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

### done JEE Main Solved Paper-2014 Total Questions - 90

• 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)
$2.2\times {{10}^{7}}Pa$

B)
$2.2\times {{10}^{6}}Pa$

C)
$2.2\times {{10}^{8}}Pa$

D)
$2.2\times {{10}^{9}}Pa$

• 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

B)
29.7 W

C)
1.57 W

D)
2.97 W

• 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.

B)
angular momentum changes both in direction and magnitude.

C)
angular momentum is conserved.

D)
angular momentum changes in magnitude but not in direction.

• 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

B)
0.05 mA

C)
0.2 mA

D)
0.02 mA

• 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

B)
6 cm

C)
16 cm

D)
22 cm

• 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)

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)

• 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)
$3\times {{10}^{4}}C/{{m}^{2}}$

B)
$6\times {{10}^{4}}C/{{m}^{2}}$

C)
$6\times {{10}^{-7}}C/{{m}^{2}}$

D)
$3\times {{10}^{-7}}C/{{m}^{2}}$

• 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.

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.

• 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)
$\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}$

B)
$\frac{1}{2}\sqrt{\frac{GM}{R}\left( 1+2\sqrt{2} \right)}$

C)
$\sqrt{\frac{GM}{R}}$

D)
$\sqrt{2\sqrt{2}\frac{GM}{R}}$

• 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

B)
14 A

C)
8 A

D)
10 A

• 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

B)
time period of oscillations is $6\tau$

C)
amplitude of motion is 3a

D)
time period of oscillations is $8\tau$

• 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

B)
6 A

C)
30 mA

D)
60 mA

• question_answer13) The forward biased diode connection is :   JEE Main  Solved  Paper-2014

A)

B)

C)

D)

• 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.

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.

• 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

B)
$\frac{1-e}{e}$

C)
$\frac{e}{1-e}$

D)
1

• 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)
$\frac{5g}{6}$

B)
g

C)
$\frac{2g}{3}$

D)
$\frac{g}{2}$

• 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.

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.

• 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)
$2gH=n{{u}^{2}}(n-2)$

B)
$gH=(n-2){{u}^{2}}$

C)
$2gH={{n}^{2}}{{u}^{2}}$

D)
$gH={{(n-2)}^{2}}{{u}^{2}}$

• 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

B)
${{f}_{1}}$and${{f}_{2}}$ both become negative

C)
${{f}_{1}}={{f}_{2}}<f$

D)
${{f}_{1}}>f$and${{f}_{2}}$becomes negative

• 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

B)
6.0 cal/s

C)
1.2 cal/s

D)
2.4 cal/s

• 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

B)
4

C)
12

D)
8

• 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)
$\frac{1+\tan \alpha }{1-\tan \alpha }$

B)
$\frac{1+\sin \alpha }{1-\cos \alpha }$

C)
$\frac{1+\sin \alpha }{1-\sin \alpha }$

D)
$\frac{1+\cos \alpha }{1-\cos \alpha }$

• 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.

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.

• 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)
${{\lambda }_{1}}={{\lambda }_{2}}=4{{\lambda }_{3}}=9{{\lambda }_{4}}$

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)
${{\lambda }_{1}}=2{{\lambda }_{2}}=2{{\lambda }_{3}}={{\lambda }_{4}}$

• 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

B)
1.6 eV

C)
1.8 eV

D)
1.1 eV

• 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)
$\frac{1}{3}m$

B)
$\frac{1}{2}m$

C)
$\frac{1}{6}m$

D)
$\frac{2}{3}m$

• 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)
$\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}$

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

C)
$a{{L}^{2}}+b{{L}^{3}}$

D)
$\frac{1}{2}(a{{L}^{2}}+b{{L}^{3}})$

• 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)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{T}}$

B)
${{R}^{2}}\sqrt{\frac{3{{\rho }_{w}}g}{T}}$

C)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{3T}}$

D)
${{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{6T}}$

• 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

B)
$\frac{1}{3}$

C)
3

D)
$\frac{3}{2}$

E)

• 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

B)
80 J

C)
120 J

D)
−120 J

• question_answer31) 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

• question_answer32) 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)
$Z=1-\frac{a}{VRT}$

• question_answer33) 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

• question_answer34) 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)
$5\times {{10}^{-3}}$

• question_answer35) 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)
${{r}_{Cs}}_{+}+{{r}_{C{{l}^{-}}}}=\frac{3a}{2}$

• question_answer36) 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.

