# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2011

### done AIEEE Solved Paper-2011 Total Questions - 90

• question_answer1) A carnot engine operation between temperatrues ${{T}_{1}}$ and ${{T}_{2}}$ has efficiency $\frac{1}{6}$. When ${{T}_{2}}$ is lowered by 62 K, its efficiency increases to$\frac{1}{3}$. Then ${{T}_{1}}$ and ${{T}_{2}}$ are respectively   AIEEE  Solved  Paper-2011

A)
310 K and 248 K

B)
372 K and 310 K

C)
372 K and 330 K

D)
330 K and 268 K

• question_answer2) A pulley of radius 2 m is rotated about its axis by a force $F=(20\,t-5{{t}^{2}})$ newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg ${{m}^{2}}$, the number of rotations made by the pulley before its direction of motion if reversed is   AIEEE  Solved  Paper-2011

A)
More than 9

B)
Less than 3

C)
More than 3 but less than 6

D)
More than 6 but less than 9

• question_answer3) Three perfect gases at absolute temperatures ${{T}_{1}},{{T}_{2}}$ and ${{T}_{3}}$ are mixed. The masses of molecules are ${{m}_{1}},{{m}_{2}}$ and ${{m}_{3}}$ and the number of molecules are ${{n}_{1}},{{n}_{2}}$ and ${{n}_{3}}$ respectively. Assuming no loss of energy, the final temperature of the mixture is   AIEEE  Solved  Paper-2011

A)
$\frac{n_{1}^{2}T_{1}^{2}+n_{2}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}$

B)
$\frac{{{T}_{1}}+{{T}_{2}}+{{T}_{3}}}{3}$

C)
$\frac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}$

D)
$\frac{{{n}_{1}}T_{1}^{2}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}$

• question_answer4) A boat is moving due east in a region where the earth's magnetic field is $5.0\times {{10}^{-5}}N{{A}^{-1}}$ due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is $1.50\,m{{s}^{-1}}$, the magnitude of the induced emf in the wire of aerial is   AIEEE  Solved  Paper-2011

A)
$0.15$ mV

B)
1 mV

C)
$0.75$ mV

D)
$0.50$ mV

• question_answer5) A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect the angular speed of the disc   AIEEE  Solved  Paper-2011

A)
First increase and then decrease

B)
Remains unchanged

C)
Continuously decreases

D)
Continuously increases

• question_answer6) Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance $d(d<<l)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance $x$ between them   AIEEE  Solved  Paper-2011

A)
$v\propto x$

B)
$v\propto {{x}^{-\frac{1}{2}}}$

C)
$v\propto {{x}^{-1}}$

D)
$v\propto {{x}^{\frac{1}{2}}}$

• question_answer7) 100 g of water is heated from ${{30}^{o}}C$ to ${{50}^{o}}C$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K)   AIEEE  Solved  Paper-2011

A)
$2.1$ kJ

B)
$4.2$ kJ

C)
$8.4$ kJ

D)
84 kJ

• question_answer8) The half life of a radioactive substance is 20 minutes. The approximate time interval $({{t}_{2}}-{{t}_{1}})$ between the time ${{t}_{2}}$ when $\frac{2}{3}$ of its has decayed and time ${{t}_{1}}$ when $\frac{1}{3}$ of its had decayed is   AIEEE  Solved  Paper-2011

A)
28 min

B)
7 min

C)
14 min

D)
20 min

• question_answer9) Energy required for the electron excitation in$L{{i}^{++}}$ from the first to the third Bohr orbit is   AIEEE  Solved  Paper-2011

A)
$122.4$ eV

B)
$12.1$ eV

C)
$36.3$ eV

D)
$108.8$ eV

• question_answer10) The electrostatic potential inside a charged spherical ball is given by $\phi =an{{r}^{2}}+b$ where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is   AIEEE  Solved  Paper-2011

A)
$-6\,\,a{{\varepsilon }_{0}}$

B)
$-24\,\pi \,a{{\varepsilon }_{0}}\gamma$

C)
$-6\,a{{\varepsilon }_{0}}\gamma$

D)
$-24\,\,\pi \,a{{\varepsilon }_{0}}\gamma$

• question_answer11) Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution $=0.03\,\,N{{m}^{-1}}$)   AIEEE  Solved  Paper-2011

