# Solved papers for JEE Main & Advanced AIEEE Paper (Held On 11 May 2011)

### done AIEEE Paper (Held On 11 May 2011) Total Questions - 89

• question_answer1) At time t = 0 s a particle starts moving along the x-axis. If its kinetic energy increases uniformly with time 't', the net force acting on it must be proportional to:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
constant

B)
t

C)
$\frac{1}{\sqrt{t}}$

D)
$\sqrt{t}$

• question_answer2) At two points P and Q on a screen in Young's double slit experiment, waves from slits ${{S}_{1}}$ and ${{S}_{2}}$ have a path difference of 0 and $\frac{\lambda }{4}$respectively. The ratio of intensities at P and Q will be:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$2:1$

B)
$\sqrt{2}:1$

C)
$4:1$

D)
$3:2$

• question_answer3) Two particles of equal mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each partial with respect to their centre of mass is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\sqrt{\frac{Gm}{4R}}$

B)
$\sqrt{\frac{Gm}{3R}}$

C)
$\sqrt{\frac{Gm}{2R}}$

D)
$\sqrt{\frac{Gm}{R}}$

• question_answer4) The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is ${{F}_{1}}$ while the minimum force needed to prevent it from sliding down is ${{F}_{2}}.$ If the inclined plane makes an angle $\theta$from the horizontal such that $\tan \theta =2\mu$then the ratio $\frac{{{F}_{1}}}{{{F}_{2}}}$ is :                  AIEEE  Solved  Paper (Held On 11 May  2011)

A)
1

B)
2

C)
3

D)
4

• question_answer5) If $400\Omega$of resistance is made by adding four $100\Omega$ resistances of tolerance 5%, then the tolerance of the combination is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
5%

B)
10 %

C)
15 %

D)
20 %

• question_answer6) An electric charge +q moves with velocity $\vec{v}=3\hat{i}+4\hat{j}+\hat{k},$in an electromagnetic field given by: $\vec{E}=3\hat{i}+\hat{j}+2\hat{k}$and $\vec{B}=\hat{i}+\hat{j}+3\hat{k}.$The y - component of the force experienced by + q is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
11q

B)
5q

C)
3q

D)
2q

• question_answer7) The current in the primary circuit of a potentiometer is 0.2 A. The specific resistance and cross-section of the potentiometer wire are $4\times {{10}^{-7}}$ohm metre and $8\times {{10}^{-7}}{{m}^{2}}$respectively. The potential gradient will be equal to :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
1 V/ m

B)
0.5 V/m

C)
0.1 V/m

D)
0.2 V/m

• question_answer8) A particle of mass 'm' is projected with a velocity $\upsilon$ making an angle of $30{}^\circ$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height 'h' is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
zero

B)
$\frac{m{{\upsilon }^{3}}}{\sqrt{2}g}$

C)
$\frac{\sqrt{3}}{16}\frac{m{{\upsilon }^{3}}}{g}$

D)
$\frac{\sqrt{3}}{2}\frac{m{{\upsilon }^{2}}}{g}$

• question_answer9) The specific heat capacity of a metal at low temperature (T) is given as : ${{C}_{p}}(kj{{K}^{-1}}k{{g}^{-1}})=32{{\left( \frac{T}{400} \right)}^{3}}$ A 100 gram vessel of this metal is to be cooled from $20{}^\circ K$ to $4{}^\circ K$ by a special refrigerator operating at room temperature $\left( 27{}^\circ C \right)$. The amount of work required to cool the vessel is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
greater than 0.148 kJ

B)
between 0.148 kJ and 0.028 kJ

C)
less than 0.028 kJ

D)
equal to 0.002 kJ

• question_answer10) A wooden cube (density of wood 'd') of side $'\ell '$ floats in a liquid of density$'\rho '$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period T'. Then, T is equal to :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$2\pi \sqrt{\frac{\ell d}{\rho g}}$

B)
$2\pi \sqrt{\frac{\ell \rho }{dg}}$

C)
$2\pi \sqrt{\frac{\ell d}{(\rho -d)g}}$

D)
$2\pi \sqrt{\frac{\ell \rho }{(\rho -d)g}}$

• question_answer11) A container with insulating walls is divided into equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{P}{2},\frac{T}{2}$

