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

### done JEE Main Paper (Held On 11 April 2014) Total Questions - 90

• question_answer1) In terms of resistance R and time T, the dimensions of ratio$\frac{\mu }{\varepsilon }$of the permeability $\mu$ and permittivity $\varepsilon$ is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$[R{{T}^{-2}}]$

B)
$[{{R}^{2}}{{T}^{-1}}]$

C)
$[{{R}^{2}}]$

D)
$[{{R}^{2}}{{T}^{2}}]$

• question_answer2) The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target ?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
1.0m

B)
4.2 m

C)
6.1 m

D)
9.8 m

• question_answer3) A body of mass 5 kg under the action of constant force $\overset{\to }{\mathop{F}}\,={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}$has velocity at$t=0s$as$\overset{\to }{\mathop{v}}\,=\left( 6\hat{i}-2\hat{j} \right)m/s$and at t = 10s as $\overset{\to }{\mathop{v}}\,=+6\hat{j}\,m/s.$ The force $\overset{\to }{\mathop{F}}\,$is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\left( -3\hat{j}+4\hat{j} \right)N$

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

C)
$\left( 3\hat{i}-4\hat{j} \right)N$

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

• question_answer4) A small ball of mass m starts at a point A with speed ${{v}_{0}}$ and moves along a frictionless track AB as shown. The track BC has coefficient of friction m. The ball comes to stop at C after travelling a distance L which is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{2h}{\mu }+\frac{v_{o}^{2}}{2\mu g}$

B)
$\frac{h}{\mu }+\frac{v_{o}^{2}}{2\mu g}$

C)
$\frac{h}{2\mu }+\frac{v_{o}^{2}}{\mu g}$

D)
$\frac{h}{2\mu }+\frac{v_{o}^{2}}{2\mu g}$

• question_answer5) The average mass of rain drops is $3.0\times {{10}^{-5}}$kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$3.0\times {{10}^{5}}J$

B)
$4.05\times {{10}^{4}}J$

C)
$3.0\times {{10}^{5}}J$

D)
$9.0\times {{10}^{4}}J$

• question_answer6) A thin bar of length L has a mass per unit length $\lambda$, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is ${{\lambda }_{O}},$ then the distance of the centre of mass from the lighter end is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{L}{2}-\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}$

B)
$\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{8M}$

C)
$\frac{L}{3}+\frac{{{\lambda }_{o}}{{L}^{2}}}{4M}$

D)
$\frac{2L}{3}-\frac{{{\lambda }_{o}}{{L}^{2}}}{6M}$

• question_answer7) From a sphere of mass M and radius R, a smaller sphere of radius$\frac{R}{2}$is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{41G{{M}^{2}}}{3600{{R}^{2}}}$

B)
$\frac{41G{{M}^{2}}}{450{{R}^{2}}}$

C)
$\frac{59\,G{{M}^{2}}}{450{{R}^{2}}}$

D)
$\frac{\,G{{M}^{2}}}{225{{R}^{2}}}$

• question_answer8) The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of ${{10}^{9}}N{{m}^{-2}}.$For a given value of pressure, the fractional compression in volume is $\frac{\Delta V}{V}.$Which of the following statements about $\frac{\Delta V}{V}$for these three liquids is correct?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Ethanol > Water > Mercury

B)
Water > Ethanol > Mercury

C)
Mercury > Ethanol > Water

D)
Ethanol > Mercury > Water

• question_answer9) A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly: (take g = 10 ms? 2 and density of water $={{10}^{3}}kg\,{{m}^{-3}}$)   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$10.7m{{s}^{-1}}$

B)
$9.6m{{s}^{-1}}$

C)
$8.5m{{s}^{-1}}$

D)
$7.6m{{s}^{-1}}$

• question_answer10) An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density ${{10}^{3}}kg/{{m}^{3}}.$ The pressure inside the bubble is $1100N{{m}^{-2}}$ greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? $(g=9.8m{{s}^{-2}})$   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
0.1m

