# Solved papers for JEE Main & Advanced AIEEE Solved Paper-2012

### done AIEEE Solved Paper-2012 Total Questions - 90

• question_answer1) A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:   AIEEE  Solved  Paper-2012

A)
$2\pi SY\alpha \Delta T$

B)
$SY\alpha \,\Delta T$

C)
$\pi SY\alpha \,\Delta T$

D)
$2SY\alpha \,\Delta T$

• question_answer2) The figure shows an experimental plot discharging of a capacitor in an RC circuit. The time constant $\tau$ of this circuit lies between:   AIEEE  Solved  Paper-2012

A)
150 sec and 200 sec

B)
0 and 50 sec

C)
50 sec and 100 sec

D)
100 sec and 150 sec

• question_answer3) In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will be :   AIEEE  Solved  Paper-2012

A)

B)

C)

D)

• question_answer4) An electromagnetic wave in vacuum has the electric and magnetic field $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\vec{X}$ and that of wave propagation by $\vec{k}$. Then.   AIEEE  Solved  Paper-2012

A)
$\vec{X}||\vec{B}$ and $\vec{k}||\vec{B}\times \vec{E}$

B)
$\vec{X}||\vec{E}$ and $\vec{k}||\vec{E}\times \vec{B}$

C)
$\vec{X}||\vec{B}$ and $\vec{k}||\vec{E}\times \vec{B}$

D)
$\vec{X}||\vec{E}$ and $\vec{k}||\vec{B}\times \vec{E}$

• question_answer5) If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between $t=0s$ to $t=\tau s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the averatge life time of the pendulum is (assuming damping is small) in seconds :   AIEEE  Solved  Paper-2012

A)
$\frac{0.693}{b}$

B)
b

C)
$\frac{1}{b}$

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

• question_answer6) Hydrogen atom is excieted from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be:   AIEEE  Solved  Paper-2012

A)
2

B)
3

C)
5

D)
6

• question_answer7) A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :   AIEEE  Solved  Paper-2012

A)
developement of air current when the plate is placed.

B)
induction of electrical charge on the plate

C)
shielding of magnetic lines of force as aluminium is a paramagnetic material.

D)
Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.

• question_answer8) The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are $10\,m/{{s}^{2}}$ and 6400 km respectively. The required energy for this work will be:   AIEEE  Solved  Paper-2012

A)
$6.4\times {{10}^{11}}$ Joules

B)
$6.4\times {{10}^{8}}$ Joules

C)
$6.4\times {{10}^{9}}$ Joules

D)
$6.4\times {{10}^{10}}$ Joules

• question_answer9) Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)                  AIEEE  Solved  Paper-2012

A)
15.4%

B)
9.1%

C)
10.5%

D)
12.5%

• question_answer10) In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If ${{I}_{m}}$ be the maximum intensity, the resultant intensity ? when they interfere at phase difference ? is given by :   AIEEE  Solved  Paper-2012

A)
$\frac{{{I}_{m}}}{9}(4+5\cos \phi )$

B)
$\frac{{{I}_{m}}}{3}\left( 1+2{{\cos }^{2}}\frac{\phi }{2} \right)$

C)
$\frac{{{I}_{m}}}{5}\left( 1+4{{\cos }^{2}}\frac{\phi }{2} \right)$

D)
$\frac{{{I}_{m}}}{9}\left( 1+8{{\cos }^{2}}\frac{\phi }{2} \right)$

• question_answer11) A liquid in a beaker has temperature $\theta (t)$ at time t and ${{\theta }_{0}}$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between ${{\log }_{e}}(\theta -{{\theta }_{0}})$ and t is :   AIEEE  Solved  Paper-2012

A)

B)

C)

D)

• question_answer12) A particle of mass m is at rest at the origin at time$t=0$. It is subjected to a force $F(t)={{F}_{0}}{{e}^{-bt}}$ in the $x$ direction. Its speed v(t) is depicted by which of the following curves?   AIEEE  Solved  Paper-2012

A)

B)

C)

D)