B)
$P,T$

C)
$P,\frac{T}{2}$

D)
$\frac{P}{2},T$

• question_answer12) In a Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength $\lambda .$ In another experiment with the same arrangement the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the  first case is ${{I}_{1}}$ and in the second case is ${{I}_{2}},$ then the ratio $\frac{{{I}_{1}}}{{{I}_{2}}}$is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
2

B)
1

C)
0.5

D)
4

• question_answer13) The output of an OR gate is connected to both the inputs of a NAND gate. The combination will serve as a:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
NOT gate

B)
NOR gate

C)
AND gate

D)
OR gate

• question_answer14) Two positive charges of magnitude 'q' are placed at the ends of a side (side 1) of a square of side '2a'. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge Q moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
zero

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1+\frac{1}{\sqrt{5}} \right)$

C)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1-\frac{2}{\sqrt{5}} \right)$

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1-\frac{1}{\sqrt{5}} \right)$

• question_answer15) Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C - R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time needed for reducing the voltage of the fully charged series combination by half is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
10 second

B)
5 second

C)
2.5 second

D)
20 second

• question_answer16) A beaker contains water up to a height ${{h}_{1}}$and kerosene of height ${{h}_{2}}$ above water so that the total height of (water + kerosene) is $({{h}_{1}}+{{h}_{2}}).$Refractive index of water is ${{\mu }_{1}}$ and that of kerosene is ${{\mu }_{2}}.$ The apparent shift in the position of the bottom of the beaker when viewed from above is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\left( 1+\frac{1}{{{\mu }_{1}}} \right){{h}_{1}}-\left( 1+\frac{1}{{{\mu }_{2}}} \right){{h}_{2}}$

B)
$\left( 1-\frac{1}{{{\mu }_{1}}} \right){{h}_{1}}+\left( 1-\frac{1}{{{\mu }_{2}}} \right){{h}_{2}}$

C)
$\left( 1+\frac{1}{{{\mu }_{1}}} \right){{h}_{2}}-\left( 1+\frac{1}{{{\mu }_{2}}} \right){{h}_{1}}$

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

• question_answer17) A metal rod of Young's modulus Y and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t{}^\circ C$, the linear stress developed in its is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{Y}{\alpha t}$

B)
$Y\alpha t$

C)
$\frac{1}{(Y\alpha t)}$

D)
$\frac{\alpha t}{Y}$

• question_answer18) A travelling wave represented by $y=A\sin ((\omega t-kx)$is superimposed on another wave represented by $y=A\sin (\omega t+kx).$The resultant is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
A wave travelling along + x direction

B)
A wave travelling along - x direction

C)
A standing wave having nodes at $x=\frac{n\lambda }{2},n=0,1,2$?..

D)
A standing wave having nodes at$x=\left( n+\frac{1}{2} \right)\frac{\lambda }{2};n=0,1,2$??

• question_answer19) A thin circular disk of radius R is uniformly charged with density $\sigma >0$per unit area. The disk rotates about its axis with a uniform angular speed $\omega .$The magnetic moment of the disk is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\pi {{R}^{4}}\sigma \omega$

B)
$\frac{\pi {{R}^{4}}}{2}\sigma \omega$

C)
$\frac{\pi {{R}^{4}}}{4}\sigma \omega$

D)
$2\pi {{R}^{4}}\sigma \omega$

• question_answer20) An aluminium sphere of 20 cm diameter is heated from $0{}^\circ C$ to $100{}^\circ C$. Its volume changes by (given that coefficient of linear expansion for aluminium ${{\alpha }_{Al}}=23\times {{10}^{-6}}{{/}^{o}}C$)     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
2.89cc

B)
9.28cc

C)
49.8 cc

D)
28.9 cc

• question_answer21) Two mercury drops (each of radius' r') merge to from bigger drop. The surface energy of the bigger drop, if T is the surface tension, is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$4\eta {{r}^{2}}T$

B)
$2\eta {{r}^{2}}T$

C)
${{2}^{8/3}}\eta {{r}^{2}}T$

D)
${{2}^{5/3}}\eta {{r}^{2}}T$

• question_answer22) If a ball of steel (density$p=7.8\text{ }gc{{m}^{-3}}$) attains a terminal velocity of $10cm\,{{s}^{-1}}$when falling in a water (Coefficient of Viscosity ${{\eta }_{water}}=8.5\times {{10}^{-4}}Pa.s$) then its terminal velocity in glycerine $(p=1.2gc{{m}^{-3}},\eta =13.2Pa.s.)$ would be, nearly:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$6.25\times {{10}^{-4}}cm\,{{s}^{-1}}$