B)
0.15m

C)
0.20m

D)
0.25m

• question_answer11) A hot body, obeying Newton's law of cooling is cooling down from its peak value $80{}^\circ C$ to an ambient temperature of $30{}^\circ C$. It takes 5 minutes in cooling down from $80{}^\circ C$ to $40{}^\circ C$. How much time will it take to cool down from $42{}^\circ C$ to $32{}^\circ C$? (Given In 2 = 0.693, In 5 = 1.609)   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
3.75 minutes

B)
8.6 minutes

C)
9.6 minutes

D)
6.5 minutes

• question_answer12) During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: $(R=8.3J{{K}^{-1}}mo{{l}^{-1}})$   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
40 K

B)
33 K

C)
20 K

D)

E)
14 K

• question_answer13) An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $8.0\times {{10}^{-3}}{{m}^{2}}.$Initially the gas is at 300 K and occupies a volume of $2.4\times {{10}^{-3}}{{m}^{3}}$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $1.0\times {{10}^{5}}N/{{m}^{2}}.$ The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible).   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
300 K

B)
800 K

C)
500 K

D)
1000 K

• question_answer14) The angular frequency of the damped oscillator is given by,$\omega =\sqrt{\left( \frac{k}{m}-\frac{{{r}^{2}}}{4{{m}^{2}}} \right)}$where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio$\frac{{{r}^{2}}}{mk}$is 8%, the change in time period compared to the undamped oscillator is approximately as follows:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
increases by 1%

B)
increases by 8%

C)
decreases by 1%

D)
decreases by 8%

• question_answer15) Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
2

B)
4

C)
8

D)
10

• question_answer16) A cone of base radius R and height h is located in a uniform electric field $\overset{\to }{\mathop{E}}\,$ parallel to its base. The electric flux entering the cone is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

B)
her

C)
2 E h R

D)
4 E h R

• question_answer17) A parallel plate capacitor is made of two plates of length l, width w and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force$F=-\frac{\partial U}{\partial x}$where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{{{Q}^{2}}d}{2\omega {{1}^{2}}{{\varepsilon }_{o}}}K$

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

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

D)
$\frac{{{Q}^{2}}w}{2d{{1}^{2}}{{\varepsilon }_{o}}}K$

• question_answer18) In the circuit shown, current (in A) through 50 V and 30 V batteries are, respectively:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
2.5 and 3

B)
3.5 and 2

C)
4.5 and 1

D)
3 and 2.5

• question_answer19) Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$3\times {{10}^{-4}}N$ toward right

B)
$6\times {{10}^{-4}}N$ toward right

C)
$9\times {{10}^{-4}}N$toward right

D)
Zero

• question_answer20) Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows: Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P):   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$A\leftrightarrow D,B\leftrightarrow P,C\leftrightarrow F$

B)
$A\leftrightarrow F,B\leftrightarrow D,C\leftrightarrow P$

C)
$A\leftrightarrow P,B\leftrightarrow F,C\leftrightarrow D$

D)
$A\leftrightarrow F,B\leftrightarrow P,C\leftrightarrow D$

• question_answer21) A coil of circular cross-section having 1000 turns and $4c{{m}^{2}}$face area is placed with its axis parallel to a magnetic field which decreases by ${{10}^{-2}}$ Wb ${{m}^{-2}}$ in 0.01 s. The e.m.f. induced in the coil is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
400 mV

B)
200 mV

C)
4 mV

D)
0.4 mV

• question_answer22) An electromagnetic wave of frequency $1\times {{10}^{14}}$hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ${{\varepsilon }_{0}}=8.8\times {{10}^{-12}}{{C}^{2}}/N-{{m}^{2}},$then average energy density of electric field will be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$35.2\times {{10}^{-10}}J/{{m}^{3}}$

B)
$35.2\times {{10}^{-11}}J/{{m}^{3}}$

C)
$35.2\times {{10}^{-12}}J/{{m}^{3}}$

D)
$35.2\times {{10}^{-13}}J/{{m}^{3}}$

• question_answer23) An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 3. What is the distance between the screen and the object?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
124.5 cm

