# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

### done JEE Main Paper (Held On 11 April 2015) Total Questions - 90

• question_answer1) If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum ${{\mu }_{0}}$can be expressed in units of: JEE Main Online Paper (Held On 11 April 2015)

A)
$\left( \frac{hc}{m{{e}^{2}}} \right)$

B)
$\left( \frac{h}{m{{e}^{2}}} \right)$

C)
$\left( \frac{h}{c{{e}^{2}}} \right)$

D)
$\left( \frac{m{{c}^{2}}}{h{{e}^{2}}} \right)$

• question_answer2) A vector $\vec{A}$ is rotated by a small angle$\Delta \theta$radians $(\Delta \theta <<1)$ to get a new vector $\vec{B}.$ In that case$|\vec{B}-\vec{A}|$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
0

B)
$|\vec{A}|\left( 1-\frac{{{\Delta }_{\theta }}2}{2} \right)$

C)
$|\vec{A}|\Delta \theta$

D)
$|\vec{B}|\Delta \theta -|\vec{A}|$

• question_answer3) A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length $L(L>>r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic) : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{m{{\upsilon }^{2}}}{L-nr}$

B)
$\frac{m{{\upsilon }^{2}}}{L-2nr}$

C)
$\frac{m{{\upsilon }^{2}}}{2(L-nr)}$

D)
zero

• question_answer4) A particle is moving in a circle of radius r under the action of a force $F=\alpha {{r}^{2}}$which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy=0 for r=0): [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\alpha {{r}^{3}}$

B)
$\frac{1}{2}\alpha {{r}^{3}}$

C)
$\frac{4}{3}\alpha {{r}^{3}}$

D)
$\frac{5}{6}\alpha {{r}^{3}}$

• question_answer5) A uniform thin rod AB of length L has linear mass density $\mu (x)=a+\frac{bx}{L},$where x is measured from A. If the CM of the rod lies at a distance of $\left( \frac{7}{12}L \right)$from A, then a and b are related as : [JEE Main Online Paper (Held On 11 April 2015)]

A)
a = b

B)
a = 2b

C)
2a = b

D)
3a = 2b

• question_answer6) A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad ${{\text{s}}^{\text{-1}}}\text{,}$the magnitude of its angular momentum about a point on the ground right under the centre of the circle is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\text{8}\text{.64}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}$

B)
$\text{11}\text{.52}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}$

C)
$\text{14}\text{.4}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}$

D)
$\text{20}\text{.16}\,\text{kg}\,{{\text{m}}^{\text{2}}}{{\text{s}}^{\text{-1}}}$

• question_answer7) Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density? (figures are not drawn to scale) [JEE Main Online Paper (Held On 11 April 2015)]

A)

B)

C)

D)

• question_answer8) A cylindrical block of wood (density $=650\,kg\,{{m}^{-3}}$), of base area $30\text{ }c{{m}^{2}}$and height 54 cm, floats in a liquid of density $900\text{ }kg{{m}^{-}}^{3}.$The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) : [JEE Main Online Paper (Held On 11 April 2015)]

A)
65 cm

B)
52 cm

C)
39 cm

D)
26 cm

• question_answer9) A beaker contains a fluid of density$\rho \,kg/{{m}^{3}},$ specific heat $S\text{ }J/kg{}^\circ C$and viscosity t| . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $(\overset{\bullet }{\mathop{Q}}\,/A)$by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta ,\left( \frac{S\Delta \theta }{h} \right)$and$\left( \frac{1}{\rho g} \right)$when $\Delta \theta$ (in ${}^\circ C$ ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(\overset{\bullet }{\mathop{Q}}\,/A)$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\eta \frac{S\Delta \theta }{h}$

B)
$\eta \left( \frac{S\Delta \theta }{h} \right)\left( \frac{1}{\rho g} \right)$

C)
$\frac{S\Delta \theta }{\eta h}$

D)
$\left( \frac{S\Delta \theta }{\eta h} \right)\left( \frac{1}{\rho g} \right)$

• question_answer10) An experiment takes 10 minutes to raise the temperature of water in a container from $0{}^\circ C$ to $100{}^\circ C$ and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be $1\text{ }cal/g\text{ }{}^\circ C$, the heat of vapourization according to this experiment will come out to be: [JEE Main Online Paper (Held On 11 April 2015)]

