Solved papers for JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

JEE Main Paper (Held On 19 May 2012) Total Questions - 90

1) A uniform tube of length 60.5 cm is held vertically with its lower end dipped in water. A sound source of frequency 500 Hz sends sound waves into the tube. When the length of tube above water is 16 cm and again when it is 50 cm, the tube resonates with the source of sound. Two lowest frequencies (in Hz), to which tube will resonate when it is taken out of water, are (approximately). JEE Main Online Paper (Held On 19 May 2012)

A)

281,562

B)

                       281,843

C)

                       276,552

D)

                       272,544

View Answer
2) Sand is being dropped on a conveyer belt at the rate of 2 kg per second. The force necessary to keep the belt moving with a constant speed of 3 \[\text{m}{{\text{s}}^{\text{-1}}}\]will be JEE Main Online Paper (Held On 19 May 2012)

A)

12N

B)

6N

C)

zero

D)

18N

View Answer
3) A block of weight crests on a horizontal floor with coefficient of static friction \[\mu .\]It is desired to make the block move by applying minimum amount of force. The angle \[\theta \] from the horizontal at which the force should be applied and magnitude of the force F are respectively. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\theta ={{\tan }^{-1}}\left( \mu \right),F=\frac{\mu W}{\sqrt{1+{{\mu }^{2}}}}\]

B)

                       \[\theta ={{\tan }^{-1}}\left( \frac{1}{\mu } \right),F=\frac{\mu W}{\sqrt{1+{{\mu }^{2}}}}\]

C)

                       \[\theta =0,F=\mu W\]

D)

                       \[\theta ={{\tan }^{-1}}\left( \frac{\mu }{1+\mu } \right),F=\frac{\mu W}{1+\mu }\]

View Answer
4) A coil of self inductance L is connected at one end of two rails as shown in figure. A connector of length l, mass m can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction B going into the page. At an instant t = 0 an initial velocity Vg is imparted to it and as a result of that it starts moving along x-axis. The displacement of the connector is represented by the figure. JEE Main Online Paper (Held On 19 May 2012)

A)



B)

C)



D)



View Answer
5) A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An Engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is (T = surface tension, \[\rho \] = density) JEE Main Online Paper (Held On 19 May 2012)

A)

\[{{\left[ \frac{T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

B)

                       \[{{\left[ \frac{6T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

C)

                       \[{{\left[ \frac{3T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

D)

                       \[{{\left[ \frac{2T}{\rho }\left( \frac{1}{r}-\frac{1}{R} \right) \right]}^{1/2}}\]

View Answer
6) The amount of heat produced in an electric circuit depends upon the current (t), resistance (R) and time (I). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be JEE Main Online Paper (Held On 19 May 2012)

A)

1%

B)

                       2%

C)

                       6%

D)

                       3%

View Answer
7) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: An inventor claims to have constructed an engine that has an efficiency of 30% when operated between the boiling and freezing points of water. This is not possible. Statement 2: The efficiency of a real engine is always less than the efficiency of a Carnot engine operating between the same two temperatures. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

B)

                       Statement 1 is true. Statement 2 is false.

C)

                       Statement 1 is false, Statement 2 is true.

D)

                       Statement 1 is true. Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

View Answer
8) The displacement \[y(t)=A\sin (\omega t+\phi )\]of a pendulum for \[\phi =\frac{2\pi }{3}\] is correctly represented by JEE Main Online Paper (Held On 19 May 2012)

A)



B)



C)



D)



View Answer
9) A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length \[\left( \frac{L}{2} \right)\]each. The rods are completely In sulated from the surroundings. If the free end If copper rod is maintained at \[100{}^\circ C\] and that of steel at \[0{}^\circ C\] then the temperature of junction is Thermal conductivity of copper is 9 times that if steel) JEE Main Online Paper (Held On 19 May 2012)

A)

\[90{}^\circ C\]

B)

\[50{}^\circ C\]

C)

\[10{}^\circ C\]

D)

\[67{}^\circ C\]

View Answer
10) Two point masses of mass \[{{m}_{1}}=fM\]and \[{{m}_{2}}=(1-f)M(f<1)\]are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities \[{{\omega }_{1}}\]) for\[{{m}_{1}}\]and \[{{\omega }_{2}}\]for\[{{m}_{2}}\]. In that case JEE Main Online Paper (Held On 19 May 2012)

A)

\[(1-f){{\omega }_{1}}=f\omega \]

B)

                       \[{{\omega }_{1}}={{\omega }_{2}}\]and independent of f

C)

                       \[f{{\omega }_{1}}=(1-f){{\omega }_{2}}\]

D)