B)
144.5 cm

C)
65.0 cm

D)
99.0 cm

• question_answer24) Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

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

C)
$\frac{7}{1}$

D)
$\frac{49}{1}$

• question_answer25) In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
200

B)
100

C)
400

D)
150

• question_answer26) A photon of wavelength l is scattered from an electron, which was at rest. The wavelength shift $\Delta \lambda$ is three times of $\lambda$ and the angle of scattering $\theta$ is $60{}^\circ$. The angle at which the electron recoiled is $\phi .$ The value of tan $\phi$ is : (electron speed is much smaller than the speed of light)   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
0.16

B)
0.22

C)
0.25

D)
0.28

• question_answer27) A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t = 0 there were no nuclei, the time when there are 50 nuclei is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
1s

B)
$2\ln \left( \frac{4}{3} \right)s$

C)
$\ln 2s$

D)
$\ln \left( \frac{4}{3} \right)s$

• question_answer28) Zener diode is connected to a battery and a load as show below: The currents, $I,{{I}_{Z}}$ and ${{I}_{L}}$ are respectively.   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
15 mA, 5 mA, 10 mA

B)
15 mA, 7.5 mA, 7.5 mA

C)
12.5 mA, 5 mA, 7.5 mA

D)
12.5 mA, 7.5 mA, 5 mA

• question_answer29) Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II (Part of electromagnetic spectrum) and select the correct code from the choices given below this lists:  (I) Doublet of sodium (a) Visible radiation (II) Wavelength corresponding to temperature associated with the isotropic radiation filling all space (b) Microwave (III) Wavelength emitted by Atomic hydrogen in Interstellar space (c) Short radio wave (IV) Wavelength of radiation arising from two close energy levels in hydrogen (d) X-rays
[JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

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

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

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

• question_answer30) In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Circuit A with G$\frac{RS}{(R-S)}$

B)
Circuit B with G = S

C)
Circuit C with G = S

D)
Circuit D with G = $\frac{RS}{(R-S)}$

• question_answer31) If ${{\lambda }_{o}}$and $\lambda$ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\sqrt{\frac{2h}{m}\left( {{\lambda }_{o}}-\lambda \right)}$

B)
$\sqrt{\frac{2hc}{m}\left( {{\lambda }_{o}}-\lambda \right)}$

C)
$\sqrt{\frac{2hc}{m}\left( \frac{{{\lambda }_{o}}-\lambda }{\lambda {{\lambda }_{o}}} \right)}$

D)
$\sqrt{\frac{2h}{m}\left( \frac{1}{{{\lambda }_{o}}}-\frac{1}{\lambda } \right)}$

• question_answer32) The appearance of colour in solid alkali meta halides is generally due to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Schottky defect

B)
Frenkel defect

C)
Interstitial position

D)
F-centres

• question_answer33) In the reaction of formation of sulphur trioxide by contact process $2S{{O}_{2}}+{{O}_{2}}\rightleftharpoons 2S{{O}_{3}}$the rate of reaction was measured as$\frac{d\left[ {{O}_{2}} \right]}{dt}=-2.5\times {{10}^{-4}}\text{mol}$$\,{{L}^{-1}}{{s}^{-1}}.$  The rate of reaction is terms of $[S{{O}_{2}}]$in mol ${{\text{L}}^{\text{-1}}}\,{{\text{s}}^{\text{-1}}}$ will be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$-1.25\times {{10}^{-4}}$

B)
$-2.50\times {{10}^{-4}}$

C)
$-3.75\times {{10}^{-4}}$

D)
$-5.00\times {{10}^{-4}}$

• question_answer34) Assuming that the degree of hydrolysis is small, the pH of 0.1 M solution of sodium acetate $({{K}_{a}}=1.0\times {{10}^{-5}})$ will be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
5.0

B)
6.0

C)
8.0

D)
9.0

• question_answer35) For the reaction, $2{{N}_{2}}{{O}_{5}}\to 4N{{O}_{2}}+{{O}_{2}},$the rate equation can be expressed in two ways$-\frac{d\left[ {{N}_{2}}{{O}_{5}} \right]}{dt}=k\left[ {{N}_{2}}{{O}_{5}} \right]$ and $+\frac{d\left[ N{{O}_{2}} \right]}{dt}=k'\left[ {{N}_{2}}{{O}_{5}} \right]$k and k' are related as:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
k = k'