A)
$0.4\,\,\pi$ m J

B)
$4\,\,\pi$ m J

C)
$0.2\,\,\pi$ m J

D)
$2\,\,\pi$ m J

• question_answer12) A resistor 'R' and $2\mu F$ capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (${{\log }_{10}}2.5=0.4$)   AIEEE  Solved  Paper-2011

A)
$3.3\times {{10}^{7}}\Omega$

B)
$1.3\times {{10}^{4}}\Omega$

C)
$1.7\times {{10}^{5}}\Omega$

D)
$2.7\times {{10}^{6}}\Omega$

• question_answer13) A current I flows in an infinitely long wire with corss section in the form of a semi-circular ring of raidus R. The magnitude of the magnetic induction along its axis is   AIEEE  Solved  Paper-2011

A)
$\frac{{{\mu }_{0}}I}{4\pi R}$

B)
$\frac{{{\mu }_{0}}I}{{{\pi }^{2}}R}$

C)
$\frac{{{\mu }_{0}}I}{2{{\pi }^{2}}R}$

D)
$\frac{{{\mu }_{0}}I}{2\pi R}$

• question_answer14) An object, moving with a speed of $6.25\,m/s$, is decelerated at a rate given by $\frac{dv}{dt}=-2.5\sqrt{v}$where v is the instantaneous speed. The time taken by the object, to come to rest, would be   AIEEE  Solved  Paper-2011

A)
8 s

B)
1 s

C)
2 s

D)
4 s

• question_answer15) Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the covex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (coNvex) surface and the bottom (glass plate) surface of the film. Statement-1:       When light reflects from the                                 air-glass plate interface, the reflected wave suffers a phase change of $\pi$. Statement-2:        The centre of the interference                                    pattern is dark.   AIEEE  Solved  Paper-2011

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

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

C)
Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1

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

• question_answer16) Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is   AIEEE  Solved  Paper-2011

A)
$-\frac{9Gm}{r}$

B)
Zero

C)
$-\frac{4Gm}{r}$

D)
$-\frac{6Gm}{r}$

• question_answer17) 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:        Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2:        The state of ionosphere varies from hour to hour, day to day and season to season.   AIEEE  Solved  Paper-2011

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

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

C)
Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1

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

• question_answer18) A fully charged capacitor C with initial charge ${{q}_{0}}$ is connected to a coil of self inductance L at $t=0$. The time at which the energy is stored equally between the electric and the magnetic fields is   AIEEE  Solved  Paper-2011

A)
$\sqrt{LC}$

B)
$\pi \sqrt{LC}$

C)
$\frac{\pi }{4}\sqrt{LC}$

D)
$2\pi \sqrt{LC}$

• question_answer19) This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1:        A metallic surface is irradiated by a monochromatic light of frequency $v>{{v}_{0}}$ (the threshold frequency). The maximum kinetic energy and the stopping potential are ${{K}_{\max }}$ and ${{V}_{0}}$ respectively. If the frequency incident on the surface is doubled, both the${{K}_{\max }}$ and ${{V}_{0}}$ are also doubled. Statement-2:        The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.   AIEEE  Solved  Paper-2011

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

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

C)
Statement-1 is true, Statement-2 is true and Statement-2 is a correct explanation for Statement-1

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

• question_answer20) Water is flowing continuously from a tap having an internal diameter $8\times {{10}^{-3}}m$. The water velocity as it leaves the tap is $0.4\,m{{s}^{-1}}$. The diameter of the water stream at a distance $2\times {{10}^{-1}}m$ below the tap is close to   AIEEE  Solved  Paper-2011

A)
$3.6\times {{10}^{-3}}m$

B)
$5.0\times {{10}^{-3}}m$

C)
$7.5\times {{10}^{-3}}m$

D)
$9.6\times {{10}^{-3}}m$

• question_answer21) A mass M, attached to a horizontal spring, executes S.H.M. with amplitude ${{A}_{1}}$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude ${{A}_{2}}$. The ratio of$\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)$is   AIEEE  Solved  Paper-2011

