# Solved papers for JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

### done JEE Main Paper (Held on 7 May 2012) Total Questions - 90

• question_answer1) Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $={{R}_{E}}$)? JEE Main Online Paper (Held On 07 May 2012)

A)

B)

C)

D)

• question_answer2) A car of mass 1000 kg is moving at a speed of 30m/s. Brakes are applied to bring the car to rest. If the net retarding force is 5000 N, the car comes to stop after travelling dm in t s. Then JEE Main Online Paper (Held On 07 May 2012)

A)
$d=150,t=5$

B)
$d=120,t=8$

C)
$d=180,t=6$

D)
$d=90,t=6$

• question_answer3) A perfect gas at $27{}^\circ C$ is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to   JEE Main Online Paper (Held On 07 May 2012)

A)
$327{}^\circ C$

B)
$200{}^\circ C$

C)
$54{}^\circ C$

D)
$300{}^\circ C$

• question_answer4) A square hole of side length i is made at a depth of h and a circular hole of radius r is made at adepth of 4h from the surface of water in a water tank kept on a horizontal surface. If $\ell <<h, r<<h$and the rate of water flow from the holes is the same, then r is equal to   JEE Main Online Paper (Held On 07 May 2012)

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

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

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

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

• question_answer5) A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is$2\times {{10}^{11}}N{{m}^{-2}}.$The percentage strain is about   JEE Main Online Paper (Held On 07 May 2012)

A)
0.16%

B)
0.32%

C)
0.08%

D)
0.24%

• question_answer6) The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is $(\sigma =5.7\times {{10}^{-8}}W\,{{m}^{-2}}{{K}^{-4}})$   JEE Main Online Paper (Held On 07 May 2012)

A)
$1.7\times {{10}^{10}}J$

B)
$1.1\times {{10}^{12}}J$

C)
$2.8\times {{10}^{8}}J$

D)
$4.6\times {{10}^{6}}J$

• question_answer7) Broadcasting antennas are generally JEE Main Online Paper (Held On 07 May 2012)

A)
vertical type

B)
both vertical and horizontal type

C)
omni directional type

D)
horizontal type

• question_answer8) The velocity of certain ions that pass undeflected through crossed electric field E = 7.7 k V/m and magnetic field B = 0.14T is   JEE Main Online Paper (Held On 07 May 2012)

A)
18km/s

B)
77km/s

C)
55km/s.

D)
1078 km/s

• question_answer9) Following are expressions for four plane simple harmonic waves (i)${{y}_{1}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{1}}} \right)$ (ii${{y}_{2}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{1}}}+\pi \right)$ (iii)${{y}_{3}}=A\cos 2\pi \left( {{n}_{1}}t+\frac{x}{{{\lambda }_{2}}} \right)$ (iv)${{y}_{4}}=A\cos 2\pi \left( {{n}_{2}}t-\frac{x}{{{\lambda }_{2}}} \right)$ The pairs of waves which will produce destructive interference and stationary waves respectively in a medium, are   JEE Main Online Paper (Held On 07 May 2012)

A)
(iii, iv), (i, ii)

B)
(i, iii), (ii, iv)

C)
(i,iv),(ii,iii)

D)
(i, ii), (iii, iv)

• question_answer10) An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

A)
$m{{v}^{3}}$

B)
$m{{v}^{2}}$

C)
$\frac{1}{2}m{{v}^{2}}$

D)
$\frac{1}{2}m{{v}^{3}}$

• question_answer11) The electron of a hydrogen atom makes a transition from the ${{(n+1)}^{th}}$orbit to the ${{n}^{th}}$ orbit. For large n the wavelength of the emitted radiation is proportional to   JEE Main Online Paper (Held On 07 May 2012)

A)
n

B)
${{n}^{3}}$

C)
${{n}^{4}}$

D)
${{n}^{2}}$

• question_answer12) The graph of an object's motion (along the x-axis) is shown in the figure. The instantaneous velocity of the object at points A and B are ${{v}_{A}}$and ${{v}_{B}}$ respectively. Then   JEE Main Online Paper (Held On 07 May 2012)