A)
530 cal/g

B)
540 cal/g

C)
550 cal/g

D)
560 cal/g

• question_answer11) Using equipartition of energy, the specific heat $(in\text{ }J\text{ }k{{g}^{-1}}{{K}^{-}}^{1})$ of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27) [JEE Main Online Paper (Held On 11 April 2015)]

A)
25

B)
410

C)
925

D)
1850

• question_answer12) A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in${{s}^{-1}}$) is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{30}\ln 3$

B)
$\frac{1}{15}\ln 3$

C)
2

D)
$\frac{1}{2}$

• question_answer13) A source of sound emits sound waves at frequency ${{f}_{0}}.$It is moving towards an observer with fixed speed ${{\upsilon }_{s}}({{\upsilon }_{s}}<\upsilon ,$ where $\upsilon$ is the speed of sound in air). If the observer were to move towards the source with speed ${{\upsilon }_{0}},$ one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as ${{\upsilon }_{0}}$is changed. The variation of f with ${{\upsilon }_{0}}$is given correctly by: [JEE Main Online Paper (Held On 11 April 2015)]

A)
graph A with slope $=\frac{{{f}_{0}}}{(\upsilon -{{\upsilon }_{s}})}$

B)
graph A with slope$=\frac{{{f}_{0}}}{(\upsilon +{{\upsilon }_{s}})}$

C)
graph B with slope $=\frac{{{f}_{0}}}{(\upsilon -{{\upsilon }_{s}})}$

D)
graph B with slope$=\frac{{{f}_{0}}}{(\upsilon +{{\upsilon }_{s}})}$

• question_answer14) A wire, of length L(=20 cm), is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges $\pm Q.[|Q|={{10}^{3}}{{\varepsilon }_{0}}$Coulomb where ${{\varepsilon }_{0}}$is the permittivity (in SI units) of free space] the net electric field at the centre 0 of the semi-circular arc would be : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$(50\times {{10}^{3}}N/C)\hat{J}$

B)
$(25\times {{10}^{3}}N/C)\hat{i}$

C)
$(25\times {{10}^{3}}N/C)\hat{j}$

D)
$(50\times {{10}^{3}}N/C)\hat{i}$

• question_answer15) An electric field $\overset{\to }{\mathop{E}}\,=\left( 25\,\hat{i}+30\hat{j} \right)N{{C}^{-1}}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at x = 2 m, y = 2 m is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
-130J

B)
-12.0J

C)
-140J

D)
-110J

• question_answer16) In figure is shown a system of four capacitors connected across a 10 V battery. Charge that will flow from switch S when it is closed is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$5\mu C$ from b to a

B)
$20\mu C$ from a to b

C)
$5\mu C$ from a to b

D)
zero

• question_answer17) In the electric network shown, when no current flows through the $4\Omega$resistor in the arm EB, the potential difference between the points A and D will be: [JEE Main Online Paper (Held On 11 April 2015)]

A)
3V

B)
4V

C)
5V

D)
6V

• question_answer18) The value of the resistor, ${{R}_{S}},$needed in the dc voltage regulator circuit shown here, equals : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$({{V}_{i}}-{{V}_{L}})/n\,{{I}_{L}}$

B)
$({{V}_{i}}+{{V}_{L}})/n\,{{I}_{L}}$

C)
$({{V}_{i}}-{{V}_{L}})/(n+1)\,{{I}_{L}}$

D)
$({{V}_{i}}+{{V}_{L}})/(n+1)\,{{I}_{L}}$

• question_answer19) Two long straight parallel wires, carrying (adjustable) currents $\,{{I}_{1}}$and $\,{{I}_{2}},$ are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product $\,{{I}_{1}}\,{{I}_{2}},$would be : [JEE Main Online Paper (Held On 11 April 2015)]

A)

B)

C)

D)

• question_answer20) A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle $2{{\theta }_{0}}$ at the centre of the circle (of which it forms an arch) then the tension in the wire is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$IBR$