                       \[{{\omega }_{1}}={{\omega }_{2}}\] and depend on f

View Answer
11) Which one of the following is the Boolean expression for NOR gate? JEE Main Online Paper (Held On 19 May 2012)

A)

\[Y=\overline{A+B}\]

B)

                       \[Y=\overline{A.B}\]

C)

                       \[Y=A.B\]

D)

                       \[Y=\overline{A}\]

View Answer
12) Two coherent plane light waves of equal amplitude makes a small angle a (« 1) with each other. They fall almost normally on a screen. If \[\lambda \] the wavelength of light waves, the fringe width \[\Delta x\]of interference patterns of the two sets of waves on the screen is JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{2\lambda }{\alpha }\]

B)

                       \[\frac{\lambda }{\alpha }\]

C)

                       \[\frac{\lambda }{\left( 2\alpha \right)}\]

D)

                       \[\frac{\lambda }{\sqrt{\alpha }}\]

View Answer
13) lonisation energy of Li (Lithium) atom in ground state is 5.4 eV. Binding energy of an electron in \[L{{i}^{+}}\]ion in ground state is 75.6 eV. Energy required to remove all three electrons of Lithium (Li) atom is     JEE Main Online Paper (Held On 19 May 2012)

A)

                      81.0 eV

B)

                       135.4eV

C)

                       203.4eV

D)

                       156.6eV

View Answer
14)                 This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Self inductance of a long solenoid of length L, total number of turns N and radius r is less than \[\frac{\pi {{\mu }_{0}}{{N}^{2}}{{r}^{2}}}{L}.\] Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current I is \[\frac{{{\mu }_{0}}NI}{L}\]in the middle of the solenoid but becomes less as we move towards its ends. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true. Statement 2 is false.

B)

                       Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

C)

                       Statement 1 is false. Statement 2 is true.

D)

                       Statement 1 is true. Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

View Answer
15) A charge of total amount Q is distributed over two concentric hollow spheres of radii r and R (R > r) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]

B)

                       \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{2\left( {{R}^{2}}+{{r}^{2}} \right)}\]

C)

                       \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]

D)

                       \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}\]

View Answer
16) N divisions on the main scale of a vernier caliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is 'a' units then the least count of the instrument is JEE Main Online Paper (Held On 19 May 2012)

A)

a

B)

                       \[\frac{a}{N}\]

C)

                       \[\frac{N}{N+1}\times a\]

D)

                       \[\frac{a}{N+1}\]

View Answer
17) The decay constants of a radioactive substance for \[\alpha \] and \[\beta \] emission are \[{{\lambda }_{\alpha }}\]and \[{{\lambda }_{\beta }}\] respectively. If the substance emits \[\alpha \] and \[\beta \] simultaneously, then the average half life of the material will be JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{2{{T}_{\alpha }}{{T}_{\beta }}}{{{T}_{\alpha }}+{{T}_{\beta }}}\]

B)

                       \[{{T}_{\alpha }}+{{T}_{\beta }}\]

C)

                       \[\frac{{{T}_{\alpha }}{{T}_{\beta }}}{{{T}_{\alpha }}+{{T}_{\beta }}}\]

D)

                       \[\frac{1}{2}\left( {{T}_{\alpha }}+{{T}_{\beta }} \right)\]

View Answer
18) A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to JEE Main Online Paper (Held On 19 May 2012)

A)

33%

B)

                       67%

C)

                       90%

D)

                       (d) 10%

View Answer
19) This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A metallic surface is irradiated by a monochromatic light of frequency \[\upsilon >{{\upsilon }_{0}}\] (the threshold frequency). If the incident frequency is now doubled, the photocurrent and the maximum kinetic energy are also doubled. Statement 2: The maximum kinetic energy of photoelectrons emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends only on the intensity of the incident light. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B)

                       Statement 1 is false. Statement 2 is true.

C)

                       Statement 1 is true, Statement 2 is false.

D)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

View Answer
20) A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be JEE Main Online Paper (Held On 19 May 2012)

A)

\[\sqrt{2}R\]

B)

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

C)

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

D)

                       R

View Answer
21) A glass prism of refractive index 1.5 is immersed in water (refractive index \[\frac{4}{3}\]) as shown in figure. A light beam incident normally on the face AB is totally reflected to reach the face BC, if JEE Main Online Paper (Held On 19 May 2012)

A)

\[\sin \theta >\frac{5}{9}\]

B)

                       \[\sin \theta >\frac{2}{3}\]

C)

                       \[\sin \theta >\frac{8}{9}\]

D)

                       \[\sin \theta >\frac{1}{3}\]

View Answer
22) An electromagnetic wave with frequency co and wavelength \[\lambda \]travels in the + y direction. Its magnetic field is along + x-axis. The vector equation for the associated electric field (of amplitude \[{{E}_{0}}\]) is JEE Main Online Paper (Held On 19 May 2012)