• question_answer13) Two electric bulbs marked 25W- 220V and 100W - 220 V are connected in series to a 440 V supply. Which of the bulbs will fuse?   AIEEE  Solved  Paper-2012

A)
both

B)
100W

C)
25W

D)
neither

• question_answer14) Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3%each, then error in the value of resistance of the wire is :   AIEEE  Solved  Paper-2012

A)
6%

B)
zero

C)
1%

D)
3%

• question_answer15) A boy can throw a stone up to amaximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be:   AIEEE  Solved  Paper-2012

A)
$20\sqrt{2}$ m

B)
10 m

C)
$10\sqrt{2}$ m

D)
20m

• question_answer16) This equation has statement 1 and Statement 2. Of the four choices given the Statements, choose the one that describes the two statements. Statement 1: Davisson-Germer experiment established the wave nature of electrons. Statement 2: If electrons have wave nature, they can interfere and show diffraction.   AIEEE  Solved  Paper-2012

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, Statement 2 is the correct explanation for statement 1

D)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation o Statement 1

• question_answer17) A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5\times {{10}^{-2}}$ N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is :                AIEEE  Solved  Paper-2012

A)
0.0125 $N{{m}^{-1}}$

B)
0.1 $N{{m}^{-1}}$

C)
0.05 $N{{m}^{-1}}$

D)
0.025 $N{{m}^{-1}}$

• question_answer18) A charge Q is uniformly distributed over the surface of non-condcting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity$\omega$. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. if we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure :   AIEEE  Solved  Paper-2012

A)

B)

C)

D)

• question_answer19) Truth table for system of four NAND gates as shown in figure is :                AIEEE  Solved  Paper-2012

A)
 A B Y 0 0 0 0 1 1 1 0 1 1 1 0

B)
 A B Y 0 0 0 0 1 0 1 0 1 1 1 1

C)
 A B Y 0 0 1 0 1 1 1 0 0 1 1 0

D)
 A B Y 0 0 1 0 1 0 1 0 0 1 1 1

• question_answer20) A radar has a power of 1kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth $=6.4\times {{10}^{6}}m$) is :   AIEEE  Solved  Paper-2012

A)
80 km

B)
16 km

C)
40 km

D)
64 km

• question_answer21) Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $=1.6725\times {{10}^{-27}}kg$, Mass of proton $=1.6725\times {{10}^{-27}}kg$, mass of electron $=9\times {{10}^{-31}}kg$)   AIEEE  Solved  Paper-2012

A)
0.73 MeV

B)
7.10 MeV

C)
6.30 MeV

D)
5.4 MeV

• question_answer22) A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :   AIEEE  Solved  Paper-2012

A)
efficiency of carnot engine cannot be made larger than 50%

B)
1200 K

C)
750 K

D)
600 K

• question_answer23) 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. If two springs ${{S}_{1}}$ and ${{S}_{2}}$ of force constants ${{k}_{1}}$and ${{k}_{2}}$, respectively, are stretched by the same force, it is found that more work is done on spring ${{S}_{1}}$ than on spring ${{S}_{2}}$. Statement 1: If stretched by the same amount, work done on ${{S}_{1}}$, will be more than that on ${{S}_{2}}$Statement 2:  ${{k}_{1}}<{{k}_{2}}$   AIEEE  Solved  Paper-2012

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, Statement 2 is the correct explanation for statement 1

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

• question_answer24) Two cars of masses ${{m}_{1}}$ and ${{m}_{2}}$ are moving in circles of radii ${{r}_{1}}$ and ${{r}_{2}}$, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is :   AIEEE  Solved  Paper-2012

A)
${{m}_{1}}{{r}_{1}}:{{m}_{2}}{{r}_{2}}$

B)
${{m}_{1}}:{{m}_{2}}$

C)
${{r}_{1}}:{{r}_{2}}$

D)
$1:1$

• question_answer25) A cylindrical tube, open at both ends, has a fundamental frequncy, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :   AIEEE  Solved  Paper-2012

A)
$f$

B)
$f/2$

C)
$3f/4$

D)
$2f$

• question_answer26) An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus on film?   AIEEE  Solved  Paper-2012