B)
$\frac{IBR}{\sin {{\theta }_{0}}}$

C)
$\frac{IBR}{2\sin {{\theta }_{0}}}$

D)
$\frac{IBR{{\theta }_{0}}}{\sin {{\theta }_{0}}}$

• question_answer21) A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north. Neutral points are found at a distance of 30 cm from the magnet on the East - West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in $A{{m}^{2}}$is close to : (Given $\frac{{{\mu }_{0}}}{4\pi }={{10}^{-7}}$ in SI units and ${{B}_{H}}=$Horizontal component of earth's magnetic field $=3.6\times {{10}^{-}}^{5}$ Tesla.) [JEE Main Online Paper (Held On 11 April 2015)]

A)
9.7

B)
4.9

C)
19.4

D)
14.6

• question_answer22) For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C', must have been connected in : [JEE Main Online Paper (Held On 11 April 2015)]

A)
series with C and has a magnitude$\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.$

B)
series with C and has a magnitude$\frac{C}{({{\omega }^{2}}LC-1)}.$

C)
parallel with C and has a magnitude$\frac{C}{({{\omega }^{2}}LC-1)}.$

D)
parallel with C and has a magnitude$\frac{1-{{\omega }^{2}}LC}{{{\omega }^{2}}L}.$

• question_answer23) For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for $\overset{\to }{\mathop{E}}\,$and $\overset{\to }{\mathop{B}}\,$field respectively? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\left( \hat{i}+2\hat{j} \right)$and$\left( 2\hat{i}-\hat{j} \right)$

B)
$\left( -2\hat{i}-3\hat{j} \right)$and$\left( 3\hat{i}-2\hat{j} \right)$

C)
$\left( 2\hat{i}+3\hat{j} \right)$and$\left( \hat{i}+2\hat{j} \right)$

D)
$\left( 3\hat{i}+4\hat{j} \right)$and$\left( 4\hat{i}-3\hat{j} \right)$

• question_answer24) A thin convex lens of focal length T is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance$\frac{a}{3}$in front of the combination. The value of 'a' is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
f

B)
2f

C)
3f

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

• question_answer25) In a Young's double slit experiment with light of wavelength$\lambda$the separation of slits is d and distance of screen is D such that $D>>d>>\lambda .$If the Fringe width is $\beta ,$ the distance from point of maximum intensity to the point where intensity falls to half of maximum intensity on either side is : [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$\frac{\beta }{4}$

C)
$\frac{\beta }{3}$

D)
$\frac{\beta }{6}$

• question_answer26) Unpolarized light of intensity in is incident on surface of a block of glass at Brewster's angle. In that case, which one of the following statements is true? [JEE Main Online Paper (Held On 11 April 2015)]

A)
transmitted light is partially polarized with intensity ${{I}_{0}}/2.$

B)
transmitted light is completely polarized with intensity less than ${{I}_{0}}/2.$

C)
reflected light is completely polarized with intensity less than ${{I}_{0}}/2.$

D)
reflected light is partially polarized with intensity ${{I}_{0}}/2.$

• question_answer27) The de - Broglie wavelength associated with the electron in the n = 4 level is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
two times the de-Broglie wavelength of the electron in the ground state

B)
four times the de-Broglie wavelength of the electron in the ground state

C)
half of the de-Broglie wavelength of the electron in the ground state

D)
1/4th of the de-Broglie wavelength of the electron in the ground state

• question_answer28) Let ${{N}_{\beta }}$ be the number of $\beta$ particles emitted by 1 gram of $N{{a}^{24}}$ radioactive nuclei (half-life = 15 hrs) in 7.5 hours, ${{N}_{\beta }}$ is close to (Avogadro number $=6.023\times {{10}^{23}}/g.$mole) : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$6.2\times {{10}^{21}}$

B)
$7.5\times {{10}^{21}}$

C)
$1.25\times {{10}^{22}}$

D)
$1.75\times {{10}^{22}}$

• question_answer29) A 2V battery is connected across AB as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to A and in other case when positive terminal of battery is connected to B will respectively be : [JEE Main Online Paper (Held On 11 April 2015)]

A)
0.2 A and 0.1 A

B)
0.4 A and 0.2 A

C)
0.1 A and 0.2 A

D)
0.2 A and 0.4 A

• question_answer30) The AC voltage across a resistance can be measured using a : [JEE Main Online Paper (Held On 11 April 2015)]