A)

\[\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{x}\]

B)

                       \[\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{x}\]

C)

                       \[\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{z}\]

D)

                       \[\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{z}\]

View Answer
23) A 6.0 volt battery is connected to two light bulbs as shown in figure. Light bulb 1 has resistance 3 ohm while light bulb 2 has resistance 6 ohm. Battery has negligible internal resistance. Which bulb will glow brighter? JEE Main Online Paper (Held On 19 May 2012)

A)

Bulb 1 will glow more first and then its brightness will become less than bulb 2

B)

                       Bulbl

C)

                       Bulb2

D)

                       Both glow equally

View Answer
24) A generator has armature resistance of \[0.1\Omega \]and develops an induced emf of 120 F when driven at its rated speed. Its terminal voltage when a current of 50 A is being drawn is JEE Main Online Paper (Held On 19 May 2012)

A)

120 V

B)

                       5V

C)

                       115 V

D)

                       70 V

View Answer
25) A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{u+v}{2}\]

B)

                       \[\frac{1}{2}\sqrt{{{u}^{2}}+{{v}^{2}}}\]

C)

                       \[\sqrt{uv}\]

D)

                       \[\sqrt{\left( \frac{{{u}^{2}}+{{v}^{2}}}{2} \right)}\]

View Answer
26) A ring is suspended from a point S on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take \[g={{\pi }^{2}}\]) JEE Main Online Paper (Held On 19 May 2012)

A)

0.15m

B)

                       1.5m

C)

                       1.0m

D)

                       0.5m

View Answer
27) The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric field E is applied at an angle\[\frac{\pi }{4}\]with the vertical direction. The electric flux through the curved surface of the hemisphere is JEE Main Online Paper (Held On 19 May 2012)

A)

\[\pi {{a}^{2}}E\]

B)

                       \[\frac{\pi {{a}^{2}}E}{\sqrt{2}}\]

C)

                       \[\frac{\pi {{a}^{2}}E}{2\sqrt{2}}\]

D)

                       \[\frac{\left( \pi +2 \right)\pi {{a}^{2}}E}{{{\left( 2\sqrt{2} \right)}^{2}}}\]

View Answer
28) A steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of JEE Main Online Paper (Held On 19 May 2012)

A)

50kg

B)

                       400kg

C)

                       100kg

D)

                       200kg

View Answer
29) Given the electric field of a complete amplitude modulated wave as\[\overset{_{\to }}{\mathop{E}}\,=\hat{i}{{E}_{C}}\left( 1+\frac{{{E}_{m}}}{{{E}_{C}}}\cos {{\omega }_{m}}t \right)\cos {{\omega }_{C}}t.\] Where the subscript c stands for the carrier wave and m for the modulating signal. The frequencies present in the modulated wave are JEE Main Online Paper (Held On 19 May 2012)

A)

\[{{\omega }_{C}}\]and\[\sqrt{\omega _{c}^{2}+\omega _{m}^{2}}\]

B)

                       \[{{\omega }_{c}},{{\omega }_{c}}+{{\omega }_{m}}\] and\[{{\omega }_{c}}-{{\omega }_{m}}\]

C)

                       \[{{\omega }_{c}}\]and\[{{\omega }_{m}}\]

D)

                       \[{{\omega }_{c}}\]and\[\sqrt{{{\omega }_{c}}{{\omega }_{m}}}\]

View Answer
30) The pressure of an ideal gas varies with volume as \[P=\alpha V,\] where a is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes 'm times its initial volume. The work done by the gas in the process is JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{\alpha V}{2}\left( {{m}^{2}}-1 \right)\]

B)

                       \[\frac{{{\alpha }^{2}}{{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]

C)

                       \[\frac{\alpha }{2}\left( {{m}^{2}}-1 \right)\]

D)

                       \[\frac{\alpha {{V}^{2}}}{2}\left( {{m}^{2}}-1 \right)\]

View Answer
31) Among the following, the molecule with the lowest dipole moment is JEE Main Online Paper (Held On 19 May 2012)

A)

\[CHC{{l}_{3}}\]

B)

                       \[C{{H}_{3}}Cl\]

C)

                       \[C{{H}_{2}}C{{l}_{2}}\]

D)

                       \[CC{{l}_{4}}\]

View Answer
32) If\[{{K}_{sp}}\]of\[Ca{{F}_{2}}\]at \[={{25}^{o}}C\]is\[1.7\times {{10}^{-10}},\]the combination amongst the following which gives a precipitate of \[Ca{{F}_{2}}\] is JEE Main Online Paper (Held On 19 May 2012)