B)
$6.45\times {{10}^{-4}}cm\,{{s}^{-1}}$

C)
$1.5\times {{10}^{-5}}cm\,{{s}^{-1}}$

D)
$1.6\times {{10}^{-5}}cm\,{{s}^{-1}}$

• question_answer23) A horizontal straight wire 20 m long extanding from to east to west falling with a speed of 5.0 M\s, at right angles to the horizontal component of the earth's magnetic field $0.30\times {{10}^{-4}}Wb/{{m}^{2}}.$The instantaneous Value of the e.m. f. induced in the wire will be :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
3 mV

B)
4.5 mV

C)
1.5 mV

D)
6.0m V

• question_answer24) After absorbring a slowly moving neutron of Mass ${{m}_{N}}$ (momentum $\approx 0$) a nucleus of mass M breaks into two nuclei of masses ${{m}_{1}}$ and $5{{m}_{1}}$$(6{{m}_{1}}=M+{{m}_{N}})$ respectively. If the de Broglic wavelength of the nucleus with mass ${{m}_{1}}$is $\lambda ,$ the de Broglie wavelength of the nucleus will be:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$5\lambda$

B)
$\lambda /5$

C)
$\lambda$

D)
$25\lambda$

• question_answer25) Which of the following four alternatives is not correct? We need modulation:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
to reduce the time lag between transmission and reception of the information signal

B)
to reduce the size of antenna

C)
to reduce the e fractional band width, that is the ratio of the signal band width to the centre frequency

D)
to increase the selectivity.

• question_answer26) If a spring of stiffness 'k' is cut into two parts 'A' and 'B' of length ${{\ell }_{A}}:{{\ell }_{B}}=2:3,$then the stiffness of spring 'A' is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

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

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

C)
$k$

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

• question_answer27) Statement -1 : A nucleus having energy ${{E}_{1}}$ decays by $\text{ }\!\!\beta\!\!\text{ -}$emission to daughter nucleus having energy ${{E}_{2}},$ but the $\text{ }\!\!\beta\!\!\text{ -}$rays are emitted with a continuous energy spectrum having end point energy ${{E}_{1}}-{{E}_{2}}.$ Statement - 2: To conserve energy and momentum in p-decay at least three particles must take part in the transformation.     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Statement-1 is correct but statement-2 is not correct.

B)
Statement-1 and Statement-2 both are correct and stateemnt-2 is the correct explanation of statement-1.

C)
Statement-1 is correct, Statement-2 is correct and Statement-2 is not the correct explanation of Statement-1

D)
Statement-1 is incorrect, Statement-2 is correct.

• question_answer28) When monochromatic red light is used instead of blue light in a convex lens, its focal length will:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
increase

B)
decrease

C)
remain same

D)
does not depend on colour of light

• question_answer29) Statement -1 : On viewing the clear blue portion of the sky through a Calcite Crystal, the intensity of transmitted light varies as the crystal is rotated. Statement - 2: The light coming from the sky is polarized due to scattering of sun light by particles in the atmosphere. The scattering is largest for blue light     AIEEE  Solved  Paper (Held On 11 May  2011)

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 statment-1

C)
Statement-1 is true, Statement-2 is true, Statement-2 is not the correct explanation of statement-1

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

• question_answer30) Statement -1 : Two longitudinal waves given by equations : ${{y}_{1}}(x,t)=2asin(\omega t-kx)$and${{y}_{2}}(x,t)=a\,sin(2\omega t-2kx)$will have equal intensity. Statement - 2: Intensity of waves of given frequency in same medium is proportional to square of amplitude only.     AIEEE  Solved  Paper (Held On 11 May  2011)

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 statment-1

C)
Statement-1 is true, Statement-2 is true, Statement-2 is not the correct explanation of Statement-1

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

• question_answer31) Identify the incorrect statement from the following:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Ozone absorbs the intense ultraviolet radiation of the sun.