A)
potentiometer

B)
moving coil galvanometer

C)
moving magnet galvanometer

D)
hot wire voltmeter

• question_answer31) $A+2B+3C\rightleftharpoons A{{B}_{2}}{{C}_{3}}$ Reaction of 6.0 g of $A,6.0\times {{10}^{23}}$atoms of B, and 0.036 mol of C yields 4.8 g of compound $A{{B}_{2}}{{C}_{3}}.$If the atomic mass of A and C are 60 and 80 amu, respectively, the atomic mass of B is (Avogadro no.$=6\times {{10}^{23}}$) : [JEE Main Online Paper (Held On 11 April 2015)]

A)
70 amu

B)
60 amu

C)
50 amu

D)
40 amu

• question_answer32) When does a gas deviate the most from its ideal behaviour? [JEE Main Online Paper (Held On 11 April 2015)]

A)
At low pressure and low temperature

B)
At low pressure and high temperature

C)
At high pressure and low temperature

D)
At high pressure and high temperature

• question_answer33) At temperature T, the average kinetic energy of any particle is $\frac{3}{2}kT.$The de Broglie wavelength follows the order : [JEE Main Online Paper (Held On 11 April 2015)]

A)
Thermal proton > Visible photon > Thermal electron

B)
Thermal proton > Thermal electron Visible photon

C)
Visible photon > Thermal electron > Thermal neutron

D)
Visible photon > Thermal neutron > Thermal electron

• question_answer34) Molecule AB has a bond length of $1.617\overset{\circ }{\mathop{\text{A}}}\,$ and a dipole moment of 0.38 D. The fractional charge on each atom (absolute magnitude) is : $({{e}_{0}}=4.802\times {{10}^{-10}}esu)$ [JEE Main Online Paper (Held On 11 April 2015)]

A)
0

B)
0.05

C)
0.5

D)
1.0

• question_answer35) For the equilibrium, $A(g)\rightleftharpoons B(g),\Delta H$is -40 kJ/mol. If the ratio of the activation energies of the forward $({{E}_{f}})$ and reverse $({{E}_{b}})$reactions is $\frac{2}{3}$then : [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{E}_{f}}=60\,kJ/mol;{{E}_{b}}=100kJ/mol$

B)
${{E}_{f}}=30\,kJ/mol;{{E}_{b}}=70kJ/mol$

C)
${{E}_{f}}=80\,kJ/mol;{{E}_{b}}=120kJ/mol$

D)
${{E}_{f}}=70\,kJ/mol;{{E}_{b}}=30kJ/mol$

• question_answer36) Determination of the molar mass of acetic acid in benzene using freezing point depression is affected by : [JEE Main Online Paper (Held On 11 April 2015)]

A)
dissociation

B)
association

C)
partial ionization

D)
complex formation

• question_answer37) The increase of pressure on ice$\rightleftharpoons$ water system at constant temperature will lead to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
no effect on the equilibrium

B)
a decrease in the entropy of the system

C)
a shift of the equilibrium in the forward direction

D)
an increase in the Gibbs energy of the system

• question_answer38) At 298 K, the standard reduction potentials are 1.51 V for$MnO_{4}^{-}|M{{n}^{2+}},1.36V$for $C{{l}_{2}}|C{{l}^{-}},1.07V$ for $B{{r}_{2}}|B{{r}^{-}},$and $0.54V$for ${{I}_{2}}|{{I}^{-}}.$At pH = 3, permanganate is expected to oxidize : $\left( \frac{RT}{F}=0.059V \right)$ [JEE Main Online Paper (Held On 11 April 2015)]

A)
$C{{l}^{-}},B{{r}^{-}}$and ${{I}^{-}}$

B)
$C{{l}^{-}}$and$B{{r}^{-}}$

C)
$B{{r}^{-}}$and${{I}^{-}}$

D)
${{I}^{-}}$only

• question_answer39) $A+2B\to C,$the rate equation for this reaction is given as Rate=k[A][B]. If the concentration of A is kept the same but that of B is doubled what will happen to the rate itself? [JEE Main Online Paper (Held On 11 April 2015)]

A)
halved

B)
the same

C)
doubled

D)