A)
7.2 m

B)
2.4 m

C)
3.2 m

D)
5.6 m

• question_answer27) A diatomic molecule is made of two masses ${{m}_{1}}$ and ${{m}_{2}}$ which are separated by a distance r. If we calculate its rotational energy by applying Bohr?s rule of angular momentum quantization, its energy will be given by : (n is an integer)   AIEEE  Solved  Paper-2012

A)
$\frac{{{({{m}_{1}}+{{m}_{2}})}^{2}}{{n}^{2}}{{h}^{2}}}{2m_{1}^{2}m_{2}^{2}{{r}^{2}}}$

B)
$\frac{{{n}^{2}}{{h}^{2}}}{2({{m}_{1}}+{{m}_{2}}){{r}^{2}}}$

C)
$\frac{2{{n}^{2}}{{h}^{2}}}{({{m}_{1}}+{{m}_{2}}){{r}^{2}}}$

D)
$\frac{({{m}_{1}}+{{m}_{2}}){{n}^{2}}{{h}^{2}}}{2{{m}_{1}}{{m}_{2}}{{r}^{2}}}$

• question_answer28) A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data :   AIEEE  Solved  Paper-2012

A)
58.59 degree

B)
58.77 degree

C)
58.65 degree

D)
59 degree

• question_answer29) This questions has statement-1 and statement-2. Of the four choices given after the statements, choose the one that best describe the two statements. An insulating solid sphere of radius R has a unioformly positive charge density $\rho$.As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero. Statement-1: When a charge ?q? is take from the centre of the surface of the sphere its potential energy changes by $\frac{q\rho }{3{{\varepsilon }_{0}}}$. Statement-2: The electric field at a distance r $(r<R)$ from the centre of the sphere is $\frac{\rho r}{3{{\varepsilon }_{0}}}$   AIEEE  Solved  Paper-2012

A)
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of statement-1.

B)
Statement 1 is true Statement 2 is false.

C)
Statement 1 is false Statement 2 is true.

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

• question_answer30) Proton, Deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively ${{r}_{p}},{{r}_{d}}$ and ${{r}_{\alpha }}$. Which one of the following relation is correct?   AIEEE  Solved  Paper-2012

A)
${{r}_{\alpha }}={{r}_{p}}={{r}_{d}}$

B)
${{r}_{\alpha }}={{r}_{p}}<{{r}_{d}}$

C)
${{r}_{\alpha }}>{{r}_{d}}>{{r}_{p}}$

D)
${{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}$

• question_answer31) Which among the following will be named as dibromidobis (ethylene diamine) chromium (III) bromide?   AIEEE  Solved  Paper-2012

A)
$[Cr\,{{(en)}_{3}}]B{{r}_{3}}$

B)
$[Cr\,{{(en)}_{2}}B{{r}_{2}}]Br$

C)
${{[Cr\,(en)B{{r}_{4}}]}^{-}}$

D)
$[Cr\,(en)B{{r}_{2}}]Br$

• question_answer32) Which method of purification is represented by the following equation: $Ti\,(s)+2{{I}_{2}}(g)\xrightarrow{523K}Ti{{I}_{4}}(g)\xrightarrow{1700K}$ $Ti(s)+2{{I}_{2}}(g)$   AIEEE  Solved  Paper-2012

A)
Zone refining

B)
Cupellation

C)
Polling

D)
Van Arkel

• question_answer33) Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :   AIEEE  Solved  Paper-2012

A)
75 pm

B)
300 pm

C)
240 pm

D)
152 pm

• question_answer34) The molecule having smallest bond angle is :   AIEEE  Solved  Paper-2012

A)
$NC{{l}_{3}}$

B)
As$C{{l}_{3}}$

C)
Sb$C{{l}_{3}}$3

D)
$PC{{l}_{3}}$

• question_answer35) Which of the following compounds can be detected by Molisch?s test :   AIEEE  Solved  Paper-2012

A)
Nitro compounds

B)
Sugars

C)
Amines

D)
Primary alcohols

• question_answer36) The incorrect expression among the following is:   AIEEE  Solved  Paper-2012

