# Solved papers for JEE Main & Advanced JEE Main Paper (Held On 9 April 2016)

### done JEE Main Paper (Held On 9 April 2016) Total Questions - 90

• question_answer1) Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t = 0 one particle has displacement A while the other one has displacement $\frac{-A}{2}$and they are moving towards each other If they cross each at time t, then t is :   JEE Main Online Paper (Held On 09 April 2016)

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

B)
$\frac{5T}{6}$

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

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

• question_answer2) To find the focal length of a convex mirror, a student records the following data :  Object pin Convex Lens Convex Mirror Image Pin 22.2 cm 32.2 cm 45.8 cm 71.2 cm
The focal length of the convex lens is${{f}_{1}}$ and that of mirror is ${{f}_{2}}.$Then taking index correction to be negligibly small, ${{f}_{1}}$and ${{f}_{2}}.$ are close to :   JEE Main Online Paper (Held On 09 April 2016)

A)
${{f}_{1}}=15.6cm$                       ${{f}_{2}}=25.4cm$

B)
${{f}_{1}}=7.8cm$                         ${{f}_{2}}=12.7cm$

C)
${{f}_{1}}=7.8cm$                         ${{f}_{2}}=25.4cm$

D)
${{f}_{1}}=12.7cm$                       ${{f}_{2}}=7.8cm$

• question_answer3) Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is$\frac{1}{4}$the area of the ellipse . (See figure) With db as the semi major axis, and ca as the semi minor axis. If ${{t}_{1}}$is the time taken for planet to go over path abc and ${{t}_{2}}$for path taken over cda then :                   JEE Main Online Paper (Held On 09 April 2016)

A)
${{t}_{1}}=3{{t}_{2}}$

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

C)
${{t}_{1}}=2{{t}_{2}}$

D)
${{t}_{1}}=4{{t}_{2}}$

• question_answer4) A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T = 0°C. If the temperature of the wire is increased and the corresponding charge in its time period is plotted against its temperature, the resulting graph is a line of slop S. If the coefficient of linear expansion of metal is a then the value of S is :   JEE Main Online Paper (Held On 09 April 2016)

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

B)
$2\alpha$

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

D)
$\alpha$

• question_answer5) The ratio of work done by an ideal monatomic gas to the heat supplied to it in an isobaric process is :   JEE Main Online Paper (Held On 09 April 2016)

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

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

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

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

• question_answer6)                 An unknown transistor needs to be identified as npn or pnp type .A multi meter, with +ve and .ve terminals, is used to measure resistance between different terminals transistor. If terminal 2 is the base of the transistor then which of the following is correct for a pnp transistor?   JEE Main Online Paper (Held On 09 April 2016)

A)
+ve terminal 3, .ve terminal 2, resistance high

B)
+ve terminal 2, .ve terminal 3, resistance low

C)
+ve terminal 1, .ve terminal 2, resistance high

D)
+ve terminal 2, .ve terminal 1, resistance high

• question_answer7) A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, un extended length L. The radii, at the upper and lower ends of this conical wire , have values R and 3R, respectively, The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower and . The equilibrium extended length, of this wire, would equal   JEE Main Online Paper (Held On 09 April 2016)

A)
$L\left( 1+\frac{1}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

B)
$L\left( 1+\frac{2}{3}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

C)
$L\left( 1+\frac{1}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

D)
$L\left( 1+\frac{2}{9}\frac{Mg}{\pi Y{{R}^{2}}} \right)$

• question_answer8) A cubical block of side 30cm is moving with velocity $2m{{s}^{-1}}$on a smooth horizontal surface. The surface has a bump ata point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :   JEE Main Online Paper (Held On 09 April 2016)

A)
9.4

B)
6.7

C)
5.0

D)
13.3

• question_answer9) In Young's double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern . When the separation between the slits is varied, the interference pattern disappears for a particular distance ${{d}_{0}}$ between the slits. If the angular resolution of the eye is$\frac{{{1}^{o}}}{60}$the value of ${{d}_{0}}$ is close to   JEE Main Online Paper (Held On 09 April 2016)

A)
2 mm

B)
1 mm

C)
3 mm

D)
4 mm

• question_answer10) Which of the following option correctly describes the variation of the speed v and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force F = -kv, where 'k' is constant , on the body ? (Graphs are schematic and not drawn to scale)   JEE Main Online Paper (Held On 09 April 2016)

A)

B)

C)

D)

• question_answer11) A series LR circuit is connected to a voltage source with $V(t)={{V}_{0}}\sin \Omega t.$After very large time current I (t) behaves as $\left( {{t}_{0}}>>\frac{L}{r} \right):$   JEE Main Online Paper (Held On 09 April 2016)