• question_answer40) Under ambient conditions, which among the following surfactants will form micelles in aqueous solution at lowest molar concentration? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$C{{H}_{3}}{{(C{{H}_{2}})}_{15}}\overset{\oplus }{\mathop{N}}\,{{(C{{H}_{3}})}_{3}}B\overset{\Theta }{\mathop{r}}\,$

B)
$C{{H}_{3}}-{{(C{{H}_{2}})}_{13}}-OSO_{3}^{-}N{{a}^{+}}$

C)
$C{{H}_{3}}-{{(C{{H}_{2}})}_{8}}-COO{{O}^{\Theta }}N{{a}^{+}}$

D)
$C{{H}_{3}}{{(C{{H}_{2}})}_{11}}\overset{\oplus }{\mathop{N}}\,{{(C{{H}_{3}})}_{3}}B{{r}^{-}}$

• question_answer41) Choose the incorrect formula out of the four compounds for an element X below : [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{X}_{2}}C{{l}_{3}}$

B)
${{X}_{2}}{{O}_{3}}$

C)
${{X}_{2}}{{(S{{O}_{4}})}_{3}}$

D)
$XP{{O}_{4}}$

• question_answer42) Calamine is an ore of : [JEE Main Online Paper (Held On 11 April 2015)]

A)
Aluminium

B)
Copper

C)
Iron

D)
Zinc

• question_answer43) Which physical property of dihydrogen is wrong? [JEE Main Online Paper (Held On 11 April 2015)]

A)
Colourless gas

B)
Odourless gas

C)
Tasteless gas

D)
Non-inflammable gas

• question_answer44) Which of the alkaline earth metal halides given below is essentially covalent in nature? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$MgC{{l}_{2}}$

B)
$BeC{{l}_{2}}$

C)
$SrC{{l}_{2}}$

D)
$CaC{{l}_{2}}$

• question_answer45) Which of the following compounds has a P-P bond? [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{H}_{4}}{{P}_{2}}{{O}_{5}}$

B)
${{H}_{4}}{{P}_{2}}{{O}_{6}}$

C)
${{H}_{4}}{{P}_{2}}{{O}_{7}}$

D)
${{(HP{{O}_{3}})}_{3}}$

• question_answer46) Chlorine water on standing loses its colour and forms : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$HCl$ only

B)
$HOCl$and $HOC{{l}_{2}}$

C)
$HCl$ and $HOCl$

D)
$HCl$ and $HCl{{O}_{2}}$

• question_answer47) Which of the following statements is false? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$CrO_{4}^{2-}$is tetrahedral in shape

B)
$C{{r}_{2}}O_{7}^{2-}$ has a $Cr-O-Cr$ bond

C)
$N{{a}_{2}}C{{r}_{2}}{{O}_{7}}$is a primary standard in volumetry

D)
$N{{a}_{2}}C{{r}_{2}}{{O}_{7}}$is less soluble than ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

• question_answer48) When concentrated HCl is added to an aqueous solution of $CoC{{l}_{2}},$its colour changes from reddish pink to deep blue. Which complex ion gives blue colour in this reaction? [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{[CoC{{l}_{6}}]}^{4-}}$

B)
${{[CoC{{l}_{6}}]}^{3-}}$

C)
${{[CoC{{l}_{4}}]}^{2-}}$

D)
${{[Co{{({{H}_{2}}O)}_{6}}]}^{2+}}$

• question_answer49) Which of the following complex ions has electrons that are symmetrically filled in both ${{t}_{2g}}$and ${{e}_{g}}$ orbitals? [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{[Co{{F}_{6}}]}^{3-}}$

B)
${{[Co{{(N{{H}_{3}})}_{6}}]}^{2+}}$

C)
${{[Mn{{(CN)}_{6}}]}^{4-}}$

D)
${{[Fe{{F}_{6}}]}^{3-}}$

• question_answer50) Addition of phosphate fertilisers to water  bodies causes : [JEE Main Online Paper (Held On 11 April 2015)]

A)
enhanced growth of algae

B)
increase in amount of dissolved oxygen in water

C)
deposition of calcium phosphate

D)
increase in fish population

• question_answer51) Match the organic compounds in column - I with the Lassaigne's test results in column - II appropriately : [JEE Main Online Paper (Held On 11 April 2015)]    Column-I Column-II (A) Aniline (i) Red color with $FeC{{l}_{3}}$ (B) Benzene sulfonic acid (ii) Violet color with sodium nitroprusside (C) Thiourea (iii) Blue color with hot and acidic solution of $FeS{{O}_{4}}$