• question_answer37) 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)
$(c), (d)$

• question_answer38) 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)
$C{{H}_{3}}Cl>C{{H}_{3}}C{{H}_{2}}Cl>{{(C{{H}_{3}})}_{2}}CHCl>{{(C{{H}_{3}})}_{3}}CCl$

• question_answer39) 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)
${{L}_{1}}<{{L}_{3}}<{{L}_{2}}<{{L}_{4}}$

• question_answer40) 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 %

• question_answer41) 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)
${{\lambda }_{C}}={{\lambda }_{\infty }}-(B)C$

• question_answer42) 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)
$-\frac{1}{2}$

• question_answer43) 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

• question_answer44) 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)

• question_answer45) 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

• question_answer46) 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.

• question_answer47) 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)
$[CoCl{{(N{{H}_{3}})}_{5}}]++5{{H}^{+}}\to C{{o}^{2+}}+5NH_{4}^{+}+C{{l}^{-}}$

• question_answer48) 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)
$(i) and (ii)$

• question_answer49) 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)
$\frac{dc}{dt}=k{{[A]}^{2}}[B]$

• question_answer50) 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)

• question_answer51) 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)
$C{{H}_{3}}N{{H}_{2}}$

• question_answer52) Which one of the following bases is not present in DNA?   JEE Main  Solved  Paper-2014

A)
Cytosine

B)
Thymine

C)
Quinoline

D)

• question_answer53) 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)
$5,1,0,+\frac{1}{2}$

• question_answer54) 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

• question_answer55) 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

• question_answer56) 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

• question_answer57) Which one is classified as a condensation polymer?   JEE Main  Solved  Paper-2014

A)
Teflon

B)
Acrylonitrile

C)
Dacron

D)
Neoprene

• question_answer58) 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)
$HCl{{O}_{4}}>HOCl>HCl{{O}_{2}}>HCl{{O}_{3}}$

• question_answer59) 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)
$\text{-1361}\text{.95 kJ mo}{{\text{l}}^{\text{-1}}}$

• question_answer60) 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)
${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

• question_answer61) 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)
$\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}$

• question_answer62) 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)
$\left( 16,\frac{272}{3} \right)$

• question_answer63) 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)
$(-\infty ,-2)\cup (2,\infty )$

• question_answer64) 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

• question_answer65) The variance of first 50 even natural numbers is:   JEE Main  Solved  Paper-2014

A)
$\frac{833}{4}$

B)
$833$

C)
$437$

D)
$\frac{437}{4}$

• question_answer66) 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)
$20\left( \sqrt{3}-1 \right)$

• question_answer67) 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)
$4\sqrt{3}-4-\frac{\pi }{3}$

• question_answer68) 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

• question_answer69) 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)
$({{B}^{-1}})'$

• question_answer70) 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)
$-x{{e}^{x+\frac{1}{x}}}+c$

• question_answer71) 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 $\frac{5}{2}$

• question_answer72) 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)
$1+{{\{g(x)\}}^{5}}$

• question_answer73) 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)
$-1$

• question_answer74) 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)
$\frac{1}{12}$

• question_answer75) 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)
$\frac{2\sqrt{13}}{9}$

• question_answer76) 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.

• question_answer77) 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)
$f'(c)=2g'(c)$

• question_answer78) 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)
$400-300\,{{\text{e}}^{\text{-t/2}}}$

• question_answer79) 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)
$\frac{1}{4}$

• question_answer80) 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)
$\frac{\pi }{2}+\frac{2}{3}$

• question_answer81) 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

• question_answer82) 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)
$2x-9y-11=0$

• question_answer83) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi co{{s}^{2}}x)}{{{x}^{2}}}$is equal to:   JEE Main  Solved  Paper-2014

A)
$\frac{\pi }{2}$

B)
1

C)
$-\pi$

D)
$\pi$

• question_answer84) 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

• question_answer85) 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)
${{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}$

• question_answer86) 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)
$2+\sqrt{3}$

• question_answer87) 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)
$110$

• question_answer88) 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)
$\frac{\pi }{2}$

• question_answer89) 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)
$\frac{2}{3}$

• question_answer90) 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)
$\alpha =2,\beta =\frac{1}{2}$