A)
I (t)

B)
l (t)

C)
I (t)

D)
l (t)

• question_answer12) A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10m{{s}^{-1}},$the car needs power $\frac{P}{2}$If it needs power while moving downhill at speed v then value of v is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$5\,m{{s}^{-1}}$

B)
$20\,m{{s}^{-1}}$

C)
$10\,m{{s}^{-1}}$

D)
$15\,m{{s}^{-1}}$

• question_answer13) A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$. With the horizontal , a point object of mass m is kept. The minimum coefficient of friction ${{\mu }_{\min }}$ between the mass and the inclined surface such that he mass does not move is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$\tan \theta$

B)
$\tan 2\theta$

C)
$3\tan \theta$

D)
$2\tan \theta$

• question_answer14) Two engines pass each other moving in opposite directions with uniform speed of 30m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before pass each other. Speed sound is 330 m/sec.   JEE Main Online Paper (Held On 09 April 2016)

A)
540 Hz

B)
648 Hz

C)
270 Hz

D)
450 Hz

• question_answer15) The potential (in volts) of a charge distribution is given by $V(z)=30-5{{z}^{2}}$for$|z|\le 1m$ $V(z)=35-10|z|$for$|z|\ge 1m.$ V(z) does not depend on x and y . If this potential is generated by a constant charge per unit volume ${{\rho }_{0}},$(in units of ${{\varepsilon }_{0}}$) which is spread over certain region ,then choose the correct statement.   JEE Main Online Paper (Held On 09 April 2016)

A)
${{\rho }_{0}}=40{{\varepsilon }_{0}}$in the entire region

B)
${{\rho }_{0}}=20{{\varepsilon }_{0}}$ in the entire region

C)
${{\rho }_{0}}=20{{\varepsilon }_{0}}$ for $|z|$in$\le 1m$and ${{\rho }_{0}}=0$else where

D)
${{\rho }_{0}}=10{{\varepsilon }_{0}}$for $|z|$in $\le 1m$and${{\rho }_{0}}=0$ else where

• question_answer16) An audio signal consists of two distinct sound : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal band width required to send both the signals together to the AM signal band width required to send just the human speech is :     JEE Main Online Paper (Held On 09 April 2016)

A)
6

B)
5

C)
3

D)
2

• question_answer17) A convex lens, of focal length 30cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of : Focal length| |Focal length| = 30 cm =120 cm   JEE Main Online Paper (Held On 09 April 2016)

A)
70 cm from the concave lens

B)
60 cm from the convex lens

C)
60 cm from the concave lens

D)
70 cm from the convex lens

• question_answer18) Three capacitors each of $4\mu F$are to be connected in such a way that the effective capacitance is $6\mu F.$ This can be done by connecting them :   JEE Main Online Paper (Held On 09 April 2016)

A)
all in series

B)
two in parallel and one in series

C)
two in series and one in parallel

D)
all in parallel

• question_answer19) To know the resistance G of a galvanometer by half deflection method, a battery of emf ${{V}_{E}}$ and resistance R is used to deflect the galvanometer by angle$\theta .$If a shunt of resistance S is needed to gat half deflection then G, R and S are related by the equation :   JEE Main Online Paper (Held On 09 April 2016)

A)
2S = G

B)
2G = S

C)
S(R+G) = RG

D)
2S(R+G) = RG

• question_answer20) In the circuit shown, the resistance r is a variable resistance. If for r = fR, the heat generation in r is maximum then the value of f is :   JEE Main Online Paper (Held On 09 April 2016)

A)
1

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

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

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

• question_answer21) A hydrogen atom makes a transition from n = 2 to n=1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited stated of the ion for the process is :   JEE Main Online Paper (Held On 09 April 2016)

A)
4

B)
5

C)
2

D)
3

• question_answer22) 200 g water is heated from $40{}^\circ C$ to $60{}^\circ C$. Ignoring the slight expansion of water, the change in its internal energy is closed to (Given specific heat of water = 4184 J/kg/K) :   JEE Main Online Paper (Held On 09 April 2016)

A)
16.7 kJ

B)
167.4kJ

C)
4.2 kJ

D)
8.4 kJ

• question_answer23) An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of $R=100\Omega ,$and maximum power of dissipation rating of 1W. The minimum voltage range of the DC source in the circuit is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$0.12V$

B)
$0.5V$

C)
$0.24$

D)
$0 . 8V$

• question_answer24) Microwave oven acts on the principle of :   JEE Main Online Paper (Held On 09 April 2016)