B)
2k = k'

C)
k = 2k'

D)
k = 4k'

• question_answer36) In some solutions, the concentration of ${{H}_{3}}{{O}^{+}}$ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Ideal solutions

B)
Colloidal solutions

C)
True solutions

D)
Buffer solutions

• question_answer37) Given $F{{e}^{3+}}(aq)+{{e}^{-}}\to F{{e}^{2+}}(aq);{{E}^{0}}=+0.77V$ $A{{l}^{3+}}(aq)+3{{e}^{-}}\to Al(s);{{E}^{0}}=-1.66V$ $B{{r}_{2}}(aq)+2{{e}^{-}}\to 2B{{r}^{-}};{{E}^{0}}=+1.09V$ Considering the electrode potentials, which of the following represents the correct order of reducing power?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$F{{e}^{2+}}<Al<B{{r}^{-}}$

B)
$B{{r}^{-}}<F{{e}^{2+}}<Al$

C)
$Al<B{{r}^{-}}<F{{e}^{2+}}$

D)
$Al<F{{e}^{2+}}<B{{r}^{-}}$

• question_answer38) The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mm Hg to 360.0 mm Hg, the final volume the gas will be:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
1.750 L

B)
3.60 L

C)
4.032 L

D)
7.50 L

• question_answer39) The molar heat capacity $({{C}_{p}})$ of $C{{D}_{2}}O$is 10 cals at 1000 K. The change in entropy associated with cooling of 32 g of $C{{D}_{2}}O$vapour from 1000 K to 100 K at constant pressure will be: (D = deuterium, atomic mass = 2 u)   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\text{23}\text{.03cal}\,\text{de}{{\text{g}}^{\text{-1}}}$

B)
$\text{-23}\text{.03cal}\,\text{de}{{\text{g}}^{\text{-1}}}$

C)
$\text{2}\text{.303cal}\,\text{de}{{\text{g}}^{\text{-1}}}$

D)
$\text{-2}\text{.303cal}\,\text{de}{{\text{g}}^{\text{-1}}}$

• question_answer40) Based on the equation: $\Delta E=-2.0\times {{10}^{-18}}J\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} \right)$the wavelength of the light that must be absorbed to excite hydrogen electron from level n = 1 to level n = 2 will be: $(h=6.625\times {{10}^{-34}}Js,C=3\times {{10}^{8}}m{{s}^{-1}})$   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$1.325\times {{10}^{-7}}m$

B)
$1.325\times {{10}^{-10}}m$

C)
$2.650\times {{10}^{-7}}m$

D)
$5.300\times {{10}^{-10}}m$

• question_answer41) Which of the following series correctly represents relations between the elements from X to Y? $X\to Y$   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$_{3}Li{{\to }_{19}}K$ Ionization enthalpy increases

B)
$_{9}F{{\to }_{35}}Br$ Electron gain enthalpy (negative sign) increases

C)
$_{6}C{{\to }_{32}}Ge$ Atomic radii increases

D)
$_{18}Ar{{\to }_{54}}Xe$ Noble character increases

• question_answer42) The correct order of bond dissociation energy among ${{N}_{2}},{{O}_{2}},O_{2}^{-}$is shown in which of the following arrangements?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
${{N}_{2}}>O_{2}^{-}>{{O}_{2}}$

B)
$O_{2}^{-}>{{O}_{2}}>{{N}_{2}}$

C)
$N_{2}^{{}}>{{O}_{2}}>O_{2}^{-}$

D)
${{O}_{2}}>O_{2}^{-}>N_{2}^{{}}$

• question_answer43) Which of the following statements about $N{{a}_{2}}{{O}_{2}}$ is not correct?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
It is diamagnetic in nature

B)
It is derivative of ${{H}_{2}}{{O}_{2}}$

C)
$N{{a}_{2}}{{O}_{2}}$oxidises $C{{r}^{3+}}$ to $CrO_{4}^{2-}$in acid medium.

