,+\frac{1}{2}\]

C)

\[5,0,0,+\frac{1}{2}\]

D)

\[5,1,0,+\frac{1}{2}\]

View Answer

54) The major organic compound formed by the reaction of 1, 1, 1 − trichloroethane with silver powder is : JEE Main Solved Paper-2014

A)

2 - Butyne

B)

2 - Butene

C)

Acetylene

D)

Ethene

View Answer

55) Given below are the half − cell reaction : \[M{{n}^{2+}}+2{{e}^{-}}\to Mn;{{E}^{o}}=-1.18V\] \[2(M{{n}^{3+}}+{{e}^{-}}\to M{{n}^{2+}});{{E}^{o}}=+1.51V.\] The \[E{}^\circ \]for \[3M{{n}^{2+}}\to Mn+2M{{n}^{3+}}\]will be JEE Main Solved Paper-2014

A)

0.33 V ; the reaction will not occur

B)

−0.33 V ; the reaction will occur

C)

−2.69 V ; the reaction will not occur

View Answer

56) The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio ofnumber of their molecule is : JEE Main Solved Paper-2014

A)

1 : 8

B)

3 : 16

C)

1 : 4

D)

7 : 32

View Answer

57) Which one is classified as a condensation polymer? JEE Main Solved Paper-2014

A)

Teflon

B)

Acrylonitrile

C)

Dacron

D)

Neoprene

View Answer

58) Among the following oxoacids, the correct decreasing order of acid strength is : JEE Main Solved Paper-2014

A)

\[HCl{{O}_{4}}>HCl{{O}_{3}}>HCl{{O}_{2}}>HOCl\]

B)

\[HCl{{O}_{2}}>HCl{{O}_{4}}>HCl{{O}_{3}}>HOCl\]

C)

\[HOCl>HCl{{O}_{2}}>HCl{{O}_{3}}>HCl{{O}_{4}}\]

D)

\[HCl{{O}_{4}}>HOCl>HCl{{O}_{2}}>HCl{{O}_{3}}\]

View Answer

59) For complete combustion of ethanol, \[{{C}_{2}}{{H}_{5}}OH(\ell )+3{{O}_{2}}(g)\to 2C{{O}_{2}}(g)+3{{H}_{2}}O(\ell ),\]the amount ofheat produced as measured in bomb calorimeter, is \[1364.47\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\] at \[25{}^\circ C\]. Assuming ideality theEnthalpy of combustion, \[\Delta \text{cH,}\] for the reaction will be : \[(\text{R = 8}\text{.314 kJ mo}{{\text{l}}^{\text{-1}}})\] JEE Main Solved Paper-2014

A)

\[\text{-1460}\text{.50 kJ mo}{{\text{l}}^{\text{-1}}}\]

B)

\[\text{-1350}\text{.50 kJ mo}{{\text{l}}^{\text{-1}}}\]

C)

\[\text{-1366}\text{.95 kJ mo}{{\text{l}}^{\text{-1}}}\]

D)

\[\text{-1361}\text{.95 kJ mo}{{\text{l}}^{\text{-1}}}\]

View Answer

60) The most suitable reagent for the conversion of \[R-C{{H}_{2}}-OH\to R-CHO\] is : JEE Main Solved Paper-2014

A)

\[Cr{{O}_{3}}\]

B)

PCC (PyridiniumChlorochromate)

C)

\[KMn{{O}_{4}}\]

D)

\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]

View Answer

61) The image of the line \[\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}\]in the plane \[2x-y+z+3=0\]is the line: JEE Main Solved Paper-2014

A)

\[\frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}\]

B)

\[\frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}\]

C)

\[\frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}\]

D)

\[\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}\]

View Answer

62) If the coefficients of \[{{x}^{3}}\]and \[{{x}^{4}}\] in the expansion of \[(1+ax+b{{x}^{2}}){{(1-2x)}^{18}}\]in powers of x are both zero, then (a, b) is equal to: JEE Main Solved Paper-2014