A)
giving rotational energy to water molecules

B)
giving vibrational energy to water molecules

C)
giving translational energy to water molecules

D)
transferring electrons from lower to higher energy levels in water molecule

• question_answer25) A magnetic dipole is acted upon by two magnetic fields which are inclined to each other a tan angle of $75{}^\circ$. One of the fields has magnitude of 15mT. The dipole attains stable equilibrium at an angle $30{}^\circ$ with this field. The magnitude of the other field (in mT) is close to :   JEE Main Online Paper (Held On 09 April 2016)

A)
11

B)
1060

C)
36

D)
1

• question_answer26) $A50\Omega$resistance is connected to a battery of 5V. A galvanometer of resistance $100\Omega$is to be used as ammeter to measure current through the resistance, for this a resistance ${{r}_{s}}$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit ?   JEE Main Online Paper (Held On 09 April 2016)

A)
${{r}_{s}}=0.5\Omega n$parallel with the galvanometer

B)
${{r}_{s}}=0.5\Omega$in series with the galvanometer

C)
${{r}_{s}}=1\Omega$ in series with galvanometer

D)
${{r}_{s}}=1\Omega$ in parallel with galvanometer

• question_answer27) When photons of wavelength ${{\lambda }_{1}}$, are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength ${{\lambda }_{2}}$are used , the corresponding stopping potential was thrice that of the above value. If light of wavelength ${{\lambda }_{3}}.$is used then find the stopping potential for this case   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{3}{2{{\lambda }_{1}}} \right]$

B)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{{{\lambda }_{2}}}-\frac{3}{{{\lambda }_{1}}} \right]$

C)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}+\frac{1}{2{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]$

D)
$\frac{hc}{e}\left[ \frac{1}{{{\lambda }_{3}}}-\frac{1}{{{\lambda }_{2}}}-\frac{1}{{{\lambda }_{1}}} \right]$

• question_answer28) In the following 'I' refers to current and other symbols have their usual meaning choose the option that corresponds to the dimensions of electrical conductivity :   JEE Main Online Paper (Held On 09 April 2016)

A)
${{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{I}^{2}}$

B)
${{M}^{-1}}{{L}^{3}}{{T}^{3}}I$

C)
$M{{L}^{-3}}{{T}^{-3}}{{I}^{2}}$

D)
${{M}^{-1}}{{L}^{-3}}{{T}^{3}}I$

• question_answer29) Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r<<R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :                 JEE Main Online Paper (Held On 09 April 2016)

A)
$x=r{{\left( \frac{H}{H+h} \right)}^{2}}$

B)
$x=r\left( \frac{H}{H+h} \right)$

C)
$x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{4}}}$

D)
$x=r{{\left( \frac{H}{H+h} \right)}^{\frac{1}{2}}}$

• question_answer30) The truth table given in fig. represents :  A B Y 0 0 0 0 1 1 1 0 1 1 1 1
JEE Main Online Paper (Held On 09 April 2016)

A)
AND - Gate

B)
OR - Gate

C)
NOR - Gate

D)
NAND - Gate

• question_answer31) The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :   JEE Main Online Paper (Held On 09 April 2016)

A)
Saccharin

B)
Sucralose

C)
Alitame

D)
Aspartane

• question_answer32) The non-metal that does not exhibit positive oxidation state is :   JEE Main Online Paper (Held On 09 April 2016)

A)
Fluorine

B)
Oxygen

C)
Chlorine

D)
Iodine

• question_answer33) The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process show below:  ${{O}_{3}}(g)+C{{l}^{\bullet }}(g)\to {{O}_{2}}(g)+Cl{{O}^{\bullet }}(g)$……(i) ${{k}_{i}}=5.2\times {{10}^{9}}L\,mo{{l}^{-1}}{{s}^{-1}}$ $Cl{{O}^{\bullet }}(g)+{{O}^{\bullet }}(g)\to {{O}_{2}}(g)+C{{l}^{\bullet }}(g)$……(ii) ${{k}_{ii}}=2.6\times {{10}^{10}}L\,mo{{l}^{-1}}{{s}^{-1}}$
The closest rate constant for the overall reaction${{O}_{3}}(g)+{{O}^{\bullet }}(g)\to 2{{O}_{2}}(g)$ is:   JEE Main Online Paper (Held On 09 April 2016)

A)
$1.4\times {{10}^{20}}L\,mo{{l}^{-1}}\,{{s}^{-1}}$

B)
$5.2\times {{10}^{9}}L\,mo{{l}^{-1}}\,{{s}^{-1}}$

C)
$3.1\times {{10}^{10}}L\,mo{{l}^{-1}}\,{{s}^{-1}}$

D)
$2.6\times {{10}^{10}}L\,mo{{l}^{-1}}\,{{s}^{-1}}$

• question_answer34) 5L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is:   JEE Main Online Paper (Held On 09 April 2016)