B)
Depletion of ozone layer is because of its chemical reactions with chlorofluoro alkanes.

C)

D)
Oxides of nitrogen in the atmosphere can cause the depletion of ozone layer.

• question_answer32) When r, P and M represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion $({{r}_{A}}/{{r}_{B}})$of two gases A and B, is given as:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$({{P}_{A}}/{{P}_{B}}){{({{M}_{\text{B}}}/{{M}_{A}})}^{1/2}}$

B)
${{({{P}_{A}}/{{P}_{B}})}^{1/2}}({{M}_{\text{B}}}/{{M}_{A}})$

C)
$({{P}_{A}}/{{P}_{B}}){{({{M}_{\text{A}}}/{{M}_{\text{B}}})}^{1/2}}$

D)
${{({{P}_{A}}/{{P}_{B}})}^{1/2}}({{M}_{\text{A}}}/{{M}_{\text{B}}})$

• question_answer33) Consider thiolanion $(R{{S}^{\Theta }})$and alkoxyanion $(R{{O}^{\Theta }}).$Which of the following statements is correct?     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$R{{S}^{\Theta }}$is less basic but more nucleophilic than $R{{O}^{\Theta }}.$

B)
$R{{S}^{\Theta }}$is more basic and more nucleophilic than $R{{O}^{\Theta }}.$

C)
$R{{S}^{\Theta }}$is more basic but less nucleophilic than $R{{O}^{\Theta }}.$

D)
$R{{S}^{\Theta }}$is less basic and less nucleophilic than $R{{O}^{\Theta }}.$

• question_answer34) The change in the optical rotation of freshly prepared solution of glucose is known as:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
racemisation

B)
specific rotation

C)
mutarotation

D)
tautomerism

• question_answer35) The molality of a urea solution in which 0.0100 g of urea, $[{{(N{{H}_{2}})}_{2}}CO]$is added to $0.3000\,d{{m}^{3}}$of water at STP is:

A)
$5.55\times {{10}^{-4}}$

B)
$33.3m$

C)
$3.33\times {{10}^{-2}}m$

D)
$0.55m$

• question_answer36) The molecular velocity of any gas is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
inversely proportional to absolute temperature.

B)
directly proportional to square of temperature.

C)
directly proportional to square root of temperature.

D)
inversely proportional to the square root of temperature.

• question_answer37) The correct order of acid strength of the following compounds:   Phenol              p-Cresol             m-Nitrophenol        p-Nitrophenol is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
D > C > A > B

B)
B > D > A > C

C)
A > B > D > C

D)
C > B > A > D

• question_answer38) The value of enthalpy change $(\Delta H)$for the reaction${{C}_{2}}{{H}_{5}}O{{H}_{(l)}}+3{{O}_{2(g)}}\to 2C{{O}_{2(g)}}+3{{H}_{2}}{{O}_{(l)}}$at 27°C is  $-1366.5\text{ }kJ\text{ }mo{{l}^{-1}}.$The value of internal energy change for the above reaction at this temperature will be :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
-1369.0 kJ

B)
-1364.0kJ

C)
-1361.5 kJ

D)
-1371.5 kJ

• question_answer39) Thermosetting polymer, Bakelite is formed by the reaction of phenol with :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$C{{H}_{3}}CHO$

B)
$HCHO$

C)
$HCOOH$

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

• question_answer40) Ozonolysis of an organic compound 'A' produces acetone and propionaldehyde in equimolar mixture. Identify 'A' from the following compounds :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
1 -Pentene

B)
2-Pentene

C)
2-Methyl-2-pentene

D)
2-MethyM -pentene

• question_answer41) Consider the reaction : $4N{{O}_{2(g)}}+{{O}_{2(g)}}\to 2{{N}_{2}}{{O}_{5}}_{(g)}'$${{\Delta }_{r}}H=-111\,kJ.$ If ${{N}_{2}}{{O}_{5(s)}}$is formed instead of ${{N}_{2}}{{O}_{5(g)}}$in the above reaction, the ${{\Delta }_{r}}H$value will be: (given, $\Delta H$of sublimation for ${{N}_{2}}{{O}_{5}}$is $54kJ\,mo{{l}^{-1}}$)     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
+54kJ