A)
${{\left( \frac{M+m}{M} \right)}^{1/2}}$

B)
$\frac{M}{M+m}$

C)
$\frac{M+m}{M}$

D)
${{\left( \frac{M}{M+m} \right)}^{1/2}}$

• question_answer22) Two particles are executing simple harmonic motion of the same amplitude A and frequency $\omega$ along the x-axis. Their mean position is separated by distance ${{X}_{0}}({{X}_{0}}>A)$. If the maximum separation between them is $({{X}_{0}}+A)$, the phase difference between their motion is   AIEEE  Solved  Paper-2011

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

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

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

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

• question_answer23) If a wire is stretched to make it 0.1% longer, its resistance will   AIEEE  Solved  Paper-2011

A)
Decrease by 0.05%

B)
Increase by 0.05%

C)
Increase by 0.2%

D)
Decrease by 0.2%

• question_answer24) A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the  fountain that gets wet is   AIEEE  Solved  Paper-2011

A)
$\pi \frac{{{v}^{2}}}{{{g}^{2}}}$

B)
$\pi \frac{{{v}^{2}}}{g}$

C)
$\pi \frac{{{v}^{4}}}{{{g}^{2}}}$

D)
$\frac{\pi }{2}\frac{{{v}^{4}}}{{{g}^{2}}}$

• question_answer25) A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats$\gamma$. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by   AIEEE  Solved  Paper-2011

A)
$\frac{(\gamma -1)}{2R}M{{v}^{2}}K$

B)
$\frac{(\gamma -1)}{2(\gamma +1)R}M{{v}^{2}}K$

C)
$\frac{(\gamma -1)}{2\gamma R}M{{v}^{2}}K$

D)
$\frac{\gamma M{{v}^{2}}}{2R}K$

• question_answer26) A screw gauge gives the following reading when used to measure the diameter of a wire.              Main scale reading:                            0 mm Circular scale reading:                        52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.              The diameter of wire from the above data is   AIEEE  Solved  Paper-2011

A)
0.005 cm

B)
0.52 cm

C)
0.052 cm

D)
0.026 cm

• question_answer27) A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is   AIEEE  Solved  Paper-2011

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

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

C)
g

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

• question_answer28) The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t)={{e}^{-\left( a{{x}^{2}}+b{{t}^{2}}+2\sqrt{ab}xt \right)}}$ This represents a   AIEEE  Solved  Paper-2011

A)
Standing wave of frequency $\frac{1}{\sqrt{b}}$

B)
Wave moving in $+x$ direction with speed $\sqrt{\frac{a}{b}}$

C)
Wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$

D)
Standing wave of frequency $\sqrt{b}$

• question_answer29) A car is fitted with a convex side-view mirror of focal length 20 cm. A second car $2.5$ m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is   AIEEE  Solved  Paper-2011

A)
15 m/s

B)
$\frac{1}{10}m/s$

C)
$\frac{1}{15}m/s$

D)
10 m/s

• question_answer30) Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z\ge 0$ has a refractive index of 2 and medium 2 with $z>0$ has a refractive index of 3. A ray of light in medium 1 given by the vector $\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is   AIEEE  Solved  Paper-2011

A)
${{75}^{o}}$

B)
${{30}^{o}}$

C)
${{45}^{o}}$

D)
${{60}^{o}}$

• question_answer31) In context of the lanthanoids, which of the following statements is not correct?   AIEEE  Solved  Paper-2011

A)
Availability of 4f electrons results in the formation of compounds in $+4$ state for all the members of the series

B)
There is a gradual decrease in the radii of the members with increasing atomic number in the series

C)
All the members exhibit $+3$ oxidation state

D)
Because of similar properties the separation of lanthanoids is not easy

• question_answer32) In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is   AIEEE  Solved  Paper-2011

A)
${{A}_{2}}{{B}_{5}}$

B)
${{A}_{2}}B$

C)
$A{{B}_{2}}$

D)
${{A}_{2}}{{B}_{3}}$

• question_answer33) The magnetic moment (spin only) of ${{[NiC{{l}_{4}}]}^{2-}}$ is   AIEEE  Solved  Paper-2011

A)
$1.41$ BM

B)
$1.82$ BM

C)
$5.46$ BM

D)
$2.82$ BM

• question_answer34) Which of the following facts about the complex $[Cr{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}$ is wrong?   AIEEE  Solved  Paper-2011