D)
It is the super oxide of sodium

• question_answer44) Which of the following statements about the depletion of ozone layer is correct?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
The problem of ozone depletion is less serious at poles because $N{{O}_{2}}$ solidifies and is not available for consuming $CI{{O}^{\bullet }}$radicals.

B)
The problem of ozone depletion is more serious at poles because ice crystals in the clouds over poles act as catalyst for photochemical reactions involving the decomposition of ozone of $C{{l}^{\bullet }}$ and $Cl{{O}^{\bullet }}$ radicals.

C)
Freons, chlorofluorocarbons, are inert. Chemically, they do not react with ozone in stratosphere.

D)
Oxides of nitrogen also do not react with ozone in stratosphere.

• question_answer45) A gaseous compound of nitrogen and hydrogen contains 12.5% (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$N{{H}_{2}}$

B)
${{N}_{3}}H$

C)
$N{{H}_{3}}$

D)
${{N}_{2}}{{H}_{4}}$

• question_answer46) Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\text{I}{{\text{F}}_{\text{7}}}$ : pentagonal bipyramid

B)
$\text{Br}{{\text{F}}_{5}}$ : trigonal bipyramid

C)
$\text{Br}{{\text{F}}_{3}}$ : planar T-shaped

D)
$\text{IC}{{\text{I}}_{3}}$: planar dimeric

• question_answer47) Consider the following equilibrium $AgCl\downarrow +2N{{H}_{3}}\rightleftharpoons {{\left[ Ag{{\left( N{{H}_{3}} \right)}_{2}} \right]}^{+}}+C{{l}^{-}}$ White precipitate of AgCl appears on adding which of the following?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$N{{H}_{3}}$                   aqueous NaCl

B)
aqueous $HN{{O}_{3}}$

C)
aqueous $N{{H}_{4}}Cl$

• question_answer48) Which of the following name formula combinations is not correct?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
 Formula ${{K}_{2}}[Pt{{\left( CN \right)}_{4}}]$ Potassium tetracyanoplatinate (II)

B)
 Formula ${{[Mn\left( CN \right)5]}^{2}}$ Pentacyanomagnate (II) ion

C)
 Formula $K[Cr{{(N{{H}_{3}})}_{2}}C{{l}_{4}}]$ Potassium diammine tetrachlorochromate (III)

D)
 Formula $[Co{{(N{{H}_{3}})}_{4}}({{H}_{2}}O)I]S{{O}_{4}}$ Magnetron value.

• question_answer49) Consider the coordination compound, $[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}.$In the formation of this complex, the species which acts as the Lewis acid is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

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

C)
$C{{o}^{3+}}$

D)
$N{{H}_{3}}$

• question_answer50) Which one of the following does not have a pyramidal shape?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
${{(C{{H}_{3}})}_{3}}N$

B)
${{(Si{{H}_{3}})}_{3}}N$

C)
$P{{(C{{H}_{3}})}_{3}}$

D)
$P{{(Si{{H}_{3}})}_{3}}$

• question_answer51) The following reaction  is known as:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Perkin reaction

B)
Gatterman-Koch Formylation

C)
Kolbe?s reaction

D)
Gattermann reaction

• question_answer52) The reagent needed for converting   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Cat. Hydrogenation

B)
${{H}_{2}}/$Lindlar Cat.

C)
$Li/N{{H}_{3}}$

D)
$LiAl{{H}_{4}}$

• question_answer53) Complete reduction of benzene-diazonium chloride with Zn/ HCl gives:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Aniline

B)
Phenylhydrazine

C)
Azobenzene

D)
Hydrazobenzene

• question_answer54) An organic compound $A,{{C}_{5}}{{H}_{8}}O;$reacts with ${{H}_{2}}O,N{{H}_{3}}$and $C{{H}_{3}}COOH$ as described below: A is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$C{{H}_{3}}CH=\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,-CHO$