B)
+219kJ

C)
-219kJ

D)
-165kJ

• question_answer42) An acid HA ionises as  $HA\underset{{}}{\leftrightarrows}{{H}^{+}}+{{A}^{-}}$ The pH of 1.0 M solution is 5. Its dissociation constant would be:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
5

B)
$5\times {{10}^{-8}}$

C)
$1\times {{10}^{-5}}$

D)
$1\times {{10}^{-10}}$

• question_answer43) The correct order of electron gain enthalpy with negative sign of F,CI, Brand I, having atomic number 9,17, 35 and 53 respectively, is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
F > CI > Br > l

B)
CI > F > Br > l

C)
Br > Cl > I > F

D)
I > Br > Cl > F

• question_answer44) The frequency of light emitted for the transition n = 4 to n = 2 of$H{{e}^{+}}$ is equal to the transition in H atom corresponding to which of the following?     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
n = 2 to n = 1

B)
n = 3 to n = 2

C)
n = 4 to n = 3

D)
n = 3 to n = 1

• question_answer45) A 5% solution of cane sugar (molar mass 342) is isotonic with 1% of a solution of an unknown solute. The molar mass of unknown solute in g/mol is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
171.2

B)
68.4

C)
34.2

D)
136.2

• question_answer46) In view of the signs of ${{\Delta }_{r}}{{G}^{o}}$ for the following reactions : $Pb{{O}_{2}}+Pb\to 2PbO,$     ${{\Delta }_{r}}{{G}^{o}}<0$ $Sn{{O}_{2}}+Sn\to 2SnO,$      ${{\Delta }_{r}}{{G}^{o}}>0,$which oxidation states are more characteristics for lead and tin ?     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
For lead +2, for tin +2

B)
For lead +4, for tin +4

C)
For lead +2, for tin +4

D)
For lead +4, for tin +2

• question_answer47) The ${{K}_{sp}}$for $Cr{{(OH)}_{3}}$is $1.6\times {{10}^{-}}^{30}.$The molar solubiity of this compound in water is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$4\sqrt{1.6\times {{10}^{-30}}}$

B)
$4\sqrt{1.6\times {{10}^{-30}}/17}$

C)
$1.6\times {{10}^{-30}}/27$

D)
$2\sqrt{1.6\times {{10}^{-30}}}$

• question_answer48) The products obtained on heating $LiN{{O}_{3}}$will be :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$L{{i}_{2}}O+N{{O}_{2}}+{{O}_{2}}$

B)
$L{{i}_{3}}N+{{O}_{2}}$

C)
$L{{i}_{3}}O+NO+{{O}_{2}}$

D)
$LiN{{O}_{3}}+{{O}_{2}}$

• question_answer49) Resistance of 0.2 M solution of an electrolyte is $50\Omega .$The specific conductance of the solution is $1.3S\,{{m}^{-1}}.$If resistance of the 0.4 M solution of the same electrolyte is $260\Omega ,$its molar conductivity is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$6.25\times {{10}^{-4}}S{{m}^{2}}\,mo{{l}^{-1}}$

B)
$625\times {{10}^{-4}}S\,{{m}^{2}}\,mo{{l}^{-1}}$

C)
$62.5\,S\,{{m}^{2}}\,mo{{l}^{-1}}$

D)
$6250\,S\,{{m}^{2}}\,mo{{l}^{-1}}$

• question_answer50) Among the ligands $N{{H}_{3}},en,C{{N}^{-}}$and CO the correct order of their increasing field strength, is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$N{{H}_{3}}<en<C{{N}^{-}}<CO$

B)
$C{{N}^{-}}<N{{H}_{3}}<CO<en$

C)
$en<C{{N}^{-}}<N{{H}_{3}}<CO$

D)
$CO<N{{H}_{3}}<en<C{{N}^{-}}$

• question_answer51) Consider the following reaction: ${{C}_{2}}{{H}_{5}}OH+{{H}_{2}}S{{O}_{4}}\to$Product Among the following, which one cannot be formed as a product under any conditions?     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Ethylene

B)
Acetylene

C)
Diethyl ether

D)
Ethyl-hydrogen sulphate

• question_answer52) The non aromatic compound among the following is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)

B)

C)

D)

• question_answer53) The number of types of bonds between two carbon atoms in calcium carbide is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
One sigma, one pi