A)
${{v}_{A}}={{v}_{B}}=0.5m/s$

B)
${{v}_{A}}=0.5m/s<{{v}_{B}}$

C)
${{v}_{A}}=0.5m/s>{{v}_{B}}$

D)
${{v}_{A}}={{v}_{B}}=2m/s$

• question_answer13) A circular hole of diameter R is cut from a disc of mass M and radius R, -the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is   JEE Main Online Paper (Held On 07 May 2012)

A)
$\left( \frac{15}{32} \right)M{{R}^{2}}$

B)
$\left( \frac{1}{8} \right)M{{R}^{2}}$

C)
$\left( \frac{3}{8} \right)M{{R}^{2}}$

D)
$\left( \frac{13}{32} \right)M{{R}^{2}}$

• question_answer14) In a Young's double slit experiment with light of wavelength$\lambda ,$ fringe pattern on the screen has fringe width $\beta .$ When two thin transparent glass(refractive index $\mu$)plates of thickness ${{t}_{1}}$ and ${{t}_{2}}$$({{t}_{1}}>{{t}_{2}})$are placed in the path of the two beams respectively, the fringe pattern will shift by a distance   JEE Main Online Paper (Held On 07 May 2012)

A)
$\frac{\beta (\mu -1)}{\lambda }\left( \frac{{{t}_{1}}}{{{t}_{2}}} \right)$

B)
$\frac{\mu \beta }{\lambda }\frac{{{t}_{1}}}{{{t}_{2}}}$

C)
$\frac{\beta \left( \mu -1 \right)}{\lambda }\left( {{t}_{1}}-{{t}_{2}} \right)$

D)
$\left( \mu -1 \right)\frac{\lambda }{\beta }\left( {{t}_{1}}+{{t}_{2}} \right)$

• question_answer15) 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: In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process.   JEE Main Online Paper (Held On 07 May 2012)

A)
Statement 1 is true. Statement 2 is true, Statement 2 is a 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 false. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

• question_answer16) 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: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.   JEE Main Online Paper (Held On 07 May 2012)

A)
Statement 1 is true. Statement 2 is false

B)
Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

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

• question_answer17) Given that K= energy, V= velocity, T= time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?   JEE Main Online Paper (Held On 07 May 2012)

A)
$[K{{V}^{-2}}{{T}^{-2}}]$

B)
$[{{K}^{2}}{{V}^{2}}{{T}^{-2}}]$

C)
$[{{K}^{2}}{{V}^{-2}}{{T}^{-2}}]$

D)
$[K{{V}^{2}}{{T}^{2}}]$

• question_answer18) A particle gets displaced by$\Delta \over line{r}=\left( 2\hat{i}+3\hat{j}+4\hat{k} \right)m$under the action of a force$\vec{F}=\left( 7\hat{i}+4\hat{j}+3\hat{k} \right).$The change in its kinetic energy is     JEE Main Online Paper (Held On 07 May 2012)

A)
38 J

B)
70J

C)
52.5 J

D)
126 J

• question_answer19) Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches   JEE Main Online Paper (Held On 07 May 2012)

A)
No charge flows in (a) but charge flows from R to L in (b)

B)
Charges flow from L to R in both (a) and (b)

C)
Charges flow from R to L in (a) and from L to R in(b)

D)
No charge flows in (a) but charge flows from L to R in (b)

• question_answer20) In an LCR circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220Vand 100 Hz is connected to it as shown?   JEE Main Online Paper (Held On 07 May 2012)

A)
800V,8A

B)
110V.1.1A

C)
300V, 3 A

D)
220V, 2.2 A

• question_answer21) This question has Statement land Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again. Statement 2: On filling the arms, the frequency of a tuning fork increases.   JEE Main Online Paper (Held On 07 May 2012)

A)
Statement 1 is true. Statement 2 is true, Statement 2 is a 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 not a correct explanation of Statement 1.