A)
The complex gives white precipitate with silver nitrate solution

B)
The complex involves ${{d}^{2}}s{{p}^{3}}$ hybridisation and is octahedral in shape

C)
The complex is paramagnetic

D)
The complex is an outer orbital complex

• question_answer35) The rate of a chemical reaction doubles for every ${{10}^{o}}C$ rise of temperature. If the temperature is raised by ${{50}^{o}}C$, the rate of the reaction increases by about   AIEEE  Solved  Paper-2011

A)
64 times

B)
10 times

C)
24 times

D)
32 times

• question_answer36) 'a' and 'b' are van der Waals' constants for gases Chlorine is more easily liquefied than ethane because   AIEEE  Solved  Paper-2011

A)
a for $C\,{{l}_{2}}>a$ for ${{C}_{2}}{{H}_{6}}$ but b for $C\,{{l}_{2}}<b$ for ${{C}_{2}}{{H}_{6}}$

B)
a and b for $C\,{{l}_{2}}>a$ and b for ${{C}_{2}}{{H}_{6}}$

C)
a and b for $C{{l}_{2}}<a$ and b for $C{{\,}_{2}}{{H}_{6}}$

D)
a for $C{{l}_{2}}<a$ for $C{{\,}_{2}}{{H}_{6}}$ but b for $C{{l}_{2}}>b$ for $C{{\,}_{2}}{{H}_{6}}$

• question_answer37) The hybridisation of orbitals of N atom in $N{{O}_{3}}^{-},N{{O}_{2}}^{+}$ and $N{{H}_{4}}^{+}$ are respectively   AIEEE  Solved  Paper-2011

A)
$s{{p}^{2}},s{{p}^{3}},sp$

B)
$sp,s{{p}^{2}},s{{p}^{3}}$

C)
$s{{p}^{2}},sp,s{{p}^{3}}$

D)
$sp,s{{p}^{3}},s{{p}^{2}}$

• question_answer38) Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at $-{{6}^{o}}C$ will be: (${{K}_{f}}$ for water $=1.86$ K $kgmo{{l}^{-1}}$ and molar mass of ethylene glycol $=62kgmo{{l}^{-1}}$)   AIEEE  Solved  Paper-2011

A)
304.60 g

B)
804.32 g

C)
204.30 g

D)
400.00 g

• question_answer39) The outer electron configuration of Gd (Atomic No.: 64) is   AIEEE  Solved  Paper-2011

A)
$4{{f}^{7}}5{{d}^{1}}6{{s}^{2}}$

B)
$4{{f}^{3}}5{{d}^{5}}6{{s}^{2}}$

C)
$4{{f}^{8}}5{{d}^{0}}6{{s}^{2}}$

D)
$4{{f}^{4}}5{{d}^{4}}6{{s}^{2}}$

• question_answer40) The structure of $I{{F}_{7}}$ is   AIEEE  Solved  Paper-2011

A)
Pentagonal bipyramid

B)
Square pyramid

C)
Trigonal bipyramid

D)
Octahedral

• question_answer41) Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of :   AIEEE  Solved  Paper-2011

A)
An acetylenic triple bond

B)
Two ethylenic double bonds

C)
A vinyl group

D)
An isopropyl group

• question_answer42) The degree of dissociation $(\alpha )$ of a weak electrolyte, ${{A}_{x}}{{B}_{y}}$ is related to van't Hoff factor (i) by the expression:   AIEEE  Solved  Paper-2011

A)
$\alpha =\frac{x+y+1}{i-1}$

B)
$\alpha =\frac{i-1}{\left( x+y-1 \right)}$

C)
$\alpha =\frac{i-1}{x+y+1}$

D)
$\alpha =\frac{x+y-1}{i-1}$

• question_answer43) A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :   AIEEE  Solved  Paper-2011

A)
518 nm

B)
1035 nm

C)
325 nm

D)
743 nm

• question_answer44) Identify the compound that exhibits tautomerism.    AIEEE  Solved  Paper-2011

A)
Phenol

B)
2?Butene

C)
Lactic acid

D)
2?Pentanone

• question_answer45) The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of $10\,d{{m}^{3}}$ at ${{27}^{o}}C$ is to a volume of $100\,d{{m}^{3}}$   AIEEE  Solved  Paper-2011