B)
Two sigma, one pi

C)
Two sigma, two pi

D)
One sigma, two pi

• question_answer54) A reactant  forms two products : $A\xrightarrow[{}]{{{k}_{1}}}B,$Activation Energy $E{{a}_{1}}$ $A\xrightarrow[{}]{{{k}_{2}}}C,$ Activation Energy $E{{a}_{2}}$ If $E{{a}_{2}}=2E{{a}_{1}},$then ${{k}_{1}}$and ${{k}_{2}}$ are related as :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
${{k}_{2}}={{k}_{1}}{{e}^{E{{a}_{1}}/RT}}$

B)
${{k}_{2}}={{k}_{1}}{{e}^{E{{a}_{2}}/RT}}$

C)
${{k}_{1}}-A{{k}_{2}}{{e}^{E{{a}_{1}}/RT}}$

D)
${{k}_{1}}-2{{k}_{2}}{{e}^{E{{a}_{2}}/RT}}$

• question_answer55) 25.          Copper crystallises in fee lattice with a unit cell edge of 361 pm. The radius of copper atom is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
108pm

B)
128pm

C)
157pm

D)
181pm

• question_answer56) The mass of potassium dichromate crystals required to oxidise $750\text{ }c{{m}^{3}}$of 0.6 M Mohr's salt solution is : (Given molar mass potassium dichromate = 294, Mohr's salt = 392)     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
0.45g

B)
22.05 g

C)
2.2 g

D)
0.49 g

• question_answer57) Which of the following has maximum number of lone pairs associated with Xe ?

A)
$Xe{{F}_{4}}$

B)
$Xe{{F}_{6}}$

C)
$Xe{{F}_{2}}$

D)
$Xe{{O}_{3}}$

• question_answer58) In the chemical reactionsthe compounds A and B respectively are:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Benzene diazonium chloride and benzonitrile

B)
Nitrobenzene and chlorobenzene

C)
Phenol and bromobenzene

D)
Fluorobenzene and phenol

• question_answer59) Which one of the following complex ions has geometrical isomers ?     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
${{[Ni{{(N{{H}_{3}})}_{5}}Br]}^{+}}$

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

C)
${{[Cr{{(N{{H}_{3}})}_{4}}(en)]}^{3+}}$

D)
${{[Co{{(en)}_{3}}]}^{3+}}$ (en - ethylenediamine)

• question_answer60) Let f be a function defined by $f(x)={{(x-1)}^{2}}+1,(x\ge 1).$ Statement -1 : The set$\{x:f(x)={{f}^{-1}}(x)\}=\{1,2\}.$ Statement - 2 : f is a bisection and ${{f}^{-1}}(x)=1+\sqrt{x-1},x\ge 1.$     AIEEE  Solved  Paper (Held On 11 May  2011)

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

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 false

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

• question_answer61) If $\omega \ne 1$ is the complex cube root of unity and matrix $H=\left[ \begin{matrix} \omega & 0 \\ 0 & \omega \\ \end{matrix} \right],$then ${{H}^{70}}$is equal to -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$0$

B)
$-H$

C)
${{H}^{2}}$

D)
$H$

• question_answer62) Let [.] denote the greatest integer function then the value of $\int\limits_{0}^{1.5}{x[{{x}^{2}}]dx}$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$0$

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

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

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

• question_answer63) The curve that passes through the point (2, 3), and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$2y-3x=0$

B)
$y=\frac{6}{x}$

C)
${{x}^{2}}+{{y}^{2}}=13$

D)
${{\left( \frac{x}{2} \right)}^{2}}+{{\left( \frac{y}{3} \right)}^{2}}=2$

• question_answer64) A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standard deviation of gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (ingm) of fishes are respectively:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
32,2

B)
32,4

C)
28,2

D)
28,4

• question_answer65) The lines x + y = | a | and ax - y = 1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$(0,\infty )$

B)
$[1,\infty )$

C)
$(-1,\infty )$

D)
$(-1,1]$

• question_answer66) If the vector $p\,\hat{i}+\hat{j}+\hat{k},\hat{i}+q\,\hat{j}+\hat{k}$and $\,\hat{i}+\hat{j}+r\,\hat{k}$$(p\ne q\ne r\ne 1)$ are coplanar, then the value of pqr - (p+q+r) is-     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
2