• question_answer22) A bar magnet of length 6 cm has a magnetic moment of $4J\,{{T}^{-1}}.$Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line.   JEE Main Online Paper (Held On 07 May 2012)

A)
$4\times {{10}^{-8}}\text{tesla}$

B)
$3.5\times {{10}^{-8}}\text{tesla}$

C)
$5\times {{10}^{-8}}\text{tesla}$

D)
$3\times {{10}^{-8}}\text{tesla}$

• question_answer23) The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line   JEE Main Online Paper (Held On 07 May 2012)

A)
OA

B)
OC

C)
OD

D)
OB

• question_answer24) In the Rutherford experiment, a-particles are scattered from a nucleus as shown. Out of the four paths, which path is not possible?   JEE Main Online Paper (Held On 07 May 2012)

A)
D

B)
B

C)
C

D)
A

• question_answer25) The electric potential V(x) in a region around the origin is given by $V(x)=4{{x}^{2}}$volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb).   JEE Main Online Paper (Held On 07 May 2012)

A)
$8{{\varepsilon }_{0}}$

B)
$-4{{\varepsilon }_{0}}$

C)
0

D)
(d)$-8{{\varepsilon }_{0}}$

• question_answer26) Two polaroids have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either Polaroid must be turned if the intensity is to drop by one-half is   JEE Main Online Paper (Held On 07 May 2012)

A)
$135{}^\circ$

B)
$90{}^\circ$

C)
$120{}^\circ$

D)
$180{}^\circ$

• question_answer27) Which of the following processes play a part in the formation of a rainbow? (i)   Refraction                        (ii) Total internal reflection (iii) Dispersion (iv) Interference   JEE Main Online Paper (Held On 07 May 2012)

A)
(i),(ii)and(iii)

B)
(i)and(ii)

C)
(i), (ii) and (iv)

D)
(iii) and (iv)

• question_answer28) A sample originally contained 1020 radioactive atoms, which emit a-particles. The ratio of $\text{ }\!\!\alpha\!\!\text{ -}$particles emitted in the third year to that emitted during the second year is 0.3. How many $\text{ }\!\!\alpha\!\!\text{ -}$particles were emitted in the first year?   JEE Main Online Paper (Held On 07 May 2012)

A)
$3\times {{10}^{18}}$

B)
$3\times {{10}^{19}}$

C)
$5\times {{10}^{18}}$

D)
$7\times {{10}^{19}}$

• question_answer29) A solid sphere having mass m and radius r rolls down an inclined plane. Then its kinetic energy is   JEE Main Online Paper (Held On 07 May 2012)

A)
$\frac{5}{7}$rotational and $\frac{2}{7}$translational

B)
$\frac{2}{7}$rotational and $\frac{5}{7}$translational

C)
$\frac{2}{5}$rotational and $\frac{3}{5}$translational

D)
$\frac{1}{2}$rotational and $\frac{1}{2}$translational

• question_answer30) Which logic gate with inputs A and B performs the same operation as that performed by the following circuit?     JEE Main Online Paper (Held On 07 May 2012)

A)
NAND gate

B)
OR gate

C)
NOR gate

D)
AND gate

• question_answer31) Which one of the following compounds is an anti-fertility drug?   JEE Main Online Paper (Held On 07 May 2012)

A)
Aspirin

B)
Chloro my cetin

C)
Saheli

D)
Penicillin

• question_answer32) The most basic compound among the following is   JEE Main Online Paper (Held On 07 May 2012)

A)
Acetanilide

B)
Benzyl amine

C)
p-Nitro aniline

D)
Aniline

• question_answer33) A battery is constructed of Cr and $N{{a}_{2}}C{{r}_{2}}{{O}_{7}}.$The unbalanced chemical equation when such a battery discharges is following: $N{{a}_{2}}C{{r}_{2}}{{O}_{7}}+Cr+{{H}^{+}}\to C{{r}^{3+}}+{{H}_{2}}O+N{{a}^{+}}$ If one Faraday of electricity is passed through the battery during the charging, the number of moles of $C{{r}^{3+}}$ removed from the solution is   JEE Main Online Paper (Held On 07 May 2012)

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

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

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

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

• question_answer34) The limiting line in Balmer series will have a frequency of (Rydberg constant, ${{R}_{\infty }}=3.29\times {{10}^{15}}$cycles/s)   JEE Main Online Paper (Held On 07 May 2012)

A)
$8.22\times {{10}^{14}}{{s}^{-1}}$

B)
$3.29\times {{10}^{15}}{{s}^{-1}}$

C)
$3.65\times {{10}^{14}}{{s}^{-1}}$

D)
$5.26\times {{10}^{13}}{{s}^{-1}}$

• question_answer35) Which of the following cannot be represented by resonance structures?   JEE Main Online Paper (Held On 07 May 2012)

A)
Dimethyl ether

B)
Nitrate anion

C)
Carboxylate anion

D)
Toluene

• question_answer36) Which of the oxide groups among the following cannot be reduced by carbon?