A)
$\frac{\Delta {{G}_{system}}}{\Delta {{S}_{total}}}=-T$

B)
In isothermal process, ${{w}_{reversible}}=-nRT\,\,\ell n\frac{{{V}_{f}}}{{{V}_{i}}}$

C)
$InK=\frac{\Delta {{H}^{o}}-T\Delta {{S}^{o}}}{RT}$

D)
$K={{e}^{-\Delta {{G}^{o}}/RT}}$

• question_answer37) The density of a solution prepared by dissolving 120 g of urea (mol. mass = 60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is :   AIEEE  Solved  Paper-2012

A)
0.50 M

B)
1.78 M

C)
1.02 M

D)
2.05 M

• question_answer38) The species which can best serve as an initiator for the cationic polymerization is :   AIEEE  Solved  Paper-2012

A)
$LiAI{{H}_{4}}$

B)
$HN{{O}_{3}}$

C)
$AlC{{l}_{3}}$

D)
$BaLi$

• question_answer39) Which of the following on thermal decomposition yields a basic as well as acidic oxide?   AIEEE  Solved  Paper-2012

A)
$NaN{{O}_{3}}$

B)
$KCl{{O}_{3}}$

C)
$CaC{{O}_{3}}$

D)
$N{{H}_{4}}N{{O}_{3}}$

• question_answer40) The standard reduction potentials for $Z{{n}^{2}}/Zn,N{{i}^{2+}}/Ni$ and $F{{e}^{2+}}/Fe$ are $-0.76,-0.23$and $-0.44$ V respectively. The reaction $X+{{Y}^{2}}+\to {{X}^{2+}}Y$ will be spontaneous when :   AIEEE  Solved  Paper-2012

A)
$X=Ni,\,Y=Fe$

B)
$X=Ni,\,Y=Zn$

C)
$X=Fe,\,Y=Zn$

D)
$X=Zn,\,Y=Ni$

• question_answer41) According to Freundlich adsorption isotherm which of the following is correct?   AIEEE  Solved  Paper-2012

A)
$\frac{x}{m}\propto {{p}^{o}}$

B)
$\frac{x}{m}\propto {{p}^{1}}$

C)
$\frac{x}{m}\propto {{p}^{1/n}}$

D)
All the above are correct for different ranges of pressure

• question_answer42) The equilibrium constant $({{K}_{c}})$ for the reaction ${{N}_{2}}(g)+{{O}_{2}}(g)\to 2NO\,\,(g)$ at temperature T is $4\times {{10}^{-4}}$. The value of ${{K}_{c}}$ for the reaction $NO(g)\to \frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}\,\,\,{{O}_{2}}(g)$ at the same temperature is :   AIEEE  Solved  Paper-2012

A)
0.02

B)
$2.5\times {{10}^{2}}$

C)
$4\times {{10}^{-4}}$

D)
50.0

• question_answer43) The compressibility factor for a real gas at high pressure is :   AIEEE  Solved  Paper-2012

A)
$1+RT/pb$

B)
1

C)
$1+pb/RT$

D)
$1-pb/RT$

• question_answer44) Which one of the following statements is correct?   AIEEE  Solved  Paper-2012

A)
All amino acids except lysine are optically active

B)
All amino acids are optically active

C)
All amino acids except glycine are optically active

D)
All amino acids except glutamic acids are optically active

• question_answer45) Aspirin is known as:   AIEEE  Solved  Paper-2012

A)
Acetyl salicylic acid

B)
Phenyl salicylate

C)
Acetyl salicylate

D)
Methyl salicylic acid

• question_answer46) Ortho-Nitrophenol is less soluble in water than p- and m- Nitrophenols because :   AIEEE  Solved  Paper-2012

A)
o-Nitrophenol is more volatile steam than those of m- and p-isomers.

B)
o-Nitrophenol shows Intramolecular H-bonding

C)
o-Nitrophenol shows intermolecular H-bonding

D)
Melting point of o-Nitrophenol is lower than those of m- and p-isomers.