A)
Butane

B)
Isobutane

C)
Ethane

D)
Propane

• question_answer35) Match the items in Column I with its main use listed in Column II:  Column I Column II (a) Silica gel (i) Transistor (b) Silicon (ii) Ion-exchanger (c) Silicone (iii) Drying agent (d) Silicate (iv) Sealant
JEE Main Online Paper (Held On 09 April 2016)

A)
(A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)

B)
(A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)

C)
(A)-(iv), (B)-(i), (C)-(ii), (D)-(iii)

D)
(A)-(ii), (B)-(iv), (C)-(i), (D)-(iii)

• question_answer36) The group of molecules having identical shape is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$PC{{l}_{5}},I{{F}_{5}},Xe{{O}_{2}}{{F}_{2}}$

B)
$B{{F}_{3}},PC{{l}_{3}},Xe{{O}_{3}}$

C)
$Cl{{F}_{3}},XeO{{F}_{2}},XeF_{3}^{+}$

D)
$S{{F}_{4}},Xe{{F}_{4}},CC{{l}_{4}}$

• question_answer37) Which one of the following species is stable in aqueous solution?   JEE Main Online Paper (Held On 09 April 2016)

A)
$MnO_{4}^{2-}$

B)
$MnO_{4}^{3-}$

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

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

• question_answer38) For the reaction, $A(g)+B(g)\to C(g)+D(g),\Delta {{H}^{0}}$and$\Delta {{S}^{0}}$  are, respectively,$-29.8kJ\,mo{{l}^{-1}}$and$-0.100kJ\,{{K}^{-1}}mo{{l}^{-1}}$at 298 K. The equilibrium constant for the reaction at 298 K is:   JEE Main Online Paper (Held On 09 April 2016)

A)
1

B)
10

C)
1.0 × 10.10

D)
1.0 × 1010

• question_answer39) Assertion : Rayon is a semisynthetic polymer whose properties are better than natural cotton. Reason : Mechanical and aesthetic properties of cellulose can be improved by acetylation.   JEE Main Online Paper (Held On 09 April 2016)

A)
Both assertion and reason are correct, and the reason is the correct explanation for the assertion.

B)
Both assertion and reason are incorrect.

C)
Assertion is incorrect statement, but the reason is correct.

D)
Both assertion and reason are correct, but the reason is not the correct explanation for the assertion.

• question_answer40) The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is :   JEE Main Online Paper (Held On 09 April 2016)

A)
4,4-dimethylpentene

B)
2,2-dimethyl-4-pentene

C)
Isopropyl-2-butene

D)
2,2-dimethyl-3-pentene

• question_answer41) The gas evolved on heating $C{{H}_{3}}MgBr$in methanol is:   JEE Main Online Paper (Held On 09 April 2016)

A)
Propane

B)
Ethane

C)
HBr

D)
Methane

• question_answer42) Identify the correct trend given below: (Atomic No.: Ti = 22, Cr = 24 and Mo = 42)   JEE Main Online Paper (Held On 09 April 2016)

A)
${{\Delta }_{o}}$of${{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}<{{[Mo{{({{H}_{2}}O)}_{6}}]}^{2+}}$and${{\Delta }_{o}}$of${{[Ti{{({{H}_{2}}O)}_{6}}]}^{3+}}>{{[Ti{{({{H}_{2}}O)}_{6}}]}^{2+}}$

B)
${{\Delta }_{o}}$of${{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}>{{[Mo{{({{H}_{2}}O)}_{6}}]}^{2+}}$and${{\Delta }_{o}}$of${{[Ti{{({{H}_{2}}O)}_{6}}]}^{3+}}<{{[Ti{{({{H}_{2}}O)}_{6}}]}^{2+}}$

C)
${{\Delta }_{o}}$of${{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}>{{[Mo{{({{H}_{2}}O)}_{6}}]}^{2+}}$and ${{\Delta }_{o}}$of${{[Ti{{({{H}_{2}}O)}_{6}}]}^{3+}}<{{[Ti{{({{H}_{2}}O)}_{6}}]}^{2+}}$

D)
${{\Delta }_{o}}$of${{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}<{{[Mo{{({{H}_{2}}O)}_{6}}]}^{2+}}$and ${{\Delta }_{o}}$of${{[Ti{{({{H}_{2}}O)}_{6}}]}^{3+}}>{{[Ti{{({{H}_{2}}O)}_{6}}]}^{2+}}$

• question_answer43) The most appropriate method of making egg-albumin sol is:   JEE Main Online Paper (Held On 09 April 2016)

A)
Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the yellow part of the content to 100 mL of 5% w/V saline solution and homogenize with a mechanical shaker.