A)
$C{{u}_{2}}O,Sn{{O}_{2}}$

B)
$CaO,{{K}_{2}}O$

C)
$PbO,F{{e}_{2}}{{O}_{4}}$

D)
$F{{e}_{2}}{{O}_{3}},ZnO$

• question_answer37) Among the following, the species having the smallest bond is   JEE Main Online Paper (Held On 07 May 2012)

A)
$N{{O}^{-}}$

B)
$N{{O}^{+}}$

C)
${{O}_{2}}$

D)
NO

• question_answer38) Based on lattice energy and other considerations, which one of the following alkali metal chloride is expected to have the highest melting point?     JEE Main Online Paper (Held On 07 May 2012)

A)
NaCI

B)
KCl

C)
LiCI

D)
RbCl

• question_answer39) The entropy of a sample of a certain substance increases by $0.836\,J\,{{K}^{-1}}$ on adding reversibly0.3344 J of heat at constant temperature. The temperature of the sample is:   JEE Main Online Paper (Held On 07 May 2012)

A)
2.5K

B)
0.3K

C)
0.016K

D)
0.4K

• question_answer40) The electron affinity of chlorine is 3.7 eV. 1 gram of chlorine is completely converted to $C{{l}^{-1}}$ ion in a gaseous state. (1 eV = 23.06 kcal $mo{{l}^{-1}}$).Energy released in the process is   JEE Main Online Paper (Held On 07 May 2012)

A)
4.8kcal

B)
7.2kcal

C)
8.2 kcal

D)
2.4 kcal

• question_answer41) Copper wire test for halogens is known as   JEE Main Online Paper (Held On 07 May 2012)

A)
Duma's Test

B)
Beilstein' s Test

C)
Liebig'sTest

D)
Lassigne's Test

• question_answer42) For 1 mol of an ideal gas at a constant temperature T, the plot of (log P) against (log V) is a(P: Pressure, V\ Volume)   JEE Main Online Paper (Held On 07 May 2012)

A)
Straight line parallel to x-axis.

B)
Straight line with a negative slope.

C)
Curve starting at origin.

D)
Straight line passing through origin.

• question_answer43) Which one of the following is a chain growth polymerisation?   JEE Main Online Paper (Held On 07 May 2012)

A)
Nucleic acid

B)
Polystyrene

C)
Protein

D)
Starch

• question_answer44) The d-electron configurations of $C{{r}^{2+}},M{{n}^{2+}},F{{e}^{2+}}$and $C{{o}^{2+}}$are ${{d}^{4}},{{d}^{5}},{{d}^{6}}$and ${{d}^{7}}$ respectively. Which one of the following will exhibit the lowest paramagnetic behaviour? (Atomic no. Cr =24, Mn = 25, Fe = 26, Co = 27).     JEE Main Online Paper (Held On 07 May 2012)

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

B)
${{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}$

C)
${{[Mn{{({{H}_{2}}O)}_{6}}]}^{2+}}$

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

• question_answer45) If x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p, Freundlic had sorption isotherm gives a straight line on plotting   JEE Main Online Paper (Held On 07 May 2012)

A)
$x/m\,vs\,p$

B)
$x/m\,vs1/\,p$

C)
$\log x/m\,vs\,\log \,p$

D)
$\log x/m\,\,vs\,p$

• question_answer46) The solubility (in mol${{L}^{-1}}$) of AgCl$({{K}_{sp}}=1.0\times {{10}^{-10}})$ in a 0.1 M KC1 solution will be   JEE Main Online Paper (Held On 07 May 2012)

A)
$1.0\times {{10}^{-9}}$

B)
$1.0\times {{10}^{-10}}$

C)
$1.0\times {{10}^{-5}}$

D)
$1.0\times {{10}^{-11}}$

• question_answer47) Among the following which is the best description of water in the solid phase?   JEE Main Online Paper (Held On 07 May 2012)

A)
Covalent solid

B)
Molecular solid

C)
Ionic solid

D)
Network solid

• question_answer48) All of the following statements apply to proteins except   JEE Main Online Paper (Held On 07 May 2012)

A)
Proteins generally have no definite melting point

B)
Proteins contain the grouping 'CONH'

C)
Proteins have high molecular weight

D)
Proteins can only contain the elements C, H, O and N.