A)
(A) - (ii);  (B) - (i);  (C) - (iii)

B)
(A) - (iii); (B) - (ii); (B) - (i)

C)
(A) - (ii); (B) - (iii); (C) - (i)

D)
(A) - (iii); (B) - (i); (C) - (ii)

• question_answer52) Which of the following pairs of compounds are positional isomers? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-CHO$and$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$

B)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$and$C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-CHO$

C)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$and$C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-C{{H}_{3}}$

D)
$C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-C{{H}_{3}}$and

• question_answer53) The number of structural isomers for${{C}_{6}}{{H}_{14}}$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
3

B)
4

C)
5

D)
6

• question_answer54) What is the major product expected from the following reaction? Where D is an isotope of Hydrogen. [JEE Main Online Paper (Held On 11 April 2015)]

A)

B)

C)

D)

• question_answer55) In the reaction sequence $2C{{H}_{3}}CHO\xrightarrow[{}]{O{{H}^{-}}}A\xrightarrow[{}]{\Delta }B;$the product B is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{2}}-OH$

B)
$C{{H}_{3}}-CH=CH-CHO$

C)
$C{{H}_{3}}-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$

D)
$C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-C{{H}_{3}}$

• question_answer56) Which compound exhibits maximum dipole moment among the following? [JEE Main Online Paper (Held On 11 April 2015)]

A)

B)

C)

D)

• question_answer57) Which one of the following structures represents the neoprene polymer? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$-{{\left( C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{C}}\,=CH-C{{H}_{2}} \right)}_{n}}-$

B)
$-{{\left( C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ CN \end{smallmatrix}}{\mathop{CH}}\, \right)}_{n}}-$

C)
$-{{\left( C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\mathop{CH}}\, \right)}_{n}}-$

D)
$-{{\left( \underset{\begin{smallmatrix} | \\ {{C}_{6}}{{H}_{5}} \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}} \right)}_{n}}-$

• question_answer58) Accumulation of which of the following molecules in the muscles occurs as a result of vigorous exercise? [JEE Main Online Paper (Held On 11 April 2015)]

A)
Glucose

B)
Glycogen

C)
L-lactic acid

D)
Pyruvic acid

• question_answer59) Which artificial sweetener contains chlorine? [JEE Main Online Paper (Held On 11 April 2015)]

A)
Aspartame

B)
Saccharin

C)
Sucralose

D)
Ali tame

• question_answer60) A pink coloured salt turns blue on heating. The presence of which cation is most likely? [JEE Main Online Paper (Held On 11 April 2015)]

A)
$C{{u}^{2+}}$

B)
$F{{e}^{2+}}$

C)
$Z{{n}^{2+}}$

D)
$C{{o}^{2+}}$

• question_answer61) Let $A=\{{{x}_{1}},{{x}_{2}},...,{{x}_{7}}\}$and $B=\{{{y}_{1}},{{y}_{2}},{{y}_{3}}\}$be two sets containing seven and three distinct elements respectively. Then the total number of functions$f:A\to B$ that are onto, if there exist exactly three elements x in A such that$f(x)={{y}_{2}},$ is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$14.{{\,}^{7}}{{C}_{2}}$

B)
$16.{{\,}^{7}}{{C}_{3}}$

C)
$12.{{\,}^{7}}{{C}_{2}}$

D)
$14.{{\,}^{7}}{{C}_{3}}$

• question_answer62) If z is a non-real complex number, then the minimum value of $\frac{\operatorname{Im}\,{{z}^{5}}}{{{(Im\,z)}^{5}}}$is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
-1

B)
-2

C)
-4

D)
-5

• question_answer63) If the two roots of the equation, $(a-1)({{x}^{4}}+{{x}^{2}}+1)+(a+1){{({{x}^{2}}+x+1)}^{2}}=0$are real and distinct, then the set of all values of 'a' is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\left( -\frac{1}{2},0 \right)$

B)
$(-\infty ,-2)\cup (2,\infty )$

C)
$\left( -\frac{1}{2},0 \right)\cup \left( 0,\frac{1}{2} \right)$

D)
$\left( 0,\frac{1}{2} \right)$

• question_answer64) If A is a $3\times 3$ matrix such that |5. adjA| = 5, then A| is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\pm \frac{1}{5}$