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

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

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

• question_answer55) In allene $({{C}_{3}}{{H}_{4}}),$the type(s) of hybridization of the carbon atoms is (are) :   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
sp and $\text{s}{{\text{p}}^{\text{3}}}$

B)
$\text{s}{{\text{p}}^{2}}$and sp

C)
only

D)
and

• question_answer56) Chlorobenzne reacts with trichloro acetaldehyde in the presence of                                                                                                     The major product formed is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)

B)

C)

D)

• question_answer57) Tischenko reaction is a modification of:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Aldol condensation

B)
Claisen condensation

C)
Cannizzaro reaction

D)
Pinacol-pinacolon reaction

• question_answer58) Which one of the following is used as Antihistamine?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Omeprazole

B)
Chloranphenicol

C)
Diphenhydramine

D)
Norethindrone

• question_answer59) Which one of the following statements is not correct?   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Alcohols are weaker acids than water

B)
Acid strength of alcohols decreases in the following $RC{{H}_{2}}>{{R}_{2}}CHOH>{{R}_{3}}COH$

C)
Carbon-oxygen bond length in methanol, $C{{H}_{3}}OH$ is shorter than that of C - O bond length in phenol.

D)
The bond angle in methanol is $108.9{}^\circ$.

• question_answer60) The gas liberated by the electrolysis of Dipotassium succinate solution is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
Ethane

B)
Ethyne

C)
Ethene

D)
PropeneAT

• question_answer61) Let f be an odd function defined on the set of real numbers such that for $x\ge 0,$$f(x)=3sinx+4cosx.$ Then f(x) at $x=-\frac{11\pi }{6}$is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

B)
$-\frac{3}{2}+2\sqrt{3}$

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

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

• question_answer62) If ${{z}_{1}},{{z}_{2}}$and ${{z}_{3}},{{z}_{4}}$are 2 pairs of complex conjugate numbers, then $\arg \left( \frac{{{z}_{1}}}{{{z}_{4}}} \right)+\arg \left( \frac{{{z}_{2}}}{{{z}_{3}}} \right)$equals:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
0

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

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

D)
$\pi$

• question_answer63) If $\alpha$ and $\beta$ are roots of the equation, ${{x}^{2}}-4\sqrt{2}kx+2{{e}^{4\ln k}}-1=0$ for some k, and ${{\alpha }^{2}}+{{\beta }^{2}}=66,$then ${{\alpha }^{3}}+{{\beta }^{2}}$is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$248\sqrt{2}$

B)
$280\sqrt{2}$

C)
$-32\sqrt{2}$

D)
$-280\sqrt{2}$

• question_answer64) Let A be a $3\times 3$matrix such that$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{matrix} \right]$Then ${{A}^{-1}}$is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\left[ \begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \\ \end{matrix} \right]$

B)
$\left[ \begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \\ \end{matrix} \right]$

C)
$\left[ \begin{matrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 0 \\ \end{matrix} \right]$

D)
$\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \\ \end{matrix} \right]$

• question_answer65) Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in $x,p{{'}_{i}}(x)$and $p'{{'}_{i}}(x)$be the first and second order derivatives of ${{p}_{i}}(x)$ respectively. Let,$A(x)=\left[ \begin{matrix} {{p}_{1}}(x) & {{p}_{1}}'(x) & {{p}_{1}}''(x) \\ {{p}_{2}}(x) & {{p}_{2}}'(x) & {{p}_{2}}''(x) \\ {{p}_{3}}(x) & {{p}_{3}}'(x) & {{p}_{3}}''(x) \\ \end{matrix} \right]$and $B(x)={{[A(x)]}^{T}}A(x).$Then determinant of B(x):   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
is a polynomial of degree 6 in x.

B)
is a polynomial of degree 3 in x.

C)
is a polynomial of degree 2 in x.

D)
does not depend on x.

• question_answer66) An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
72 (7!)

B)
18 (7!)

C)
40 (7!)

D)
36 (7!)