• question_answer49) ${{K}_{1}},{{K}_{2}}$and${{K}_{3}}$ are the equilibrium constants of the following reactions (I), (II) and (III)respectively: (i)${{N}_{2}}+2{{O}_{2}}2N{{O}_{2}}$(ii)$2N{{O}_{2}}{{N}_{2}}+2{{O}_{2}}$                 (iii)$N{{O}_{2}}\frac{1}{2}{{N}_{2}}+{{O}_{2}}$ The correct relation from the following is   JEE Main Online Paper (Held On 07 May 2012)

A)
${{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{K}_{3}}}$

B)
${{K}_{1}}=\frac{1}{{{K}_{2}}}=\frac{1}{{{({{K}_{3}})}^{2}}}$

C)
${{K}_{1}}=\sqrt{{{K}_{2}}}={{K}_{3}}$

D)
${{K}_{1}}=\frac{1}{{{K}_{2}}}={{K}_{3}}$

• question_answer50) The concentrated sulphuric acid that is peddled commercial is $95%{{H}_{2}}S{{O}_{4}}$ by weight. If the density of this commercial acid is 1.834 g$c{{m}^{-3}},$ the molarity of this solution is   JEE Main Online Paper (Held On 07 May 2012)

A)
17.8 M

B)
12.0 M

C)
10.5M

D)
15.7M

• question_answer51) A solid has a 'bcc' structure. If the distance of nearest approach between two atoms is 1.73A,the edge length of the cell is   JEE Main Online Paper (Held On 07 May 2012)

A)
314.20pm

B)
1.41pm

C)
200pm

D)
216pm

• question_answer52) Reaction rate between two substance A and B is expressed as following:$\text{rate}\,\text{=k }\!\![\!\!\text{ A}{{\text{ }\!\!]\!\!\text{ }}^{\text{n}}}{{\text{ }\!\![\!\!\text{ B }\!\!]\!\!\text{ }}^{\text{m}}}$ If the concentration of A is doubled and concentration of B is made half of initialcon centration, the ratio of the new rate to the earlier rate will be:     JEE Main Online Paper (Held On 07 May 2012)

A)
$m+n$

B)
$n-m$

C)
$\frac{1}{{{2}^{\left(m+n \right)}}}$

D)
${{2}^{\left( n-m \right)}}$

• question_answer53) How many cyclic structures are possible for${{C}_{4}}{{H}_{6}}?$   JEE Main Online Paper (Held On 07 May 2012)

A)
3

B)
5

C)
6

D)
4

• question_answer54) Which is not the correct Statement? (At.nos.$\text{Ce}=\text{58},\text{Lu}=\text{71},\text{La}=\text{57},\text{Yb}=\text{7}0$)     JEE Main Online Paper (Held On 07 May 2012)

A)
Colour of $Y{{b}^{3+}}$ ion is pink.

B)
$L{{a}^{3+}}$is diamagnetic.

C)
$C{{e}^{4+}}$ has${{f}^{0}}$ configuration.

D)
$L{{u}^{3+}}$had${{f}^{14}}$ configuration.

• question_answer55) In which of the following arrangements, the sequence is not strictly according to the property written against it?   JEE Main Online Paper (Held On 07 May 2012)

A)
$C{{O}_{2}}<Si{{O}_{2}}<Sn{{O}_{2}}<Pb{{O}_{2}}$: increasing oxidising power

B)
$N{{H}_{3}}<P{{H}_{3}}<As{{H}_{3}}<Sb{{H}_{3}}$: increasing basic strength

C)
$HF < HCl < HBr < HI$: increasing acid strength

D)
$B<C<O<N$: increasing first ionization enthalpy.