B)
$\pm \,5$

C)
$\pm \,1$

D)
$\pm \,\frac{1}{25}$

• question_answer65) $\left| \begin{matrix} {{x}^{2}}+x & x+1 & x-2 \\ 2{{x}^{2}}+3x-1 & 3x & 3x-3 \\ {{x}^{2}}+2x+3 & 2x-1 & 2x-1 \\ \end{matrix} \right|=ax-12,$then 'a' is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
12

B)
24

C)
-12

D)
-24

• question_answer66) If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
10

B)
12

C)
9

D)
6

• question_answer67) The term independent of x in the binomial expansion of$\left( 1-\frac{1}{x}+3{{x}^{5}} \right){{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{8}}$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
400

B)
406

C)
-400

D)
-496

• question_answer68) The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
7290

B)
320

C)
640

D)
2430

• question_answer69) If $\sum\limits_{n=1}^{5}{\frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3},}$then k is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{55}{336}$

B)
$\frac{17}{105}$

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

D)
$\frac{19}{112}$

• question_answer70) Let k be a non-zero real number. If\begin{align} & f(x)=\left\{ \frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{k} \right)\log \left( 1+\frac{x}{4} \right)},x\ne 0 \right. \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,12\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,x=0 \\ \end{align} is a continuous function, then the value of k is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
1

B)
2

C)
3

D)
4

• question_answer71) The equation of a normal to the curve,$\sin y=x\sin \left( \frac{\pi }{3}+y \right)$ at $x=0,$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$2x+\sqrt{3}y=0$

B)
$2x-\sqrt{3}x=0$

C)
$2y+\sqrt{3}x=0$

D)
$2x-\sqrt{3}y=0$ $x=0\Rightarrow y=0$

• question_answer72) Let k and K be the minimum and the maximum values of the function$f(x)=\frac{{{(1+x)}^{0.6}}}{1+{{x}^{0.6}}}$in $[0,1]$respectively, then the ordered pair (k, K) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$(1,{{2}^{0.6}})$

B)
$({{2}^{-0.4}}1,{{2}^{0.6}})$

C)
$({{2}^{-0.6}},1)$

D)
$({{2}^{-0.4}},1)$

• question_answer73) From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g=32\text{ }m/{{s}^{2}},$is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
100

B)
88

C)
128

D)
112

• question_answer74) 2015 / If $\int_{{}}^{{}}{\frac{\log \left( t+\sqrt{1+{{t}^{2}}} \right)}{\sqrt{1+{{t}^{2}}}}}dt=\frac{1}{2}{{\left( g(t) \right)}^{2}}+C,$where C is a constant, then g(2) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$2\log (2+\sqrt{5})$

B)
$\log (2+\sqrt{5})$

C)
$\frac{1}{\sqrt{5}}\log (2+\sqrt{5})$

D)
$\frac{1}{2}\log (2+\sqrt{5})$

• question_answer75) Let $f:R\to R$be a function such that$f(2-x)=f\,(2+x)$ and$f(4-x)=f\,(4+x),$for all $x\in R$and $\int\limits_{0}^{2}{f(x)}dx=5.$Then the value of $\int\limits_{10}^{50}{f(x)}\,dx$is:

A)
80

B)
100

C)
125

D)
200

• question_answer76) Let $f:(-1,1)\to R$ be a continuous function. If $\int\limits_{0}^{\sin x}{f(t)dt}=\frac{\sqrt{3}}{2}x,$ then$f\left( \frac{\sqrt{3}}{2} \right)$is equal to : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{\sqrt{3}}{2}$

B)
$\sqrt{3}$

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

D)
$\frac{1}{2}$

• question_answer77) The solution of the differential equation $ydx-(x+2{{y}^{2}})dy=0$is$x=f(y).$ If $f(-1)=1,$ then$f(1)$is equal to: [JEE Main Online Paper (Held On 11 April 2015)]

A)
4

B)
3

C)
2

D)
1

• question_answer78) A straight line L through the point (3, - 2) is inclined at an angle of 60° to the line $\sqrt{3}x+y=1.$If L also intersects the x-axis, then the equation of L is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$y+\sqrt{3}x+2-3\sqrt{3}=0$