• question_answer67) The coefficient of ${{x}^{50}}$in the binomial expansion of${{(1+x)}^{1000}}+x{{(1+x)}^{999}}+{{x}^{2}}$${{(1+x)}^{998}}+....+{{x}^{1000}}$ is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{\left( 1000 \right)!}{\left( 50 \right)!\left( 950 \right)!}$

B)
$\frac{\left( 1000 \right)!}{\left( 49 \right)!\left( 951 \right)!}$

C)
$\frac{\left( 1001 \right)!}{\left( 51 \right)!\left( 950 \right)!}$

D)
$\frac{\left( 1001 \right)!}{\left( 50 \right)!\left( 951 \right)!}$

• question_answer68) In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:

A)
7

B)
21

C)
28

D)
42

• question_answer69) The sum of the first 20 terms common between the series 3 + + 11 + 15 + ......... and 1 + 6 + 11 + 16 + ......, is   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
4000

B)
4020

C)
4200

D)
4220

• question_answer70) If$\underset{x\to 2}{\mathop{\lim }}\,\frac{\tan \left( x-2 \right)\left\{ {{x}^{2}}+\left( k-2 \right)x-2k \right\}}{{{x}^{2}}-4x+4}=5,$then k is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
0

B)
1

C)
2

D)
3

• question_answer71) Let f(x) = x|x|, g(x) = sin x and h(x) = (gof) (x). Then

A)
h(x) is not differentiable at x = 0.

B)
h(x) is differentiable at x = 0, but h¢(x) is not continuous at x = 0

C)
h?(x) is continuous at x = 0 but it is not differentiable at x = 0

D)
h?(x) is differentiable at x = 0

• question_answer72) For the curve $y=3\sin \theta \cos \theta ,x={{e}^{\theta }}\sin \theta ,$$0\le \theta \le \pi ,$the tangent is parallel to x-axis when $\theta$is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{3\pi }{4}$

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

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

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

• question_answer73) Two ships A and B are sailing straight away from a fixed point O along routes such that $\angle AOB$ is always $120{}^\circ$. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/ hr):   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{260}{\sqrt{37}}$

B)
$\frac{260}{37}$

C)
$\frac{80}{\sqrt{37}}$

D)
$\frac{80}{37}$

• question_answer74) The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius $=\sqrt{3}$ is:

A)
$\frac{4}{3}\sqrt{3}\pi$

B)
$\frac{8}{3}\sqrt{3}\pi$

C)
$4\pi$

D)
$2\pi$

• question_answer75) The integral$\int_{{}}^{{}}{x{{\cos }^{-1}}}\left( \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right)dx(x>0)$is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$-x+1(1+{{x}^{2}})ta{{n}^{-1}}x+c$

B)
$x-(1+{{x}^{2}})co{{t}^{-1}}x+c$

C)
$-x+(1+{{x}^{2}})co{{t}^{-1}}x+c$

D)
$x-(1+{{x}^{2}})ta{{n}^{-1}}x+c$

• question_answer76) If for $n\ge 1,{{P}_{n}}=\int\limits_{1}^{e}{{{\left( \log x \right)}^{n}}dx,}$then${{P}_{10}}-90{{P}_{8}}$ then is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
-9

B)
10e

C)
-9 e

D)
10

• question_answer77) If the general solution of the differential equation$y'=\frac{y}{x}+\Phi \left( \frac{x}{y} \right),$for some function $\Phi ,$ is given by $\ln |cx|=x,$where c is an arbitrary constant, then $\Phi (2)$is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
4

B)
$\frac{1}{4}$

C)
-4

D)
$-\frac{1}{4}$

• question_answer78) A stair-case of length l rests against a vertical wall and a floor of a room. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the stair-case begins to slide on the floor, then the locus of P is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
an ellipse of eccentricity$\frac{1}{2}$

B)
an ellipse of eccentricity$\frac{\sqrt{3}}{2}$

C)
a circle of radius$\frac{1}{2}$

D)
a circle of radius$\frac{\sqrt{3}}{2}l$

• question_answer79) The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{2\sqrt{3}}{15}$