• question_answer56) The IUPAC name of the compoundis   JEE Main Online Paper (Held On 07 May 2012)

A)
1,2-Propoxide

B)
Propylene oxide

C)
1,2-Oxo propane

D)
1,2-Epoxy propane

• question_answer57) Green house gases can be arranged in 'Global Warming Potential' sequence as   JEE Main Online Paper (Held On 07 May 2012)

A)
${{N}_{2}}O>CFC>C{{H}_{4}}>C{{O}_{2}}$

B)
$CFC>{{N}_{2}}O>C{{H}_{4}}>C{{O}_{2}}$

C)
$CFC>C{{O}_{2}}>{{N}_{2}}O>C{{H}_{4}}$

D)
$C{{O}_{2}}>CFC>{{N}_{2}}O>C{{H}_{4}}$

• question_answer58) Among the following the order of reactivity towards nucieophilic addition is   JEE Main Online Paper (Held On 07 May 2012)

A)
$C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}>HCHO$

B)
$HCHO>C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}$

C)
$C{{H}_{3}}CHO>HCHO>C{{H}_{3}}COC{{H}_{3}}$

D)
$C{{H}_{3}}COC{{H}_{3}}>C{{H}_{3}}CHO>HCHO$

• question_answer59) ${{C}_{2}}{{H}_{5}}Br\xrightarrow[{}]{AgCN}X\xrightarrow[Zn-Hg/HCl]{\operatorname{Re}duction}Y,$Here Y is   JEE Main Online Paper (Held On 07 May 2012)

A)
Ethyl methyl amine

B)
n-propylamine

C)
Isopropylamine

D)
Ethylamine

• question_answer60) The ratio of number of oxygen atoms (0) in 16.0 gozone $({{O}_{3}}),$ 28.0 g carbon monoxide (CO) and16.0 oxygen $({{O}_{2}})$ is (Atomic mass: C = 12,0 = 16and Avogadro's constant${{N}_{A}}=6.0\times {{10}^{23}}mo{{l}^{-1}}$)   JEE Main Online Paper (Held On 07 May 2012)

A)
3:1:2

B)
1:1:2

C)
3:1:1

D)
1:1:1

• question_answer61) If$A=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),B=\left( \begin{matrix} \alpha +1 \\ 0 \\ 0 \\ \end{matrix} \right)$be two matrices, then $A{{B}^{T}}$is a non-zero matrix for |a| not equal to   JEE Main Online Paper (Held On 07 May 2012)

A)
2

B)
0

C)
1

D)
3

• question_answer62) If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of$6\pi c{{m}^{2}}hr,$then the rate (in mm/hr) at which the radius of the circular sheet increases is   JEE Main Online Paper (Held On 07 May 2012)

A)
1.0

B)
0.1

C)
1.1

D)
2.0

• question_answer63) The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is   JEE Main Online Paper (Held On 07 May 2012)

A)
63

B)
189

C)
728

D)
364

• question_answer64) The value of k for which the equation$(k-2){{x}^{2}}+8x+k+4=0$has both roots real, distinct and negative is   JEE Main Online Paper (Held On 07 May 2012)

A)
6

B)
3

C)
4

D)
1

• question_answer65) Let y (x) be a solution of $\frac{\left( 2+\sin x \right)}{\left( 1+y \right)}\frac{dy}{dx}=\cos x.$ If $y(0)=2,$then $y\left( \frac{\pi }{2} \right)$equals     JEE Main Online Paper (Held On 07 May 2012)

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

B)
2

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

D)
3

• question_answer66) If the eccentricity of a hyperbola $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,$which passes through (k, 2), is $\frac{\sqrt{13}}{3},$ then the value of ${{k}^{2}}$ is   JEE Main Online Paper (Held On 07 May 2012)

A)
18

B)
8

C)
1

D)
2

• question_answer67) If $\int\limits_{e}^{x}{tf(t)dt}=\sin x-x\cos x-\frac{{{x}^{2}}}{2},$for all$x\in R-\{0\},$then the value of$f\left( \frac{\pi }{6} \right)$ is   JEE Main Online Paper (Held On 07 May 2012)

A)
1/2

B)
1

C)
0

D)
-1/2

• question_answer68) If the number of 5-element subsets of the set$A=\{{{a}_{1}},{{a}_{2}},....,{{a}_{20}}\}$ of 20 distinct elements is k times the number of 5-element subsets containing${{a}_{4}},$then k is   JEE Main Online Paper (Held On 07 May 2012)