B)
Break an egg carefully and transfer the transparent part of the content to 100 mL of 5% w/V saline solution and stir well.

C)
Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the white part of the content to 100 mL of 5% w/V saline solution and homogenize with a mechanical shaker.

D)
Break an egg carefully and transfer only the yellow part of the content to 100 mL of 5% w/V saline solution and stir well.

• question_answer44) Which one of the following complexes will consume more equivalents of aqueous solution of $Ag(N{{O}_{3}})$?   JEE Main Online Paper (Held On 09 April 2016)

A)
$N{{a}_{3}}[CrC{{l}_{6}}]$

B)
$[Cr{{({{H}_{2}}O)}_{5}}Cl]C{{l}_{2}}$

C)
$[Cr{{({{H}_{2}}O)}_{6}}]C{{l}_{3}}$

D)
$[N{{a}_{2}}(CrC{{l}_{5}})({{H}_{2}}O)]$

• question_answer45) At very high pressures, the compressibility factor of one mole of a gas is given by :   JEE Main Online Paper (Held On 09 April 2016)

A)
$1+\frac{pb}{RT}$

B)
$\frac{pb}{RT}$

C)
$1-\frac{b}{(VRT)}$

D)
$1-\frac{pb}{RT}$

• question_answer46) A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following:   JEE Main Online Paper (Held On 09 April 2016)

A)
Both$\Delta H$ and $\Delta S$ are positive.

B)
$\Delta H$is negative while $\Delta S$ is positive.

C)
$\Delta H$is positive while$\Delta S$is negative.

D)
Both $\Delta S$and $\Delta S$ are negative.

• question_answer47) Which intermolecular force is most responsible in allowing xenon gas to liquefy?   JEE Main Online Paper (Held On 09 April 2016)

A)
Instantaneous dipole-induced dipole

B)
Ionic

C)
Ion-dipole

D)
Dipole-dipole

• question_answer48) Identify the incorrect statement regarding heavy water:   JEE Main Online Paper (Held On 09 April 2016)

A)
It reacts with $Ca{{C}_{2}}$to produce ${{C}_{2}}{{D}_{2}}$ and $Ca{{(OD)}_{2}}.$

B)
It is used as a coolant in nuclear reactors.

C)
It reacts with $A{{l}_{4}}{{C}_{3}}$ to produce $C{{D}_{4}}$ and $Al{{(OD)}_{3}}.$

D)
It reacts with $S{{O}_{3}}$to form deuterated sulphuric acid $({{D}_{2}}S{{O}_{4}}).$

• question_answer49) A particular adsorption process has the following characteristics:  (i) It arises due to vander Waals forces and (ii) it is reversible. Identify the correct statement that describes the above adsorption process:
JEE Main Online Paper (Held On 09 April 2016)

A)
Enthalpy of adsorption is greater than $100 \text{kJ}\,\text{mo}{{\text{l}}^{\text{-1}}}.$

B)

C)
Adsorption increases with increase in temperature.

D)
Energy of activation is low.

• question_answer50) The plot shows the variation of .ln Kp versus temperature for the two reactions.  $M(s)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}MO(s)$and $C(s)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}CO(s)$
Identify the correct statement:   JEE Main Online Paper (Held On 09 April 2016)

A)
At T > 1200 K, carbon will reduce MO(s) to M(s).

B)
At T < 1200 K, oxidation of carbon is unfavourable.

C)
Oxidation of carbon is favourable at all temperatures.

D)
At $T<1200K,$ the reaction $MO(s)+C(s)\to M(s)+CO(g)$is spontaneous.

• question_answer51) BOD stands for:   JEE Main Online Paper (Held On 09 April 2016)

A)
Biochemical Oxygen Demand

B)
Biochemical Oxidation Demand

C)
Biological Oxygen Demand

D)
Bacterial Oxidation Demand

• question_answer52) What will occur if a block of copper metal is dropped into a beaker containing a solution of$1MZnS{{O}_{4}}?$   JEE Main Online Paper (Held On 09 April 2016)

A)
The copper metal will dissolve and zinc metal will be deposited.

B)
The copper metal will dissolve with evolution of oxygen gas.

C)
The copper metal will dissolve with evolution of hydrogen gas.

D)
No reaction will occur.