A)
$42.3$ J $mo{{l}^{-1}}$ ${{K}^{-1}}$

B)
$38.3$J $mo{{l}^{-1}}$ ${{K}^{-1}}$

C)
$35.8$ J $mo{{l}^{-1}}$ ${{K}^{-1}}$

D)
$32.3$ J $mo{{l}^{-1}}$ ${{K}^{-1}}$

• question_answer46) Silver Mirror test is given by which one of the following compounds?   AIEEE  Solved  Paper-2011

A)
Benzophenone

B)
Acetaldehyde

C)
Acetone

D)
Formaldehyde

• question_answer47) Trichloroacetaldehyde was subject to Cannizzaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :   AIEEE  Solved  Paper-2011

A)
Chloroform

B)
2, 2, 2-Trichloroethanol

C)
Trichloromethanol

D)
2, 2, 2-Trichloropropanol

• question_answer48) The reduction potential of hydrogen half-cell will be negative if :   AIEEE  Solved  Paper-2011

A)
$p({{H}_{2}})=2$ atm and $[{{H}^{+}}]=2.0$ M

B)
$p({{H}_{2}})=1$ atm and $[{{H}^{+}}]=2.0$ M

C)
$p({{H}_{2}})=1$ atm and $[{{H}^{+}}]=1.0$ M

D)
$p({{H}_{2}})=2$ atm and $[{{H}^{+}}]=1.0$ M

• question_answer49) Phenol is heated with a solution of mixture of KBr and $KBr{{O}_{3}}$. The major product obtained in the above reaction is:   AIEEE  Solved  Paper-2011

A)
2, 4, 6-Tribromophenol

B)
2-Bromophenol

C)
3-Bromophenol

D)
4-Bromophenol

• question_answer50) Among the following the maximum covalent character is shown by the compound   AIEEE  Solved  Paper-2011

A)
$MgC{{l}_{2}}$

B)
$FeC{{l}_{2}}$

C)
$SnC{{l}_{2}}$

D)
$AlC{{l}_{2}}$

• question_answer51) Boron cannot form which one of the following anions?   AIEEE  Solved  Paper-2011

A)
$BO_{2}^{-}$

B)
$BE_{6}^{3-}$

C)
$BH_{4}^{-}$

D)
$B(OH)_{4}^{-}$

• question_answer52) Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is.   AIEEE  Solved  Paper-2011

A)
Ethyl ethanoate

B)
Diethyl ether

C)
2?Butanone

D)
Ethyl chloride

• question_answer53) Which of the following reagents may be used to distinguish between phenol and benzoic acid?   AIEEE  Solved  Paper-2011

A)
Neutral $FeC{{l}_{3}}$

B)
Aqueous $NaOH$

C)
Tollen's reagent

D)
Molisch reagent

• question_answer54) A vessel at 1000 K contains $C{{O}_{2}}$ with a pressure of $0.5$ atm. Some of the $C{{O}_{2}}$ is converted into CO on the addition of graphite. If the total pressure at equilibrium is $0.8$ atm, the value of K is.   AIEEE  Solved  Paper-2011

A)
$0.18$ atm

B)
$1.8$ atm

C)
3 atm

D)
$0.3$ atm

• question_answer55) The strongest acid amongst the following compounds is :   AIEEE  Solved  Paper-2011

A)
$ClC{{H}_{2}}C{{H}_{2}}C{{H}_{2}}COOH$

B)
$C{{H}_{3}}COOH$

C)
$HCOOH$

D)
$C{{H}_{3}}C{{H}_{2}}CH(Cl)C{{O}_{2}}H$

• question_answer56) Which one of the following orders presents the correct sequence of the increasing basic nature of the given oxides?   AIEEE  Solved  Paper-2011

A)
${{K}_{2}}O<N{{a}_{2}}O<A{{l}_{2}}{{O}_{3}}<MgO$

B)
$A{{l}_{2}}{{O}_{3}}<MgO<N{{a}_{2}}O<{{K}_{2}}O$

C)
$MgO<{{K}_{2}}O<A{{l}_{2}}{{O}_{3}}<N{{a}_{2}}O$

D)
$N{{a}_{2}}O<{{K}_{2}}O<MgO<A{{l}_{2}}{{O}_{3}}$

• question_answer57) A 5.2 molal aqueous solution of methyl alcohol, $C{{H}_{3}}OH$ is supplied. What is the mole fraction of methyl alcohol in the solution?   AIEEE  Solved  Paper-2011