A)
5

B)
$\frac{20}{7}$

C)
4

D)
$\frac{10}{3}$

• question_answer69) If the system of equations $x+y+z=6$ $x+2y+3z=10$ $x+2y+\lambda z=0$ has a unique solution, then $\lambda$ is not equal to   JEE Main Online Paper (Held On 07 May 2012)

A)
1

B)
0

C)
2

D)
3

• question_answer70) If the straight lines $\text{x}+\text{3y}=\text{4},\text{3x}+\text{y}=\text{4}$and $\text{x}+\text{y}=0$form a triangle, then the triangle is   JEE Main Online Paper (Held On 07 May 2012)

A)
scalene

B)
equilateral triangle

C)
isosceles

D)
right angled isosceles

• question_answer71) Let fix)be an indefinite integral of ${{\cos }^{3}}x.$ Statement 1:f(x) is a periodic function of period$\pi .$ Statement 2: ${{\cos }^{3}}x$ is a periodic function.   JEE Main Online Paper (Held On 07 May 2012)

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

B)
Both the Statements are true, but Statement2 is not the correct explanation of Statement1.

C)
Both the Statements are true, and Statement2 is correct explanation of Statement 1.

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

• question_answer72) The parabola${{y}^{2}}=x$ divides the circle ${{x}^{2}}+{{y}^{2}}=2$into two parts whose areas are in the ratio   JEE Main Online Paper (Held On 07 May 2012)

A)
$9\pi +2:3\pi -2$

B)
$9\pi -2:3\pi +2$

C)
$7\pi -2:2\pi -3$

D)
$7\pi +2:3\pi +2$

• question_answer73) The equation of the circle passing through the point (1,2) and through the points of intersection of${{x}^{2}}+{{y}^{2}}-4x-6y-21=0$and $3x+4y+5=0$ is given by   JEE Main Online Paper (Held On 07 May 2012)

A)
${{x}^{2}}+{{y}^{2}}+2x=2y+11=0$

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

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

D)
${{x}^{2}}+{{y}^{2}}+2x+2y-11=0$

• question_answer74) The frequency distribution of daily working expenditure of families in a locality is as follows:  Expenditure in Rs. (x): 0-50 50-100 100-150 150-200 200-250 No. of families (f): 24 33 37 B 25
If the mode of the distribution is " 140, then the value of b is   JEE Main Online Paper (Held On 07 May 2012)

A)
34

B)
31

C)
26

D)
36

• question_answer75) The sum of the series${{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}$is   JEE Main Online Paper (Held On 07 May 2012)

A)
$m{{(2m+1)}^{2}}$

B)
${{m}^{2}}(m+2)$

C)
${{m}^{2}}(2m+1)$

D)
$m{{(m+2)}^{2}}$

• question_answer76) The point of intersection of the lines$({{a}^{3}}+3)x+ay+a-3=0$and$({{a}^{5}}+2)x+(a+2)y+2a+3=0$(a real) lies on they-axis for   JEE Main Online Paper (Held On 07 May 2012)

A)
no value of a

B)
more than two values of a

C)
exactly one value of a

D)
exactly two values of a

• question_answer77) ABCD is parallelogram. The position vectors of A and C are respectively,$3\hat{i}+3\hat{j}+5\hat{k}$ and$\hat{i}-5\hat{j}-5\hat{k}$.If M is the midpoint of the diagonal$\overset{\to }{\mathop{OM}}\,$then the magnitude of the projection of on$\overset{\to }{\mathop{OC}}\,,$ where O is the origin, is   JEE Main Online Paper (Held On 07 May 2012)

A)
$7\sqrt{51}$

B)
$\frac{7}{\sqrt{50}}$

C)
$7\sqrt{50}$

D)
$\frac{7}{\sqrt{51}}$

• question_answer78) The range of the function $f\left( x \right)=\frac{x}{1+|x|},x\in R,$is   JEE Main Online Paper (Held On 07 May 2012)

A)
R

B)
-1,1

C)
R- {0}

D)
[-1, 1]

• question_answer79) If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is   JEE Main Online Paper (Held On 07 May 2012)

A)
16

B)
18

C)
50

D)
15

• question_answer80) If $\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}$and$\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}$are coplanar vectors, then$\lambda$is equal to

A)
0

B)
-1

C)
2

D)
1

• question_answer81) Statement 1:$y=mx-\frac{1}{m}$is always a tangent to the parabola, ${{y}^{2}}=-4x$for all non-zero values of w. Statement 2: Every tangent to the parabola, ${{y}^{2}}=-4x$ will meet its axis at a point whose abscissa is non-negative.   JEE Main Online Paper (Held On 07 May 2012)

A)
Statement 1 is true, Statement 2 is true; Statement 2 is a 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 a correct explanation of Statement 1.