A)

\[\left( 16,\frac{251}{3} \right)\]

B)

\[\left( 14,\frac{251}{3} \right)\]

C)

\[\left( 14,\frac{272}{3} \right)\]

D)

\[\left( 16,\frac{272}{3} \right)\]

View Answer

63) If \[a\in R\]and the equation \[-3{{(x-[x])}^{2}}+2(x-[x])+{{a}^{2}}=0\](where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of alie in the interval: JEE Main Solved Paper-2014

A)

\[(-1,0)\cup (0,1)\]

B)

\[(-2,-1)\]

C)

\[(-\infty ,-2)\cup (2,\infty )\]

View Answer

64) If \[\left[ \vec{a}\times \vec{b}\,\vec{b}\times \vec{c}\,\vec{c}\times \vec{a} \right]=\lambda {{\left[ \vec{a}\,\vec{b}\,\,\vec{c} \right]}^{2}}\]then\[\lambda \]is equal to: JEE Main Solved Paper-2014

A)

2

B)

3

C)

0

D)

1

View Answer

65) The variance of first 50 even natural numbers is: JEE Main Solved Paper-2014

A)

\[\frac{833}{4}\]

B)

\[833\]

C)

\[437\]

D)

\[\frac{437}{4}\]

View Answer

66) A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is \[45{}^\circ\]. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is: JEE Main Solved Paper-2014

A)

\[40\left( \sqrt{2}-1 \right)\]

B)

\[40\left( \sqrt{3}-\sqrt{2} \right)\]

C)

\[20\sqrt{2}\]

D)

\[20\left( \sqrt{3}-1 \right)\]

View Answer

67) The integral\[\int\limits_{0}^{\pi }{\sqrt{1+4{{\sin }^{2}}\frac{x}{2}-4\sin \frac{x}{2}}dx}\]equals: JEE Main Solved Paper-2014

A)

\[\pi -4\]

B)

\[\frac{2\pi }{3}-4-4\sqrt{3}\]

C)

\[4\sqrt{3}-4\]

D)

\[4\sqrt{3}-4-\frac{\pi }{3}\]

View Answer

68) The statement \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\] is: JEE Main Solved Paper-2014

A)

equivalent to \[p\leftrightarrow q\]

B)

equivalent to \[\tilde{\ }p\leftrightarrow q\]

C)

a tautology

D)

a fallacy

View Answer

69) If A is an \[3\times 3\] non ? singular matrix such that AA′ = A′A and B = A−1 A′, then BB′ equals: JEE Main Solved Paper-2014

A)

\[I+B\]

B)

\[I\]

C)

\[{{B}^{-1}}\]

D)

\[({{B}^{-1}})'\]

View Answer

70) The integral\[\int_{{}}^{{}}{\left( 1+x-\frac{1}{x} \right)}{{e}^{x+\frac{1}{x}}}dx\]is equal to JEE Main Solved Paper-2014

A)

\[(x-1){{e}^{x+\frac{1}{x}}}+c\]

B)

\[x{{e}^{x+\frac{1}{x}}}+c\]

C)

\[(x+1){{e}^{x+\frac{1}{x}}}+c\]

D)

\[-x{{e}^{x+\frac{1}{x}}}+c\]

View Answer

71) If z is a complex number such that\[|z|\ge 2,\]then the minimum value of \[\left| z+\frac{1}{2} \right|:\] JEE Main Solved Paper-2014

A)

is equal to \[\frac{5}{2}\]

B)

lies in the interval (1, 2)

C)

is strictly greater than \[\frac{5}{2}\]

D)

is strictly greater than \[\frac{3}{2}\]but less than \[\frac{5}{2}\]

View Answer

72) If g is the inverse of a function f and \[(x)=\frac{1}{1+{{x}^{5}}},\]then g′ (x) is equal to : JEE Main Solved Paper-2014