A)

\[1\times {{10}^{-2}}M\,C{{a}^{2+}}\]and\[1\times {{10}^{-3}}M\,{{F}^{-}}\]

B)

\[1\times {{10}^{-4}}M\,C{{a}^{2+}}\]and\[1\times {{10}^{-4}}M\,{{F}^{-}}\]

C)

\[1\times {{10}^{-2}}M\,C{{a}^{2+}}\]and\[1\times {{10}^{-5}}M\,{{F}^{-}}\]

D)

\[1\times {{10}^{-3}}M\,C{{a}^{2+}}\]and\[1\times {{10}^{-5}}M\,{{F}^{-}}\]

View Answer
33) The correct order of ligands in the spectro chemical series is JEE Main Online Paper (Held On 19 May 2012)

A)

\[C{{l}^{-}}>en>C{{N}^{-}}>NC{{S}^{-}}\]

B)

                       \[C{{l}^{-}}>en>NC{{S}^{-}}>C{{l}^{-}}\]

C)

                       \[NC{{S}^{-}}>C{{N}^{-}}>C{{l}^{-}}>en\]

D)

                       \[en>C{{N}^{-}}>C{{l}^{-}}>NC{{S}^{-}}\]

View Answer
34) The value of\[{{K}_{p}}\]for the equilibrium reaction\[{{N}_{2}}{{O}_{4}}(g)2N{{O}_{2}}(g)\]is 2. The percentage dissociation of \[{{N}_{2}}{{O}_{4}}(g)\]at a pressure of 0.5 atm is JEE Main Online Paper (Held On 19 May 2012)

A)

25

B)

                       88

C)

                       50

D)

                       71

View Answer
35) The order of basicity of the compounds is JEE Main Online Paper (Held On 19 May 2012)

A)

\[IV>I>III>II\]

B)

                       \[I>III>II>IV\]

C)

                       \[III>I>IV>II\]

D)

                       \[II>I>III>IV\]

View Answer
36) Ammonium chloride crystallizes in a body centred cubic lattice with edge length of unit cell of 390 pm. If the size of chloride ion is 180 pm, the size of ammonium ion would be JEE Main Online Paper (Held On 19 May 2012)

A)

174pm

B)

                       158pm

C)

                       142pm

D)

                       126pm

View Answer
37) Which pair of elements with the given atomic numbers is expected to have similar properties? JEE Main Online Paper (Held On 19 May 2012)

A)

40,72

B)

                       20,36

C)

                       10,28

D)

                       11,12

View Answer
38) Extraction of zinc from zinc blende is achieved By JEE Main Online Paper (Held On 19 May 2012)

A)

roasting followed by self-reduction

B)

                       electrolytic reduction

C)

                       roasting followed by reduction with carbon

D)

                       roasting followed by reduction with another metal

View Answer
39) Liquids A and B form an ideal solution. At \[30{}^\circ C\], the total vapour pressure of a Solution containing 1 mol of A and 2 mol of B is 250 mm Hg. The total vapour pressure becomes 300 mm Hg when 1 more mol of A is added to the first solution. The vapour pressures of pure A and B at the same temperature are JEE Main Online Paper (Held On 19 May 2012)

A)

150,450 mm Hg

B)

125,150 mm Hg

C)

450,150 mm Hg

D)

250,300 mm Hg

View Answer
40) The IUPAC name of the following compound is JEE Main Online Paper (Held On 19 May 2012)

A)

(E)-2-hepten-4-yne

B)

                       Z)-5-hepten-3-yne

C)

                       (E)-5-hepten-3-yne

D)

                       (Z)-2-hepten-4-yne

View Answer
41) Which of the following paramagnetic ions would exhibit a magnetic moment (spin only) of the order of 5 BM? (At. Nos. \[Mn=25,Cr=24,V=23,Ti=22\]) JEE Main Online Paper (Held On 19 May 2012)

A)

\[M{{n}^{2+}}\]

B)

                       \[T{{i}^{2+}}\]

C)

                       \[{{V}^{2+}}\]

D)

                       \[C{{r}^{2+}}\]

View Answer
42) Which one of the following will react most vigorously with water? JEE Main Online Paper (Held On 19 May 2012)

A)

Li

B)

                       K

C)

                       Rb

D)

                       Na

View Answer
43) Which of the following has the square planar structure? JEE Main Online Paper (Held On 19 May 2012)

A)

\[Xe{{F}_{4}}\]

B)

                       \[NH_{4}^{+}\]

C)

                       \[BF_{4}^{-}\]

D)

                       \[CC{{l}_{4}}\]

View Answer
44) The major product obtained in the photobromination of 2-methyl butane is JEE Main Online Paper (Held On 19 May 2012)

A)

2-bromo-2-methylbutane

B)

                       1-bromo-2-methylbutane

C)

