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

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

1) 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)

\[\sqrt{t}\]

View Answer
2) 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)

\[3:2\]

View Answer
3) 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)

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

View Answer
4) 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

View Answer
5) 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 %

View Answer
6) 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

View Answer
7) 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

View Answer
8) 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)

\[\frac{\sqrt{3}}{2}\frac{m{{\upsilon }^{2}}}{g}\]

View Answer
9) 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

View Answer
10) 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)

\[2\pi \sqrt{\frac{\ell \rho }{(\rho -d)g}}\]

View Answer
11) 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)

\[\frac{P}{2},T\]

View Answer
12) 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

View Answer
13) 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

View Answer
14) 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)

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

View Answer
15) 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

View Answer
16) 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)

\[\left( 1-\frac{1}{{{\mu }_{1}}} \right){{h}_{2}}+\left( 1-\frac{1}{{{\mu }_{2}}} \right){{h}_{1}}\]

View Answer
17) 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)

\[\frac{\alpha t}{Y}\]

View Answer
18) 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\[x=\left( n+\frac{1}{2} \right)\frac{\lambda }{2};n=0,1,2\]??

View Answer
19) 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)

\[2\pi {{R}^{4}}\sigma \omega \]

View Answer
20) 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

View Answer
21) 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)

\[{{2}^{5/3}}\eta {{r}^{2}}T\]

View Answer
22) 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)

\[1.6\times {{10}^{-5}}cm\,{{s}^{-1}}\]

View Answer
23) 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

View Answer
24) 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)

\[25\lambda \]

View Answer
25) 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.

View Answer
26) 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)

\[\frac{5}{2k}\]

View Answer
27) 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.

View Answer
28) 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

View Answer
29) 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.

View Answer
30) 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.

View Answer
31) 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)

Ozone absorbs infrared radiation.

D)

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

View Answer
32) 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)

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

View Answer
33) 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 \[R{{O}^{\Theta }}.\]

View Answer
34) 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

View Answer
35) 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)

\[0.55m\]

View Answer
36) 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.

View Answer
37) 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

View Answer
38) 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

View Answer
39) 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)

\[C{{H}_{3}}C{{H}_{2}}CHO\]

View Answer
40) 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

View Answer
41) 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

View Answer
42) 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)

\[1\times {{10}^{-10}}\]

View Answer
43) 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

View Answer
44) 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

View Answer
45) 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

View Answer
46) 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

View Answer
47) 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)

\[2\sqrt{1.6\times {{10}^{-30}}}\]

View Answer
48) 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)

\[LiN{{O}_{3}}+{{O}_{2}}\]

View Answer
49) 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)

\[6250\,S\,{{m}^{2}}\,mo{{l}^{-1}}\]

View Answer
50) 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)

\[CO<N{{H}_{3}}<en<C{{N}^{-}}\]

View Answer
51) 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

View Answer
52) The non aromatic compound among the following is: AIEEE Solved Paper (Held On 11 May 2011)

A)

B)

C)

D)

View Answer
53) 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

View Answer
54) 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)

\[{{k}_{1}}-2{{k}_{2}}{{e}^{E{{a}_{2}}/RT}}\]

View Answer
55) 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

View Answer
56) 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

View Answer
57) 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)

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

View Answer
58) 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

View Answer
59) 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)

View Answer
60) 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.

View Answer
61) 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)

\[H\]

View Answer
62) 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)

\[\frac{5}{4}\]

View Answer
63) 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)

\[{{\left( \frac{x}{2} \right)}^{2}}+{{\left( \frac{y}{3} \right)}^{2}}=2\]

View Answer
64) 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

View Answer
65) 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)

\[(-1,1]\]

View Answer
66) 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

View Answer
67) 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)

\[3\sqrt{5}\]

View Answer
68) 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)

\[\vec{a}+\vec{c}\]

View Answer
69) 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)

\[2x3y=1\]

View Answer
70) 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)

\[N>190\]

View Answer
71) 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

View Answer
72) 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

View Answer
73) 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)

\[{{x}^{2}}+{{y}^{2}}+x+y-2=0\]

View Answer
74) 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)

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

View Answer
75) 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}

View Answer
76) 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

View Answer
77) 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)

\[\frac{\alpha -\beta }{200}\]

View Answer
78) 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)

\[1-\frac{1}{y}+\frac{{{e}^{\frac{1}{y}}}}{e}\]

View Answer
79) 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

View Answer
80) 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

View Answer
81) 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)

\[\frac{2\pi }{9},\frac{\pi }{4},\frac{4\pi }{9},\frac{\pi }{2},\frac{3\pi }{4},\frac{8\pi }{9}\]

View Answer
82) 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

View Answer
83) 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.

View Answer
84) 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)

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

View Answer
85) 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)

\[P({{A}^{c}})-P(B)\]

View Answer
86) 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

View Answer
87) 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)

\[\sqrt{66}\]

View Answer
88) 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.

View Answer
89) 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)

\[2af(a)+{{a}^{2}}f'(a)\]

View Answer

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