A)

\[1+{{x}^{5}}\]

B)

\[5{{x}^{4}}\]

C)

\[\frac{1}{1+{{\left\{ g(x) \right\}}^{5}}}\]

D)

\[1+{{\{g(x)\}}^{5}}\]

View Answer

73) If\[\alpha ,\beta \ne 0,\]and\[f(n)={{\alpha }^{n}}+{{\beta }^{n}}\]and\[\left| \begin{matrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) & 1+f(4) \\ \end{matrix} \right|=K\]\[{{(1-\alpha )}^{2}}{{(1-\beta )}^{2}}{{(\alpha -\beta )}^{2}},\]then K is equal to: JEE Main Solved Paper-2014

A)

\[\alpha \beta \]

B)

\[\frac{1}{\alpha \beta }\]

C)

\[1\]

D)

\[-1\]

View Answer

74) Let \[{{f}_{k}}(x)=\frac{1}{k}(si{{n}^{k}}x+co{{s}^{k}}x),\]where\[x\in R\]and\[k\ge 1.\]Then\[{{f}_{4}}(x)-{{f}_{6}}(x)\]equals: JEE Main Solved Paper-2014

A)

\[\frac{1}{6}\]

B)

\[\frac{1}{3}\]

C)

\[\frac{1}{4}\]

D)

\[\frac{1}{12}\]

View Answer

75) Let \[\alpha \] and \[\beta \] be the roots of equation \[p{{x}^{2}}+qx+r=0,p\ne 0.\]If p, q, r are in A.P. and \[\frac{1}{\alpha }+\frac{1}{\beta }=4,\]then the value of \[|\alpha -\beta |\]is : JEE Main Solved Paper-2014

A)

\[\frac{\sqrt{61}}{9}\]

B)

\[\frac{2\sqrt{17}}{9}\]

C)

\[\frac{\sqrt{34}}{9}\]

D)

\[\frac{2\sqrt{13}}{9}\]

View Answer

76) Let A and B be two events such that \[P(\overline{A\cup B})=\frac{1}{16}.P(A\cap B)=\frac{1}{4}\]and\[P(\overline{A})=\frac{1}{4},\]where\[\overline{A}\]stands for the complement of the event A. Then the events A and B are : JEE Main Solved Paper-2014

A)

mutually exclusive and independent.

B)

equally likely but not independent.

C)

independent but not equally likely.

D)

independent and equally likely.

View Answer

77) If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6,then for some \[c\in \}0,1[:\] JEE Main Solved Paper-2014

A)

\[2f'(c)=g'(c)\]

B)

\[2f'(c)=3g'(c)\]

C)

\[f'(c)=g'(c)\]

D)

\[f'(c)=2g'(c)\]

View Answer

78) Let the population of rabbits surviving at a time t be governed by the differential equation\[\frac{dp(t)}{dt}=\frac{1}{2}p(t)-200.\] If \[p(0)=100,\]then p(t) equals : JEE Main Solved Paper-2014

A)

\[400-300\,{{\text{e}}^{\text{t/2}}}\]

B)

\[300-200\,{{\text{e}}^{\text{-t/2}}}\]

C)

\[600-500\,{{\text{e}}^{\text{t/2}}}\]

D)

\[400-300\,{{\text{e}}^{\text{-t/2}}}\]

View Answer

79) Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to : JEE Main Solved Paper-2014

A)

\[\frac{\sqrt{3}}{\sqrt{2}}\]

B)

\[\frac{\sqrt{3}}{2}\]

C)

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

D)

\[\frac{1}{4}\]

View Answer

80) The area of the region described by \[A=\{(x,\text{ }y):{{x}^{2}}+{{y}^{2}}\le 1\]and \[{{y}^{2}}\le 1-x\}\]is JEE Main Solved Paper-2014

A)

\[\frac{\pi }{2}+\frac{4}{3}\]