                       1-bromo-3-methylbutane

D)

                       2-bromo-3-methylbutane

View Answer
45) If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated with it would become JEE Main Online Paper (Held On 19 May 2012)

A)

one fourth

B)

                       half

C)

                       four times

D)

                       two times

View Answer
46) When \[C{{O}_{2(g)}}\]is passed over red hot coke it partially gets reduced to \[CO(g).\]Upon passing L of \[C{{O}_{2}}(g)\] over red hot coke, the total volume of the gases increased to 700 mL. The composition of the gaseous mixture at STP is JEE Main Online Paper (Held On 19 May 2012)

A)

\[C{{O}_{2}}=300mL;CO=400mL\]

B)

                       \[C{{O}_{2}}=0.0mL;CO=700mL\]

C)

                       \[C{{O}_{2}}=200mL;CO=500mL\]

D)

                       \[C{{O}_{2}}=350mL;CO=350mL\]

View Answer
47) For a reaction \[A\to \]Products, a plot of \[\log {{t}_{1/2}}\] versus \[\log {{a}_{0}}\]is shown in the figure. If the initial concentration of A is represented by \[{{a}_{0}}\] the order of the reaction is JEE Main Online Paper (Held On 19 May 2012)

A)

one

B)

                       zero

C)

                       two

D)

                       three

View Answer
48) An open vessel at 300 K is heated till 2/5th of the air in it is expelled. Assuming that the volume of the vessel remains constant, the temperature to which the vessel is heated, is JEE Main Online Paper (Held On 19 May 2012)

A)

1500 K

B)

                       400 K

C)

                       500 K

D)

                       750 K

View Answer
49) Which of the following is a polyamide? JEE Main Online Paper (Held On 19 May 2012)

A)

Teflon

B)

                       Orion

C)

                       Nylon

D)

                       Terylene

View Answer
50) The compound of xenon with zero dipole moment is JEE Main Online Paper (Held On 19 May 2012)

A)

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

B)

                       \[Xe{{F}_{4}}\]

C)

                       \[XeO{{F}_{4}}\]

D)

                       \[Xe{{O}_{2}}\]

View Answer
51) The standard potentials of\[A{{g}^{+}}/Ag,H{{g}_{2}}^{2+}/2Hg,\]\[C{{u}^{2+}}/Cu\] and \[M{{g}^{2+}}/Mg\] electrodes are 0.80,0.79, 0.34 and -2.37 V, respectively. An aqueous solution which contains one mole per litre of the salts of each of the four metals is electrolyzed. With increasing voltage, the correct sequence of deposition of the metals at the cathode is JEE Main Online Paper (Held On 19 May 2012)

A)

\[Ag,Hg,Cu,Mg\]

B)

                       \[Cu,Hg,Ag\]only

C)

                       \[Ag,Hg,Cu\]only

D)

                       \[Mg,Cu,Hg,Ag\]

View Answer
52) The product of the reaction between ethyl benzene and N-bromosuccinamide is JEE Main Online Paper (Held On 19 May 2012)

A)



B)



C)



D)



View Answer
53) On addition of 1 mL of 10% NaCl solution to 10 mL gold sol in the presence of 0.025 g of starch, the coagulation is just prevented. Starch has gold number JEE Main Online Paper (Held On 19 May 2012)

A)

2.5

B)

                       25

C)

                       0.25

D)

                       0.025

View Answer
54) Which of the following is a non-reducing sugar? JEE Main Online Paper (Held On 19 May 2012)

A)

Lactose

B)

Fructose

C)

Sucrose

D)

Maltose

View Answer
55) Fog is a colloidal solution of     JEE Main Online Paper (Held On 19 May 2012)

A)

solid particles dispersed in gas

B)

                       solid particles dispersed in a liquid

C)

                       liquid particles dispersed in gas

D)

                       gaseous particles dispersed in a liquid

View Answer
56) The enthalpy of neutralisation of \[N{{H}_{4}}OH\]with HCl is -51.46 kJ \[\text{mo}{{\text{l}}^{-1}}\] and the enthalpy of neutralisation of NaOH with HCl is -55.90 kJ \[\text{mo}{{\text{l}}^{-1}}\]. The enthalpy of ionisation of\[N{{H}_{4}}OH\] His               JEE Main Online Paper (Held On 19 May 2012)

A)

                \[\text{-107}\text{.36}\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]

B)

                \[\text{-4}\text{.44}\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]

C)

                \[\text{+107}\text{.36}\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]

D)

                \[\text{+4}\text{.44}\,\text{kJ}\,\text{mo}{{\text{l}}^{-1}}\]

View Answer
57) Aspirin can be prepared by the reaction of JEE Main Online Paper (Held On 19 May 2012)