• question_answer53) The test to distinguish primary, secondary and tertiary amine is:   JEE Main Online Paper (Held On 09 April 2016)

A)
Mustard oil test

B)
${{C}_{6}}{{H}_{5}}S{{O}_{2}}Cl$

C)
Sandmeyer's reaction

D)
Carbylamine reaction

• question_answer54) The total number of orbitals associated with the principal quantum number 5 is:   JEE Main Online Paper (Held On 09 April 2016)

A)
5

B)
20

C)
25

D)
10

• question_answer55) The correct order of the solubility of alkaline-earth metal sulphates in water is:   JEE Main Online Paper (Held On 09 April 2016)

A)
Mg < Sr < Ca < Ba

B)
Mg > Ca> Sr > Ba

C)
Mg > Sr > Ca > Ba

D)
Mg < Ca < Sr < Ba

• question_answer56) An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% sulphur is: (atomic weight of S = 32 amu)   JEE Main Online Paper (Held On 09 April 2016)

A)
300 g $\text{mo}{{\text{l}}^{\text{-1}}}$

B)
400 g $\text{mo}{{\text{l}}^{\text{-1}}}$

C)
200 g $\text{mo}{{\text{l}}^{\text{-1}}}$

D)
600 g $\text{mo}{{\text{l}}^{\text{-1}}}$

• question_answer57) Bouveault-Blanc reduction reaction involves:   JEE Main Online Paper (Held On 09 April 2016)

A)
Reduction of an anhydride with $LiAl{{H}_{4}}.$

B)
Reduction of an ester with $Na/{{C}_{2}}{{H}_{5}}OH.$

C)
Reduction of a carbonyl compound with Na/Hg and HCl.

D)
Reduction of an acyl halide with H2/Pd.

• question_answer58) Consider the following sequence for aspartic acid: The pl (isoelectric point) of aspartic acid is:   JEE Main Online Paper (Held On 09 April 2016)

A)
5.74

B)
3.65

C)
2.77

D)
1.88

• question_answer59) The amount of arsenic pentasulphide that can be obtained when 35.5 g arsenic acid is treated with excess ${{H}_{2}}S$in the presence of conc. HCl (assuming 100% conversion)   JEE Main Online Paper (Held On 09 April 2016)

A)
0.25 mol

B)
0.125 mol

C)
0.333 mol

D)
0.50 mol

• question_answer60) The solubility of ${{N}_{2}}$in water at 300 K and 500 torr partial pressure is 0.01 g ${{\text{L}}^{\text{-1}}}$. The solubility (in g ${{\text{L}}^{\text{-1}}}$) at 750 torr partial pressure is :   JEE Main Online Paper (Held On 09 April 2016)

A)
0.02

B)
0.015

C)
0.0075

D)
0.005

• question_answer61) If A and B are any two events such that P(A) =2/5 and $P(A\cap B)=3/20,$then the conditional probability, $P(A/(A'\cap B')),$where A' denotes the complement of A, is equal to :

A)
$\frac{8}{17}$

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

C)
$\frac{5}{17}$

D)
$\frac{11}{20}$

• question_answer62) For $x\in R,x\ne 0,x\ne 1,$let${{f}_{0}}(x)=\frac{1}{1-x}$and${{f}_{n+1}}(x)={{f}_{0}}(f{{(}_{n}}(X)),$n = 0, 1, 2, ........ Then the value of ${{f}_{100}}(3)+{{f}_{1}}\left( \frac{2}{3} \right)+{{f}_{2}}\left( \frac{3}{2} \right)$is equal to:   JEE Main Online Paper (Held On 09 April 2016)

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

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

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

D)
$\frac{8}{3}$

• question_answer63) The distance of the point (1, .2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes $x-y+2z=3$ and $2x-2y+z+12=0$, is     JEE Main Online Paper (Held On 09 April 2016)

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

B)
2

C)
$\sqrt{2}$

D)
$2\sqrt{2}$

• question_answer64) If the equations ${{x}^{2}}+bx-1=0$and ${{x}^{2}}+x+b=0$have a common root different from . 1, then | b | is equal to   JEE Main Online Paper (Held On 09 April 2016)

A)
$\sqrt{2}$

B)
2

C)
$\sqrt{3}$

D)
3

• question_answer65) If $2\int\limits_{0}^{1}{{{\tan }^{-1}}xdx}=\int\limits_{0}^{1}{{{\cot }^{-1}}}(1-x+{{x}^{2}})dx$then$\int\limits_{0}^{1}{{{\tan }^{-1}}}(1-x+{{x}^{2}})dx$is equal to:   JEE Main Online Paper (Held On 09 April 2016)

A)
$\log 2$

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

C)
$\log 4$

D)
$\frac{\pi }{2}-\log 4$

• question_answer66) If $P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]$and$Q=PA{{P}^{T}},$then${{P}^{T}}{{Q}^{2015}}P$is     JEE Main Online Paper (Held On 09 April 2016)