B)

\[\frac{\pi }{2}-\frac{4}{3}\]

C)

\[\frac{\pi }{2}-\frac{2}{3}\]

D)

\[\frac{\pi }{2}+\frac{2}{3}\]

View Answer

81) Let a, b, c and d be non−zero numbers. If the point of intersection of the lines \[4ax+2ay+c=0\]and \[5bx+2by+d=\] lies in the fourth quadrant and is equidistant from the two axes then : JEE Main Solved Paper-2014

A)

2bc − 3ad = 0

B)

2bc + 3ad = 0

C)

3bc − 2ad = 0

D)

3bc + 2ad = 0

View Answer

82) Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R (7, 3). The equation ofthe line passing through (1, −1) and parallel to PS is : JEE Main Solved Paper-2014cc

A)

\[4x-7y-11=0\]

B)

\[2x+9y+7=0\]

C)

\[4x+7y+3=0\]

D)

\[2x-9y-11=0\]

View Answer

83) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi co{{s}^{2}}x)}{{{x}^{2}}}\]is equal to: JEE Main Solved Paper-2014

A)

\[\frac{\pi }{2}\]

B)

1

C)

\[-\pi \]

D)

\[\pi \]

View Answer

84) If \[X=\{{{4}^{n}}-1:n\varepsilon N\}\] and\[Y=\{9(n-1):n\varepsilon N\},\] where N is the set of natural numbers, then \[X\cup Y\] is equal to : JEE Main Solved Paper-2014

A)

N

B)

Y − X

C)

X

D)

Y

View Answer

85) The locus of the foot of perpendicular drawn from the centre of the ellipse \[{{x}^{2}}+3{{y}^{2}}=6\] on any tangent to it is : JEE Main Solved Paper-2014

A)

\[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]

B)

\[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]

C)

\[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]

D)

\[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]

View Answer

86) Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is : JEE Main Solved Paper-2014

A)

\[\sqrt{2}+\sqrt{3}\]

B)

\[3+\sqrt{2}\]

C)

\[2-\sqrt{3}\]

D)

\[2+\sqrt{3}\]

View Answer

87) If \[{{(10)}^{9}}+2{{(11)}^{1}}{{(10)}^{8}}+3{{(11)}^{2}}{{(10)}^{7}}+...+10\]\[{{(11)}^{9}}=k{{(10)}^{9}},\]then k is equal to : JEE Main Solved Paper-2014

A)

\[\frac{121}{10}\]

B)

\[\frac{441}{100}\]

C)

\[100\]

D)

\[110\]

View Answer

88) The angle between the lines whose direction cosines satisfy the equations \[\ell +m+n=0\]and\[{{\ell }^{2}}={{m}^{2}}+{{n}^{2}}\]is : JEE Main Solved Paper-2014

A)

\[\frac{\pi }{3}\]

B)

\[\frac{\pi }{4}\]

C)

\[\frac{\pi }{6}\]

D)

\[\frac{\pi }{2}\]

View Answer

89) The slope of the line touching both the parabolas \[{{y}^{2}}=4x\]and \[{{x}^{2}}=-32y\]is : JEE Main Solved Paper-2014

A)

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

B)

\[\frac{3}{2}\]

C)

\[\frac{1}{8}\]

D)

\[\frac{2}{3}\]

View Answer

90) If x = −1 and x = 2 are extreme points of \[f(x)=\alpha log|x|+\beta {{x}^{2}}+x\]then : JEE Main Solved Paper-2014

A)

\[\alpha =-6,\beta =\frac{1}{2}\]

B)

\[\alpha =-6,\beta =-\frac{1}{2}\]

C)

\[\alpha =2,\beta =-\frac{1}{2}\]

D)

\[\alpha =2,\beta =\frac{1}{2}\]

View Answer

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done JEE Main Solved Paper-2014 Total Questions - 90

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JEE Main Solved Paper-2014

JEE Main Solved Paper-2014 Total Questions - 90