A)

Salicyldehyde with acetic anhydride in presence of\[{{H}_{2}}S{{O}_{4}}\]

B)

                       Salicylic acid with metnanol in presence of\[{{H}_{2}}S{{O}_{4}}\]

C)

                       Salicylic acid with acetic anhydride in presence of \[{{H}_{2}}S{{O}_{4}}\]

D)

                       Cinnamic acid with acetic anhydride in presence of\[{{H}_{2}}S{{O}_{4}}\]

View Answer
58) Beilstein test is used for the estimation of which one of the following elements? JEE Main Online Paper (Held On 19 May 2012)

A)

S

B)

                       Cl

C)

                       C and H

D)

                       N

View Answer
59) Square-planar geometry is shown by JEE Main Online Paper (Held On 19 May 2012)

A)

\[[PtC{{l}_{2}}{{(N{{H}_{3}})}_{2}}]\]

B)

                       \[{{[NiC{{l}_{4}}]}^{2-}}\]

C)

                       \[MnO_{4}^{-}\]

D)

                       \[CrO_{4}^{2-}\]

View Answer
60) Reagent used to convert allyl alcohol to acrole in is JEE Main Online Paper (Held On 19 May 2012)

A)

\[Mn{{O}_{2}}\]

B)

                       \[{{H}_{2}}{{O}_{2}}\]

C)

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

D)

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

View Answer
61) The equation of the normal to the parabola, \[{{x}^{2}}=8y\]at \[x=4\]is JEE Main Online Paper (Held On 19 May 2012)

A)

\[x+2y=0\]

B)

                       \[x+y=2\]

C)

                       \[x-2y=0\]

D)

                       \[x+y=6\]

View Answer
62) The value of the integral\[\int\limits_{0}^{0.9}{\left[ x-2\left[ x \right] \right]dx,}\]where [.] denotes the greatest integer function is JEE Main Online Paper (Held On 19 May 2012)

A)

0.9

B)

                       1.8

C)

                       -0.9

D)

                       0

View Answer
63) If a, b, c, are non zero complex numbers satisfying \[{{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+{{\text{c}}^{\text{2}}}=0\]and\[\left| \begin{matrix}    {{b}^{2}}+{{c}^{2}} & ab & ac \\    ab & {{c}^{2}}+{{a}^{2}} & bc \\    ac & bc & {{a}^{2}}+{{b}^{2}} \\ \end{matrix} \right|=k{{a}^{2}}{{b}^{2}}{{c}^{2}},\]is equal to JEE Main Online Paper (Held On 19 May 2012)

A)

1

B)

                       3

C)

                       4

D)

                       2

View Answer
64) If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{8}{15}\]

B)

\[\frac{4}{15}\]

C)

\[\frac{2}{15}\]

D)

\[\frac{1}{15}\]

View Answer
65) The sum of the series \[1+\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]upto n terms is. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\frac{7}{6}n+\frac{1}{6}-\frac{2}{{{3.2}^{n-1}}}\]

B)

                       \[\frac{5}{3}n-\frac{7}{6}+\frac{2}{{{2.3}^{n-1}}}\]

C)

                       \[n+\frac{1}{2}-\frac{1}{{{2.3}^{n}}}\]

D)

                       \[n-\frac{1}{3}-\frac{1}{{{3.2}^{n-1}}}\]

View Answer
66) If\[a+b+c=0,\left| \overset{\to }{\mathop{a}}\, \right|=3,\left| \overset{\to }{\mathop{b}}\, \right|=5\]and\[\left| \overset{\to }{\mathop{c}}\, \right|=7,\]then the angle between \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\]is then f(1) equals. JEE Main Online Paper (Held On 19 May 2012)

A)

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

B)

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

C)

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

D)

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

View Answer
67) If\[f\left( x \right)=\int_{{}}^{{}}{\left( \frac{{{x}^{2}}+{{\sin }^{2}}x}{1+{{x}^{2}}} \right)}\sec x\,dx\]and\[f(0)=0,\]then f(1) equals. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\tan 1-\frac{\pi }{4}\]

B)

                       \[\tan 1+1\]

C)

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

D)

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

View Answer
68) Let\[p,q,r\in R\]and \[r>p>0.\]If the quadratic equation\[p{{x}^{2}}+qx+r=0\] has two complex roots \[\alpha \]and \[\beta ,\]then\[|\alpha |+|\beta |\]is. JEE Main Online Paper (Held On 19 May 2012)

A)

equal to 1

B)

                       less than 2 but not equal to 1

C)

                       greater than 2

D)

                       equal to 2

View Answer
69) If three distinct points A, B, C are given in the 2- dimensional coordinate plane such that the ratio of the distance of each one of them from the point (1, 0) to the distance from (- 1,0) is equal to \[\frac{1}{2},\]then the circum centre of the triangle ABC is at, the point. JEE Main Online Paper (Held On 19 May 2012)