• question_answer82) Let ${{Z}_{1}}$and ${{Z}_{2}}$be any two complex number. Statement1:$\left| {{Z}_{1}}-{{Z}_{2}} \right|\ge \left| {{Z}_{1}} \right|-\left| {{Z}_{2}} \right|$ Statement 2: $\left| {{Z}_{1}}+{{Z}_{2}} \right|\le \left| {{Z}_{1}} \right|+\left| {{Z}_{2}} \right|$   JEE Main Online Paper (Held On 07 May 2012)

A)
Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

B)
Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C)
Statement 1 is true. Statement 2 is false.

D)
Statement 1 is false. Statement 2 is true.

• question_answer83) Let X and Y are two events such that$P\left( X\cup Y \right)=P(X\cap Y).$ Statement1:$P(X\cap Y')=P\left( X'\cap Y \right)=0$ Statement 2; $P(X)+P=2P\left( X\cap Y \right)$   JEE Main Online Paper (Held On 07 May 2012)

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

B)
Statement 2 is not a correct explanation of Statement 1.

C)
Statement 1 is true. Statement 2 is false.

D)
Statement 1 is true. Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

• question_answer84) If$f(y)=1-(y-1)+{{(y-1)}^{2}}-{{(y-1)}^{3}}$$+...-{{(y-1)}^{17}},$then the coefficient of ${{y}^{2}}$ in it is   JEE Main Online Paper (Held On 07 May 2012)

A)
$^{17}{{C}_{2}}$

B)
$^{17}{{C}_{3}}$

C)
$^{18}{{C}_{2}}$

D)
$^{18}{{C}_{3}}$

• question_answer85) The values of a for which the two points (1, a, 1)and (-3, 0, a) lie on the opposite sides of the plane $\text{3x}+\text{4y}-\text{12z}+\text{13}=0,$ satisfy   JEE Main Online Paper (Held On 07 May 2012)

A)
$0<a<\frac{1}{3}$

B)
$-1<a<0$

C)
$a<-1$or    $a<\frac{1}{3}$

D)
$a=0$

• question_answer86) $\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x-\sin x}{x} \right)\sin \left( \frac{1}{x} \right)$   JEE Main Online Paper (Held On 07 May 2012)

A)
equals 1

B)
equals 0

C)
does not exist

D)
equals? 1

• question_answer87) A line with positive direction cosines passes through the point P (2, - 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane $2x+y+z=9$ at point Q, then the length PQ equals   JEE Main Online Paper (Held On 07 May 2012)

A)
$\sqrt{2}$

B)
2

C)
$\sqrt{3}$

D)
1

• question_answer88) Let$f(x)=\sin x,g(x)=x.$ Statement1:$f(x)\le g(x)$ for x in $(0,\infty )$ Statement2:$f(x)\le 1$ for x in $(0,\infty )$ but $g(x)\to \infty$as$x\to \infty .$   JEE Main Online Paper (Held On 07 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 true. Statement 2 is true, Statement 2 is not a correct explanation for Statement!.

D)
Statement 1 is false. Statement 2 is true.

• question_answer89) The Statement that is TRUE among the following is   JEE Main Online Paper (Held On 07 May 2012)

A)
The contrapositive of$3x+2=8\Rightarrow x=2$is$x\ne 2$$\Rightarrow$$3x+2\ne 8.$

B)
The converse of $=0\Rightarrow x=0$ is $x\ne 0\Rightarrow \tan x=0.$

C)
$p\Rightarrow q$ is equivalent to$p\vee \tilde{\ }q.$

D)
$p\vee q$and$p\wedge q$ have the same truth table.

• question_answer90) If$x+|y|=2y,$ then y as a function of x, at x = 0 is

A)
differentiable but not continuous

B)
continuous but not differentiable

C)
continuous as well as differentiable

D)
neither continuous nor differentiable