A)
$\left[ \begin{matrix} 2015 & 1 \\ 0 & 2015 \\ \end{matrix} \right]$

B)
$\left[ \begin{matrix} 1 & 2015 \\ 0 & 1 \\ \end{matrix} \right]$

C)
$\left[ \begin{matrix} 0 & 2015 \\ 0 & 0 \\ \end{matrix} \right]$

D)
$\left[ \begin{matrix} 2015 & 0 \\ 1 & 2015 \\ \end{matrix} \right]$

• question_answer67) If$\int_{{}}^{{}}{\frac{dx}{{{\cos }^{3}}x\sqrt{2\sin 2x}}={{(\tan x)}^{A}}}+C{{(\tan x)}^{B}}+k,$ where k is a constant of integration, then A + B + C equals   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{16}{5}$

B)
$\frac{21}{5}$

C)
$\frac{7}{10}$

D)
$\frac{27}{10}$

• question_answer68) The point (2, 1) is translated parallel to the line $L:x-y=4$by $2\sqrt{3}$units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$2x+2y=1-\sqrt{6}$

B)
$x=y=3-3\sqrt{6}$

C)
$x+y=2-\sqrt{6}$

D)
$x+y=3-2\sqrt{6}$

• question_answer69) If the function $f(x)=\left\{ \begin{matrix} -x, & x<1 \\ a+{{\cos }^{-1}} & (x+b),1\le x\le 2 \\ \end{matrix} \right.$ is differentiable at x = 1, then$\frac{a}{b}$is equal to :

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

B)
$-1-{{\cos }^{-1}}(2)$

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

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

• question_answer70) The value of$\sum\limits_{r=1}^{15}{{{r}^{2}}}\left( \frac{^{15}{{C}_{r}}}{^{15}{{C}_{r-1}}} \right)$is equal to   JEE Main Online Paper (Held On 09 April 2016)

A)
1085

B)
560

C)
680

D)
1240

• question_answer71) In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively $3\hat{i}+\hat{j}-\hat{k},-\hat{i}+3\hat{j}+p\hat{k}$and$5\hat{i}+q\hat{j}-4\hat{k},$then the point (p, q) lies on a line   JEE Main Online Paper (Held On 09 April 2016)

A)
parallel to y-axis

B)
making an acute angle with the positive direction of x-axis

C)
parallel to x-axis

D)
making an obtuse angle with the position direction of x-axis.

• question_answer72) If$\underset{x\to \infty }{\mathop{Lim}}\,{{\left( 1+\frac{a}{x}-\frac{4}{{{x}^{2}}} \right)}^{2x}}={{e}^{3}},$then ?a? is equal to:   JEE Main Online Paper (Held On 09 April 2016)

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

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

C)
2

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

• question_answer73) The number of $x\in [0,2\pi ]$for which$\left| \sqrt{2{{\sin }^{4}}x+18{{\cos }^{2}}x}-\sqrt{2{{\cos }^{4}}x+18{{\sin }^{2}}x} \right|=1$   JEE Main Online Paper (Held On 09 April 2016)

A)
6

B)
4

C)
8

D)
2

• question_answer74) If m and M are the minimum and the maximum values of $4+\frac{1}{2}{{\sin }^{2}}2x-2{{\cos }^{4}}x,x\in R,$then M-m is equal to   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{7}{4}$

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

C)
$\frac{9}{4}$

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

• question_answer75) If a variable line drawn through the intersection of the lines$\frac{x}{3}+\frac{y}{4}=1$and$\frac{x}{4}+\frac{y}{3}=1,$ meets the coordinate axes at A and B, $(A\ne B),$ then the locus of the midpoint of AB is   JEE Main Online Paper (Held On 09 April 2016)

A)
$7xy=6(x+y)$

B)
$6xy=7(x+y)$

C)
$4{{(x+y)}^{2}}-28(x+y)+49=0$

D)
$14{{(x+y)}^{2}}-97(x+y)+168=0$

• question_answer76) If f(x) is a differentiable function in the interval $(0,\,\,\infty )$ such that f(1) = 1 and $\underset{t\to x}{\mathop{Lim}}\,\frac{{{t}^{2}}f(x)-{{x}^{2}}f(t)}{t-x}=1,$for each x > 0, then $f\left( \frac{3}{2} \right)$ is equal to :   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{13}{6}$

B)
$\frac{23}{18}$

C)
$\frac{25}{9}$

D)
$\frac{31}{18}$

• question_answer77) If the tangent at a point P, with parameter t, on the curve $x=4{{t}^{2}}+3,y=8{{t}^{3}}-1,t\in R,$meets the curve again at a point Q, then the coordinates of Q are :   JEE Main Online Paper (Held On 09 April 2016)