A)

\[\left( \frac{5}{3},0 \right)\]

B)

                       (0,0)

C)

                       \[\left( \frac{1}{3},0 \right)\]

D)

                       (3,0)

View Answer
70) If the line \[y=mx+1\] meets the circle \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}+\text{3x}=0\]in two points equidistant from and on opposite sides of x-axis, then. JEE Main Online Paper (Held On 19 May 2012)

A)

3m+2=0

B)

                       3m-2=0

C)

                       2m+3=0

D)

                       2m-3=0

View Answer
71) Let f: [1, 3]\[\to \] R be a function satisfying \[\frac{x}{[x]}\le f\left( x \right)\le \sqrt{6-x},\]for all \[x\ne 2\]and f(2) = 1, where R is the set of all real numbers and [x] denotes the largest integer less than or equal to x. Statement 1: \[\underset{x\to {{2}^{-}}}{\mathop{\lim }}\,f\left( x \right)\] exists. Statement 2: f is continuous at x = 2. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

B)

Statement 1 is false. Statement 2 is true.

C)

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

D)

Statement 1 is true, Statement 2 is false.

View Answer
72) The general solution of the differential equation \[\frac{dy}{dx}+\frac{2}{x}y={{x}^{2}}\]is JEE Main Online Paper (Held On 19 May 2012)

A)

\[y=c{{x}^{-3}}-\frac{{{x}^{2}}}{4}\]

B)

                       \[y=c{{x}^{3}}-\frac{{{x}^{2}}}{4}\]

C)

                       \[y=c{{x}^{2}}+\frac{{{x}^{3}}}{5}\]

D)

                       \[y=c{{x}^{-2}}+\frac{{{x}^{3}}}{5}\]

View Answer
73) A value of \[{{\tan }^{-1}}\left( \sin \left( {{\cos }^{-1}}\left( \sqrt{\frac{2}{3}} \right) \right) \right)\]is JEE Main Online Paper (Held On 19 May 2012)

A)

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

B)

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

C)

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

D)

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

View Answer
74) Let p and q be two Statements. Amongst the following, the Statement that is equivalent to \[p\to q\] is JEE Main Online Paper (Held On 19 May 2012)

A)

\[p\wedge \tilde{\ }q\]

B)

                       \[\tilde{\ }p\vee q\]

C)

                       \[\tilde{\ }p\wedge q\]

D)

                       \[p\vee \tilde{\ }q\]

View Answer
75) If the three planes \[x=5,2x-5a+3z-2=0\]and \[3bx+y-3z=0\] contain a common line, then (a, b) is equal to JEE Main Online Paper (Held On 19 May 2012)

A)

\[\left( \frac{8}{15},-\frac{1}{5} \right)\]

B)

                       \[\left( \frac{1}{5},-\frac{8}{15} \right)\]

C)

                       \[\left( -\frac{8}{15},\frac{1}{5} \right)\]

D)

                       \[\left( -\frac{1}{5},\frac{8}{15} \right)\]

View Answer
76) If\[f(x)=3{{x}^{10}}-7{{x}^{8}}+5{{x}^{6}}-21{{x}^{3}}+3{{x}^{2}}-7,\]then \[\underset{\alpha \to 0}{\mathop{\lim }}\,\frac{f\left( 1-\alpha \right)-f\left( 1 \right)}{{{\alpha }^{3}}+3\alpha }\]is JEE Main Online Paper (Held On 19 May 2012)

A)

\[-\frac{53}{3}\]

B)

                       \[\frac{53}{3}\]

C)

                       \[-\frac{55}{3}\]

D)

                       \[\frac{55}{3}\]

View Answer
77) Let Z and? F be complex numbers such that \[|Z|=|W|,\] and arg Z denotes the principal argument of Z. Statement 1. If arg Z+ arg \[W=\pi ,\]then \[Z=-\overline{W}.\] Statement1: \[|Z|=|W|,\]implies arg Z- arg \[\overline{W}=\pi .\] JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,

B)

                       Statement 2 is a correct explanation for Statement 1.

C)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

D)

                       Statement 1 is false, Statement 2 is true.

View Answer
78) Consider a quadratic equation \[\text{a}{{\text{x}}^{\text{2}}}+\text{bx}+\text{c}=0,\]where \[\text{2a}+\text{3b}+\text{6c}=0\] and let\[g\left( x \right)=a\frac{{{x}^{3}}}{3}+b\frac{{{x}^{2}}}{2}+cx.\] Statement 1: The quadratic equation has at least one root in the interval (0, 1). Statement 2: The Rolle's theorem is applicable to function g(x) on the interval [0, 1]. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is false, Statement 2 is true.