A)
$0.050$

B)
$0.100$

C)
$0.190$

D)
$0.086$

• question_answer58) The presence or absence of hydroxy group on which carbon atom of sugar differentiates RNA and DNA?   AIEEE  Solved  Paper-2011

A)
4th

B)
1st

C)
2nd

D)
3rd

• question_answer59) Which of the following statement is wrong?   AIEEE  Solved  Paper-2011

A)
${{N}_{2}}{{O}_{4}}$ has two resonance structures

B)
The stability of hydrides increases from $N{{H}_{3}}$ to $Bi{{H}_{3}}$ in group 15 of the periodic table

C)
Nitrogen cannot form $d\pi -p\pi$ bond

D)
Single N - N bond is weaker than the single P - P bond

• question_answer60) Which of the following statements regarding sulphur is incorrect?   AIEEE  Solved  Paper-2011

A)
The oxidation state of sulphur is never less than $+4$ in its compounds

B)
${{S}_{2}}$ molecule is paramagnetic

C)
The vapour at ${{200}^{o}}C$ consists mostly of ${{S}_{8}}$ rings

D)
At ${{600}^{o}}C$ the gas mainly consists of ${{S}_{2}}$ molecules

• question_answer61) Consider 5 independent Bernoulli?s trials each with probability of success $\rho$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $\rho$ lies in the interval.   AIEEE  Solved  Paper-2011

A)
$\left( \frac{11}{12},1 \right]$

B)
$\left( \frac{1}{2},\frac{3}{4} \right]$

C)
$\left( \frac{3}{4},\frac{11}{12} \right]$

D)
$\left[ 0,\frac{1}{2} \right]$

• question_answer62) The coefficient of ${{x}^{7}}$in the expansion of${{(1-x-{{x}^{2}}+{{x}^{3}})}^{6}}$ is;   AIEEE  Solved  Paper-2011

A)
132

B)
144

C)
$-132$

D)
$-144$

• question_answer63) $\underset{x\to 2}{\mathop{\lim }}\,\left( \frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2} \right)$.   AIEEE  Solved  Paper-2011

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

B)
Does not exist

C)
Equals $\sqrt{2}$

D)
Equals $-\sqrt{2}$

• question_answer64) Let R be the set of real numbers. Statement-1: $A=\{(x,y)\in R\times R:y-x$ is an integer} is an equivalence relation on R. Statement-2: $B=\{(x,y)\in R\times R:x=\alpha y$ for some rational number ?} is an equivalence relation on R.   AIEEE  Solved  Paper-2011

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

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-1

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

• question_answer65) Let $\alpha ,\beta$ be real and z be a complex number. If ${{z}^{2}}+\alpha z+\beta =0$ has two distinct roots on the line Re $z=1$, then it is necessary that.   AIEEE  Solved  Paper-2011

A)
$\beta \in (1,\infty )$

B)
$\beta \in (0,1)$

C)
$\beta \in (-1,0)$

D)
$\left| \beta \right|=1$

• question_answer66) $\frac{{{d}^{2}}x}{d{{y}^{2}}}$ equals.   AIEEE  Solved  Paper-2011

A)
$-\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right){{\left( \frac{dy}{dx} \right)}^{-3}}$

B)
${{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}$

C)
$-{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{-1}}{{\left( \frac{dy}{dx} \right)}^{-3}}$

D)
$\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right){{\left( \frac{dy}{dx} \right)}^{-2}}$

• question_answer67) The number of values of k for which the linear equations $4x+ky+2z=0$ $kx+4y+z=0$ $\left. 2x+2y+z=0 \right|$ possess a non-zero solution is.   AIEEE  Solved  Paper-2011

A)
Zero

B)
3

C)
2

D)
1

• question_answer68) Statement-1: The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line : $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$. Statement-2: The line: $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).   AIEEE  Solved  Paper-2011