A)
$({{t}^{2}}+3,-{{t}^{3}}-1)$

B)
$({{t}^{2}}+3,{{t}^{3}}-1)$

C)
$(16{{t}^{2}}+3,-64{{t}^{3}}-1)$

D)
$(4{{t}^{2}}+3,-4{{t}^{3}}-1)$

• question_answer78) If the tangent at a point on the ellipse$\frac{{{x}^{2}}}{27}+\frac{{{y}^{2}}}{3}=1$meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :   JEE Main Online Paper (Held On 09 April 2016)

A)
9

B)
$\frac{9}{2}$

C)
$9\sqrt{3}$

D)
$3\sqrt{3}$

• question_answer79) The point represented by 2+i in the Arg and plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :   JEE Main Online Paper (Held On 09 April 2016)

A)
2 + 2i

B)
- 2 - 2i

C)
1 + i

D)
- 1 - i

• question_answer80) A circle passes through (-2, 4). Which one of the following equations can represent a diameter of this circle?   JEE Main Online Paper (Held On 09 April 2016)

A)
$4x+5y-6=0$

B)
$5x+2y+4=0$

C)
$2x-3y+10=0$

D)
$3x+4y-3=0$

• question_answer81) The number of distinct real roots of the equation,$\left| \begin{matrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \\ \end{matrix} \right|=0$in the interval $\left[ -\frac{\pi }{4},\frac{\pi }{4} \right]$is:   JEE Main Online Paper (Held On 09 April 2016)

A)
4

B)
1

C)
2

D)
3

• question_answer82) The shortest distance between the lines$\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$and$\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}$lies in the interval :   JEE Main Online Paper (Held On 09 April 2016)

A)
(2, 3]

B)
[0, 1)

C)
(3, 4]

D)
[1, 2)

• question_answer83) If the four letter words (need not be meaningful) are to be formed using the letters from the word MEDITERRANEAN. such that the first letter is R and the fourth letter is E, then the total number of all such words is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{11!}{{{(2!)}^{3}}}$

B)
59

C)
110

D)
56

• question_answer84) Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $\text{9e}{{\text{-}}^{\text{2}}}\text{-18e}+\text{5}=0.$ If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of hyperbola, then ${{a}^{2}}-{{b}^{2}}$is equal to   JEE Main Online Paper (Held On 09 April 2016)

A)
- 7

B)
- 5

C)
5

D)
7

• question_answer85) Consider the following two statements : P : If 7 is an odd number, then 7 is divisible by 2. Q : If 7 is a prime number, then 7 is an odd number. If ${{V}_{1}}$is the truth value of contrapositive of P and ${{V}_{2}}$ is the truth value of contrapositive of Q, then the ordered pair $({{V}_{1}},{{V}_{2}})$ equals :   JEE Main Online Paper (Held On 09 April 2016)

A)
(F, T)

B)
(T, F)

C)
(F, F)

D)
(T, T)

• question_answer86) The minimum distance of a point on the curve $y={{x}^{2}}-4$ from the origin is :   JEE Main Online Paper (Held On 09 April 2016)

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

B)
$\frac{\sqrt{19}}{2}$

C)
$\sqrt{\frac{15}{2}}$

D)
$\sqrt{\frac{19}{2}}$

• question_answer87) Let x, y, z be positive real numbers such that  $\text{x}+\text{y}+\text{z}=\text{12}$and ${{x}^{3}}{{y}^{4}}{{z}^{5}}=(0.1){{(600)}^{3}}.$Then ${{x}^{3}}+{{y}^{3}}+{{z}^{3}}$ is equal to   JEE Main Online Paper (Held On 09 April 2016)

A)
270

B)
258

C)
216

D)
342

• question_answer88) If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :   JEE Main Online Paper (Held On 09 April 2016)

A)
10

B)
20.2

C)
5.05

D)
10.1

• question_answer89) For$x\in R,x=-1,$if ${{(1+x)}^{2016}}+x{{(1+x)}^{2015}}+{{x}^{2}}$${{(1+x)}^{2014}}+...........+{{x}^{2016}}=$$\sum\limits_{i=0}^{2016}{{{a}_{i}}{{x}^{i}},}$then${{a}_{17}}$is equal to:   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{2016!}{16!}$

B)
$\frac{2017!}{2000!}$

C)
$\frac{2017!}{17!2000!}$

D)
$\frac{2016!}{17!1999!}$

• question_answer90) The area (in sq. units) of the region described by $A=\{(x,y)|y\ge {{x}^{2}}-5x+4,x+y\ge 1,y\le 0\}$is :   JEE Main Online Paper (Held On 09 April 2016)

A)
$\frac{7}{2}$

B)
$\frac{13}{6}$

C)
$\frac{17}{6}$

D)
$\frac{19}{6}$