B)

Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,

C)

Statement 2 is not a correct explanation for Statement 1.

D)

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

View Answer
79) Suppose \[\theta \] and \[\phi (\ne 0)\] are such that \[(\theta +\phi ),\sec \theta \]and \[\sec (\theta -\phi )\] are in A.P. If \[\cos \theta =k\cos \left( \frac{\phi }{2} \right)\] for some k, then A; is equal to JEE Main Online Paper (Held On 19 May 2012)

A)

\[\pm \sqrt{2}\]

B)

                       \[\pm 1\]

C)

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

D)

                       \[\pm 2\]

View Answer
80) Statement!: The shortest distance between the is lines \[\frac{x}{2}=\frac{y}{-1}=\frac{z}{2}\]and\[\frac{x-1}{4}=\frac{y-1}{-2}=\frac{z-1}{4}\]is\[\sqrt{2}.\] Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true, Statement 2 is false.

B)

                       Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1;

C)

                       Statement 1 is false, Statement 2 is true.

D)

                       Statement 1 is true. Statement 2 is true, , Statement 2 is not a correct explanation for Statement 1.

View Answer
81) If \[n{{=}^{m}}{{C}_{2}},\]then the value of \[^{n}{{C}_{2}}\] is given by JEE Main Online Paper (Held On 19 May 2012)

A)

\[3{{(}^{m+1}}{{C}_{4}})\]

B)

                       \[^{m-1}{{C}_{4}}\]

C)

                       \[^{m+1}{{C}_{4}}\]

D)

                       \[2{{(}^{m+2}}{{C}_{4}})\]

View Answer
82) If P(5) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set 5'= {1,2,3} to the set P(5) is JEE Main Online Paper (Held On 19 May 2012)

A)

24

B)

                       8

C)

                       336

D)

                       320

View Answer
83) The number of arrangements that can be formed from the letters a, b, c, d, e, /taken 3 at a time without repetition and each arrangement containing at least one vowel, is JEE Main Online Paper (Held On 19 May 2012)

A)

96

B)

                       128

C)

                       24

D)

                       72

View Answer
84) The weight W of a certain stock of fish is given by W=nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as \[n=2{{t}^{2}}+3\]and \[w={{t}^{2}}-t+2,\]then the rate of change of W with respect to t at t = 1 is JEE Main Online Paper (Held On 19 May 2012)

A)

1

B)

                       8

C)

                       13

D)

                       5

View Answer
85) The area of the region bounded by the curve \[y={{x}^{3}},\] and the lines, y= 8, and x = 0, is JEE Main Online Paper (Held On 19 May 2012)

A)

8

B)

                       12

C)

                       10

D)

                       16

View Answer
86) If \[\overset{\to }{\mathop{a}}\,=\hat{i}-2\hat{j}+3\hat{k},\overset{\to }{\mathop{b}}\,=2\hat{i}+3\hat{j}-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=r\hat{i}+\hat{j}+\left( 2r-1 \right)\hat{k}\]are three vectors such that \[\overset{\to }{\mathop{c}}\,\] is parallel to the plane of \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,,\] then r is equal to JEE Main Online Paper (Held On 19 May 2012)

A)

1

B)

                       -1

C)

                       0

D)

                       2

View Answer
87) Let L be the liney = 2x, in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point \[\left( \frac{4}{5},\frac{3}{5} \right).\] Statement 2: The points (0,1) and\[\left( \frac{4}{5},\frac{3}{5} \right)\] lie on opposite sides of the line L and are at equal distance from it. JEE Main Online Paper (Held On 19 May 2012)

A)

Statement 1 is true. Statement 2 is false.

B)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

C)

                       Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

D)

                       Statement 1 is false. Statement 2 is true.

View Answer
88) The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is JEE Main Online Paper (Held On 19 May 2012)

A)

10

B)

                       20

C)

                       15

D)

                       12

View Answer
89) If the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]coincide with the foci of the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25},\]then \[{{b}^{2}}\] is equal to JEE Main Online Paper (Held On 19 May 2012)

A)

8

B)

                       10

C)

                       7

D)

                       9

View Answer
90) If \[{{A}^{T}}\]denotes the transpose of the matrix\[A=\left[ \begin{matrix}    0 & 0 & a \\    0 & b & c \\    d & e & f \\ \end{matrix} \right],\]where a, b, c, d, e and f are integers such that \[abd\ne 0,\] then the number of such matrices for which \[{{A}^{-1}}={{A}^{T}}\]is JEE Main Online Paper (Held On 19 May 2012)

A)

2(3!)

B)

                       3(2!)

C)

                       23

D)

                       32

View Answer