B)
$\frac{4\sqrt{3}}{15}$

C)
$\frac{4\sqrt{3}}{5}$

D)
$\frac{2\sqrt{3}}{5}$

• question_answer80) The set of all real values of $\lambda$for which exactly two common tangents can be drawn to the circles ${{x}^{2}}+{{y}^{2}}4x4y+6=0$and ${{x}^{2}}+{{y}^{2}}10x10y+\lambda =0$is the interval:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
(12, 32)

B)
(18, 42)

C)
(12, 24)

D)
(18, 48)

• question_answer81) Let ${{L}_{1}}$be the length of the common chord of the curves ${{x}^{2}}+{{y}^{2}}=9$ and${{y}^{2}}=8x,$ and ${{L}_{2}}$ be the length of the latus rectum of ${{y}^{2}}=8x,$ then:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
${{L}_{1}}>{{L}_{2}}$

B)
${{L}_{1}}={{L}_{2}}$

C)
${{L}_{1}}<{{L}_{2}}$

D)
$\frac{{{L}_{1}}}{{{L}_{2}}}=\sqrt{2}$

• question_answer82) Let $P(3sec\theta ,2tan\theta )$and $Q(3sec\phi ,2tan\phi )$ where $\theta +\phi =\frac{\pi }{2},$be two distinct points on the hyperbola $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1.$Then the ordinate of the point of intersection of the normals at P and Q is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{11}{3}$

B)
$-\frac{11}{3}$

C)
$\frac{13}{2}$

D)
$-\frac{13}{2}$

• question_answer83) Let A (2, 3, 5), B (? 1, 3, 2) and $C(\lambda ,5,\mu )$be the vertices of a DABC. If the median through A is equally inclined to the coordinate axes, then:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$5\lambda -8\mu =0$

B)
$8\lambda -5\mu =0$

C)
$10\lambda -7\mu =0$

D)
$7\lambda -10\mu =0$

• question_answer84) The plane containing the line $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$and parallel to the line$\frac{x}{1}=\frac{y}{1}=\frac{z}{4}$passes through the point:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$(1, - 2, 5)$

B)
$(1, 0, 5)$

C)
$(0, 3, -5)$

D)
$(-1, -3, 0)$

• question_answer85) If $\overset{\to }{\mathop{{{\left| c \right|}^{2}}}}\,=60$and $\overset{\to }{\mathop{c}}\,\times \left( \hat{i}+2\hat{j}+5\hat{k} \right)=\overset{\to }{\mathop{0}}\,,$then a value of$\overset{\to }{\mathop{c}}\,.\left( -7\hat{i}+2\hat{j}+3\hat{k} \right)$is: [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$4\sqrt{2}$

B)
12

C)
24

D)
122

• question_answer86) A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that $x\in A$is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

B)
$\frac{64}{127}$

C)
$\frac{63}{128}$

D)
$\frac{31}{128}$

• question_answer87) If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P (X = 3), then E(X), the mean of variable X, is   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
2 ? p

B)
3 ? p

C)
$\frac{p}{2}$

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

• question_answer88) If $2\cos \theta +\sin \theta =1\left( \theta \ne \frac{\pi }{2} \right),$then $7\cos \theta +6\sin \theta$is equal to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

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

B)
2

C)
$\frac{11}{2}$

D)
$\frac{46}{5}$

• question_answer89) The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be $\alpha .$ After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to $\beta .$ Then the height (in metres) of the tower is:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
$\frac{2\sin \alpha \sin \beta }{\sin \left( \beta -\alpha \right)}$

B)
$\frac{\sin \alpha \sin \beta }{\cos \left( \beta -\alpha \right)}$

C)
$\frac{2\sin \left( \beta -\alpha \right)}{\sin \alpha \sin \beta }$

D)
$\frac{\cos \left( \beta -\alpha \right)}{\sin \alpha \sin \beta }$

• question_answer90) The proposition $\tilde{\ }\left( p\vee \tilde{\ }q \right)\vee \tilde{\ }\left( p\vee q \right)$is logically equivalent to:   [JEE Main Online Paper ( Held On 11 Apirl  2014 )

A)
p

B)
q

C)
$\tilde{\ }p$

D)
$\tilde{\ }q$