B)
0

C)
-1

D)
-2

• question_answer67) The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along a straight line x = y = z is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$10\sqrt{3}$

B)
$5\sqrt{3}$

C)
$3\sqrt{10}$

D)
$3\sqrt{5}$

• question_answer68) Let $\vec{a},\vec{b},\vec{c}$be three non-zero vectors which are pairwise non-collinear. If $\vec{a}+3\vec{b}$is collinear with $\vec{c}$ and $\vec{b}+2\vec{c}$is collinear with $\vec{a}+3\vec{b}+6\vec{c}$ is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\vec{a}$

B)
$\vec{c}$

C)
$\vec{0}$

D)
$\vec{a}+\vec{c}$

• question_answer69) lf A(2,-3) and B(-2,1) are two vertices of a triangle and third vertex moves on the line $2x+3y=9,$ then the locus of the centroid of the triangle is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$xy=1$

B)
$2x+3y=1$

C)
$2x+3y=3$

D)
$2x3y=1$

• question_answer70) There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$N\le 100$

B)
$100<N\le 140$

C)
$140<N\le 190$

D)
$N>190$

• question_answer71) Define F(x) as the product of two real functions ${{f}_{1}}(x)=x,x\in R,$and ${{f}_{2}}(x)=\left\{ \begin{matrix} \sin \frac{1}{x}, & if\,x\ne 0\, \\ 0, & if\,x=0 \\ \end{matrix} \right.$as follows: $F(x)=\left\{ \begin{matrix} {{f}_{1}}(x).{{f}_{2}}(x), & if\,x\ne 0\, \\ 0, & if\,x=0 \\ \end{matrix} \right.$ Statement -1 : F(x) is continuous on R. Statement - 2 : ${{f}_{1}}(x)$ and ${{f}_{2}}(x)$ are continuous on R     AIEEE  Solved  Paper (Held On 11 May  2011) .

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

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 false

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

• question_answer72) Statement -1 : For each natural number $n,{{(n+1)}^{7}}-{{n}^{7}}-1$is divisible by 7. Statement - 2 : For each natural number $n,{{n}^{7}}-n$is divisible by 7.     AIEEE  Solved  Paper (Held On 11 May  2011)

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

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 false

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

• question_answer73) The equation of the circle passing through the point (1,0) and (0,1) and having the smallest radius is -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
${{x}^{2}}+{{y}^{2}}-2x-2y+1=0$

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

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

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

• question_answer74) The equation of the hyperbola whose foci are (-2, 0) and (2, 0) and eccentricity is 2 is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

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

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

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

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

• question_answer75) If the trivial solution is the only solution of the system of equations $x-ky+z=0$ $kx+3y-kz=0$ $3x+y-z=0$ then the set of all values of k is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
R-{2,-3}

B)
R-{2}

C)
R-{-3}

D)
{2,-3}

• question_answer76) Sachin and Rahul attempted to solve a quadratic equaiton. Sachin made a mistake in writing down the constant term and ended up in roots (4,3). Rahul made a mistake in writing down coefficient of x to get roots (3,2). The correct roots of equation are :           AIEEE  Solved  Paper (Held On 11 May  2011)

A)
6,1

B)
4,3

C)
-6,-1

D)
-4,-3

• question_answer77) Let ${{a}_{n}}$ be the ${{n}^{th}}$ term of an A.P. If $\sum\limits_{r=1}^{100}{{{a}_{2r}}=\alpha }$ and $\sum\limits_{r=1}^{100}{{{a}_{2r}}-1=\beta },$ then the common difference of the A.P. is     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\alpha -\beta$

B)
$\frac{\alpha -\beta }{100}$

C)
$\beta -\alpha$

D)
$\frac{\alpha -\beta }{200}$

• question_answer78) Consider the differential equation ${{y}^{2}}dx+\left( x-\frac{1}{y} \right)dy=0.$If y  = 1, then x is given by:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$4-\frac{2}{y}-\frac{{{e}^{\frac{1}{y}}}}{e}$