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

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-1

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

• question_answer69) Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ?Suman is brilliant and dishonest if and only if Suman is rich? can be expressed as.   AIEEE  Solved  Paper-2011

A)
$\sim (P\wedge \sim R)\leftrightarrow Q$

B)
$\sim P\wedge (Q_{2}^{2}\sim R)$

C)
$\sim (Q_{2}^{2}(P\wedge R))$

D)
$\sim Q\leftrightarrow \sim P\wedge R$

• question_answer70) The lines ${{L}_{1}}:y-x=0$ and ${{L}_{2}}:2x+y=0$ intersect the line ${{L}_{3}}:y+2=0$ at P and Q respectively. The bisector of the acute angle between ${{L}_{1}}$ and ${{L}_{2}}$ intersects ${{L}_{3}}$ at R. Statements 1 : The ratio PR : RQ equals $2\sqrt{2}:\sqrt{5}$. Statement 2 : In any traingle, bisector of an angle divides the triangle into two similar triangles.   AIEEE  Solved  Paper-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 Statement-1

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

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

• question_answer71) A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after.   AIEEE  Solved  Paper-2011

A)
21 months

B)
18 months

C)
19 months

D)
20 months

• question_answer72) Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity $(-3,1)$$\sqrt{\frac{2}{5}}$ is.   AIEEE  Solved  Paper-2011

A)
$5{{x}^{2}}+3{{y}^{2}}-32=0$

B)
$3{{x}^{2}}+5{{y}^{2}}-32=0$

C)
$5{{x}^{2}}+3{{y}^{2}}-48=0$

D)
$3{{x}^{2}}+5{{y}^{2}}-15=0$

• question_answer73) If $A={{\sin }^{2}}x+{{\cos }^{4}}x$, then for all real $x$.   AIEEE  Solved  Paper-2011

A)
$\frac{3}{4}\le A\le \frac{13}{16}$

B)
$\frac{3}{4}\le A\le 1$

C)
$\frac{13}{16}\le A\le 1$

D)
$1\le A\le 2$

• question_answer74) The value of $\int\limits_{0}^{1}{\frac{8\log \left( 1+x \right)}{1+{{x}^{2}}}dx}$ is.   AIEEE  Solved  Paper-2011

A)
$\log 2$

B)
$\pi \log 2$

C)
$\frac{\pi }{8}\log 2$

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

• question_answer75) If the angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\lambda }$and the plane $x+2y+3z=4$ is ${{\cos }^{-1}}\left( \sqrt{\frac{5}{14}} \right)$, then $\lambda$ equals.   AIEEE  Solved  Paper-2011

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

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

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

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

• question_answer76) For $x\in \left( 0,\frac{5\lambda }{2} \right)$, define $f\left( x \right)=\int\limits_{0}^{x}{\sqrt{t}\sin t\,\,dt}$ Then $f$ has.   AIEEE  Solved  Paper-2011

A)
Local maximum at $\pi$ and local $2\pi$

B)
Local maximum at $\pi$ and $2\pi$

C)
Local minimum at $\pi$ and $2\pi$

D)
Local minimum at $\pi$ and local maximum at $2\pi$

• question_answer77) The domain of the function $f(x)=\frac{1}{\sqrt{\left| x \right|-x}}$ is.   AIEEE  Solved  Paper-2011

A)
$\left( -\infty ,\infty \right)-\{0\}$

B)
$\left( -\infty ,\infty \right)$

C)
$\left( 0,\infty \right)$

D)
$\left( -\infty ,0 \right)$

• question_answer78) If the mean deviation about the median of the numbers $a,2a,\,........\,,50a$ is 50, then $\left| a \right|$ equals.   AIEEE  Solved  Paper-2011

A)
5

B)
2

C)
3

D)
4

• question_answer79) If $\vec{a}=\frac{1}{\sqrt{10}}(3\hat{i}+\hat{k})$ and $b=\frac{1}{7}(2\hat{i}+3\hat{j}-6\hat{k})$, then the value of $(2\vec{a}-\vec{b}.[(\vec{a}\times \vec{b})\times (\vec{a}+2\vec{b})]$is.   AIEEE  Solved  Paper-2011