B)
$y-\sqrt{3}x+2+3\sqrt{3}=0$

C)
$\sqrt{3}y-x+3+2\sqrt{3}=0$

D)
$\sqrt{3}y+x-3+2\sqrt{3}=0$

• question_answer79) If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is $3x+4y+3=0,$ then the equation of the circumcircle of this triangle is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
${{x}^{2}}+{{y}^{2}}-2x-2y-2=0$

B)
${{x}^{2}}+{{y}^{2}}-2x-2y-14=0$

C)
${{x}^{2}}+{{y}^{2}}-2x-2y+2=0$

D)
${{x}^{2}}+{{y}^{2}}-2x-2y-7=0$

• question_answer80) If a circle passing through the point (-1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is : [JEE Main Online Paper (Held On 11 April 2015)]

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

B)
$\frac{5}{2}$

C)
3

D)
5

• question_answer81) If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{2}$

B)
$\frac{2\sqrt{2}-1}{2}$

C)
$\sqrt{2}-1$

D)
$\frac{\sqrt{2}-1}{2}$

• question_answer82) Let PQ be a double ordinate of the parabola, ${{y}^{2}}=-4x,$where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$9{{y}^{2}}=4x$

B)
$9{{y}^{2}}=-4x$

C)
$3{{y}^{2}}=2x$

D)
$3{{y}^{2}}=-2x$

• question_answer83) The shortest distance between the z-axis and the line $x+y+2z-3=0=2x+3y+4z-4,$ is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
1

B)
2

C)
3

D)
4

• question_answer84) A plane containing the point (3, 2, 0) and the line $\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}$also contains the point : [JEE Main Online Paper (Held On 11 April 2015)]

A)
(0, -3, 1)

B)
(0, 7, 10)

C)
(0, 7, -10)

D)
(0, 3, 1)

• question_answer85) In a parallelogram $ABCD,\left| \overrightarrow{AB} \right|=a,\left| \overrightarrow{AD} \right|=b$and $\left| \overrightarrow{AC} \right|=c,$ then $\overrightarrow{AB}.\overrightarrow{AB}$ has the value : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{2}\left( {{a}^{2}}-{{b}^{2}}+{{c}^{2}} \right)$

B)
$\frac{1}{4}\left( {{a}^{2}}+{{b}^{2}}-{{c}^{2}} \right)$

C)
$\frac{1}{3}\left( {{b}^{2}}+{{c}^{2}}-{{a}^{2}} \right)$

D)
$\frac{1}{2}\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}} \right)$

E)
None of these

• question_answer86) If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{26}$

B)
$\frac{1}{27}$

C)
$\frac{1}{21}$

D)
$\frac{1}{15}$

• question_answer87) If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{1}{16}$

B)
$\frac{9}{16}$

C)
$\frac{3}{4}$

D)
$\frac{15}{16}$

• question_answer88) If $\cos \alpha +\cos \beta =\frac{3}{2}$and $\sin \alpha +\sin \beta =\frac{1}{2}$and $\theta$is the arithmetic mean of $\alpha$ and $\beta ,$ then $\sin 2\theta +\cos 2\theta$is equal to: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{3}{5}$

B)
$\frac{4}{5}$

C)
$\frac{7}{5}$

D)
$\frac{8}{5}$

• question_answer89) Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $\alpha$at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from 0 is 'a' ; then the distance between two consecutive poles, is: [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\frac{h\sin \alpha +a\cos \alpha }{9\sin \alpha }$

B)
$\frac{h\cos \alpha -a\sin \alpha }{9\cos \alpha }$

C)
$\frac{h\cos \alpha -a\sin \alpha }{9\sin \alpha }$

D)
$\frac{h\sin \alpha +a\cos \alpha }{9\cos \alpha }$

• question_answer90) Consider the following statements : P : Suman is brilliant. Q : Suman is rich. R : Suman is honest. The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as : [JEE Main Online Paper (Held On 11 April 2015)]

A)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\wedge R$

B)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee R$

C)
$\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee \tilde{\ }R$

D)
$\tilde{\ }Q\leftrightarrow P\wedge \tilde{\ }R$