B)
$3-\frac{1}{y}+\frac{{{e}^{\frac{1}{y}}}}{e}$

C)
$1+\frac{1}{y}-\frac{{{e}^{\frac{1}{y}}}}{e}$

D)
$1-\frac{1}{y}+\frac{{{e}^{\frac{1}{y}}}}{e}$

• question_answer79) Let $f:R\to [0,\infty )$ be such that $\underset{x\to 5}{\mathop{\lim }}\,f(x)$ exists and $\underset{x\to 5}{\mathop{\lim }}\,\frac{{{(f(x))}^{2}}-9}{\sqrt{|x-5|}}=0$ Then $\underset{x\to 5}{\mathop{\lim }}\,f(x)$equals:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
0

B)
1

C)
2

D)
3

• question_answer80) Statement-1 : Determinant of a skew-symmetric matrix of order 3 is zero. Statement - 2 : For any matrix $A,\det {{(A)}^{T}}=\det (A)$ and $\det (-A)=-det(A).$ Where det denotes the determinant of matrix B. Then :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Both statements are true

B)
Both statements are false

C)
Statement-1 is false and statement-2

D)
Statement-1 is true and statement-2 is false

• question_answer81) The possible values of $\theta \in (0,\pi )$such that $\sin (\theta )+sin(4\theta )+sin(7\theta )=0$are :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{\pi }{4},\frac{5\pi }{12},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}$

B)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{35\pi }{36}$

C)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}$

D)
$\frac{2\pi }{9},\frac{\pi }{4},\frac{4\pi }{9},\frac{\pi }{2},\frac{3\pi }{4},\frac{8\pi }{9}$

• question_answer82) The area bounded by the curves ${{y}^{2}}=4x$and ${{x}^{2}}=4y$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\frac{32}{3}$

B)
$\frac{16}{3}$

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

D)
0

• question_answer83) Let f be a function defined by - $f(x)=\left\{ \begin{matrix} \frac{\tan x}{x} & ,x\ne 0 \\ 1 & ,x=0 \\ \end{matrix} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\ne 0$ Statement -1 : x = 0 is point of minima of f Statement-2 : f'(0) =0.     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.

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 false.

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

• question_answer84) The only statement among the following that is a tautology is -     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$A\wedge (A\vee B)$

B)
$A\vee (A\wedge B)$

C)
$[A\wedge (A\to B)]\to B$

D)
$B\to [A\wedge (A\to B)]$

• question_answer85) Let A, B, C be pariwise independent events with P > 0 and $P(A\cap B\cap C)=0.$ Then $P({{A}^{c}}\cap {{B}^{c}}/C).$     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$P(1)-P({{B}^{c}})$

B)
$P({{A}^{c}})+P({{B}^{c}})$

C)
$P({{A}^{c}})-P({{B}^{c}})$

D)
$P({{A}^{c}})-P(B)$

• question_answer86) Let for $a\ne {{a}_{1}}\ne 0,$ $f(x)=a{{x}^{2}}+bx+c,g9x)={{a}_{1}}{{x}^{2}}+{{b}_{1}}x+{{c}_{1}}$and$p(x)=f(x)-g(x).$ If p(x) = 0 only for x = -1 and p(-2) = 2, then the value of p is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
3

B)
9

C)
6

D)
18

• question_answer87) The length of the perpendicular drawn from the point (3, -1,11) to the line $\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$\sqrt{29}$

B)
$\sqrt{33}$

C)
$\sqrt{53}$

D)
$\sqrt{66}$

• question_answer88) Consider the following relation R on the set of real square matrices of order 3. $R=\{(A,B)|A={{P}^{-1}}BP$for some invertible matrix P}. Statement -1 : R is equivalence relation. Statement - 2 : For any two invertible $3\times 3$ matrices M and N,${{(MN)}^{-1}}={{N}^{-1}}{{M}^{-1}}.$     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
Statement-1 is true, statement-2 is a correct explanation for statement-1.

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 false.

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

• question_answer89) If function f(x) is differentiate at x = a, then $\underset{x\to a}{\mathop{\lim }}\,\frac{{{x}^{2}}f(a)-{{a}^{2}}f(x)}{x-a}$is:     AIEEE  Solved  Paper (Held On 11 May  2011)

A)
$-{{a}^{2}}f'(a)$

B)
$af(a)-{{a}^{2}}f\,'(a)$

C)
$2af(a)-{{a}^{2}}f\,'(a)0$

D)
$2af(a)+{{a}^{2}}f'(a)$