A)
3

B)
$-5$

C)
$-3$

D)
5

• question_answer80) The values of p and q for which the function f(x)=\left\{ \begin{align} & \frac{\sin (p+1)x+sinx}{x},\,\,\,\,\,\,x & q,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\ & \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{3/2}}},\,\,\,\,\,\,\,x>0 \\ \end{align} \right.  is continuous for all $x$ in R, are.   AIEEE  Solved  Paper-2011

A)
$p=\frac{1}{2},q=\frac{3}{2}$

B)
$p=\frac{1}{2},q=-\frac{3}{2}$

C)
$p=\frac{5}{2},q=\frac{1}{2}$

D)
$p=-\frac{3}{2},q=\frac{1}{2}$

• question_answer81) The two circles ${{x}^{2}}+{{y}^{2}}=ax$ and${{x}^{2}}+{{y}^{2}}={{c}^{2}}(c>0)$ touch each other, if   AIEEE  Solved  Paper-2011

A)
$\left| a \right|=2c$

B)
$2\left| a \right|=c$

C)
$\left| a \right|=c$

D)
$a=2c$

• question_answer82) Let I be the purchase value of an equipment and                                                                                                       $V(t)$  be the value after it has been used for t years. The value                                                                                                       $V(t)$  depreciates at a rate given by differential equation                                                                            $\frac{dV(t)}{dt}=-k(T-t)$, where $k>0$ is a constant and T is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is.   AIEEE  Solved  Paper-2011

A)
${{e}^{-kT}}$

B)
${{T}^{2}}-\frac{I}{k}$

C)
$I-\frac{k{{T}^{2}}}{2}$

D)
$I-\frac{k{{\left( T-t \right)}^{\left. 2 \right|}}}{2}$

• question_answer83) If C and D are two events such that $C\subset D$ and $P(D)\ne 0$, then the correct statement among the following is.   AIEEE  Solved  Paper-2011

A)
$P(C|D)=\frac{P(D)}{P(C)}$

B)
$P(C|D)=P(C)$

C)
$P(C|D)\ge P(C)$

D)
$P(C|D)<P(C)$

• question_answer84) Let A and B be two symmetric matrices of order 3. Statement-1: A(BA) and (AB)A are symmetric matrices. Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.   AIEEE  Solved  Paper-2011

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

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-1

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

• question_answer85) If $\omega \,(\ne 1)$ is a cube root of unity, and${{(1+\omega )}^{7}}=A+B\omega$. Then (A, B) equals.   AIEEE  Solved  Paper-2011

A)
(?1, 1)

B)
(0, 1)

C)
(1, 1)

D)
(1, 0)

• question_answer86) Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^{9}{{C}_{3}}$. Statement-2: The number of ways of choosing any 3 places from 9 different places is $^{9}{{C}_{3}}$.   AIEEE  Solved  Paper-2011

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

B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

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

• question_answer87) The shortest distance between line $y-x=1$ and curve $x={{y}^{2}}$ is.   AIEEE  Solved  Paper-2011

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

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

C)
$\frac{3\sqrt{2}}{8}$

D)
$\frac{8}{3\sqrt{2}}$

• question_answer88) The area of the region enclosed by the curves $y=x$, $x=e,y=\frac{1}{x}$ and the positive x-axis is.   AIEEE  Solved  Paper-2011

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

B)
$\frac{1}{2}$ square units

C)
1 square units

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

• question_answer89) If $\frac{dy}{dx}=y+3>0$ and $y(0)=2$, then $y(In\,\,2)$ is equal to.   AIEEE  Solved  Paper-2011

A)
$-2$

B)
7

C)
5

D)
13

• question_answer90) The vectors $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying $\vec{b}\times \vec{c}=\vec{b}\times \vec{d}$and $\vec{a}.\,\vec{d}=0$. Then the vector $\vec{d}$ is equal to   AIEEE  Solved  Paper-2011

A)
$\vec{c}-\left( \frac{\vec{a}.\,\vec{c}}{a.\,\vec{b}} \right)\vec{b}$

B)
$\vec{b}-\left( \frac{\vec{b}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{c}$

C)
$\vec{b}+\left( \frac{\vec{a}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{b}$

D)
$\vec{b}+\left( \frac{\vec{b}.\,\vec{c}}{\vec{a}.\,\vec{b}} \right)\vec{c}$