• question_answer47) How many chiral compounds are possible on monochlorination of 2- methyl butane?   AIEEE  Solved  Paper-2012

A)
8

B)
2

C)
4

D)
6

• question_answer48) Very pure hydrogen (99.9) can be made by which of the following processes?   AIEEE  Solved  Paper-2012

A)
Reaction of methane with steam

B)
Mixing natural hydrocarbons of high molecular weight

C)
Electrolysis of water

D)
Reaction of salts like hydrides with water

• question_answer49) The electrons identified by quantum numbers n and $\ell$ : (a) $n=4,\,\,\ell =1$                         (b) $n=4,\,\,\ell =0$ (c) $n=3,\,\,\ell =2$                         (d) $n=3,\,\,\ell =1$can be placed in order of increasing energy as :   AIEEE  Solved  Paper-2012

A)
$(c)<(d)<(b)<(a)$

B)
$(d)<(b)<(c)<(a)$

C)
$(b)<(d)<(a)<(c)$

D)
$(a)<(c)<(b)<(d)$

• question_answer50) For a first order reaction (A) $\to$ products the concentration of A changes from 0.1 M to 0.025Min 40minutes. The rate of reaction when the concentration of A is 0.01 M is :   AIEEE  Solved  Paper-2012

A)
$1.73\times {{10}^{-5}}$ M/min

B)
$3.47\times {{10}^{-4}}$ M/min

C)
$3.47\times {{10}^{-5}}$ M/min

D)
$1.73\times {{10}^{-4}}$ M/min

• question_answer51) Iron exhibits $+2$ and $+3$ oxidation states. Which of the following statements about iron is incorrect?   AIEEE  Solved  Paper-2012

A)
Ferrous oxide is more basic in nature than the ferric oxide.

B)
Ferrous compounds are relatively more ionic than the corresponding ferric compounds

C)
Ferrous compounds are less volatile than the corresponding ferric compounds

D)
Ferrous compounds are more easily hydrolysed than the corresponding ferric compounds.

• question_answer52) The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, ${{K}_{a}}$ of the acid is :   AIEEE  Solved  Paper-2012

A)
$3\times {{10}^{-1}}$

B)
$1\times {{10}^{-3}}$

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

D)
$1\times {{10}^{-7}}$

• question_answer53) Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of mono substituted alkyl halide?   AIEEE  Solved  Paper-2012

A)
Tertiary butyl chloride

B)
Neopentane

C)
Isohexane

D)
Neohexane

• question_answer54) ${{K}_{f}}$ for water is $1.86$K kg $mo{{l}^{-1}}$. If your automobile radiator holds $1.0$ kg of water, how may grams of ethylene glycol $({{C}_{2}}{{H}_{6}}{{O}_{2}})$ must you add to get the freezing point of the solution lowered to $-{{2.8}^{o}}C$?   AIEEE  Solved  Paper-2012

A)
72 g

B)
93 g

C)
39 g

D)
27 g

• question_answer55) What is DDT among the following :   AIEEE  Solved  Paper-2012

A)
Greenhouse gas

B)
A fertilizer

C)

D)

• question_answer56) The increasing order of the ionic radii of the given isoelectronic species is :   AIEEE  Solved  Paper-2012

A)
$C{{l}^{-}},C{{a}^{2+}},{{K}^{+}},{{S}^{2-}}$

B)
${{S}^{2-}},C{{l}^{-}},C{{a}^{2+}},{{K}^{+}}$

C)
$C{{a}^{2+}},{{K}^{+}},C{{l}^{-}},{{S}^{2-}}$

D)
${{K}^{+}},{{S}^{2-}},C{{a}^{2+}},C{{l}^{-}}$

• question_answer57) $2-$ Hexyne gives trans $-2-$Hexene on treatment with :   AIEEE  Solved  Paper-2012

A)
$Pt/{{H}_{2}}$

B)
$Li/N{{H}_{3}}$

C)
$Pd/BaS{{O}_{4}}$

D)
$LiAI{{H}_{4}}$

• question_answer58) Iodoform can be prepared from all except :   AIEEE  Solved  Paper-2012

A)
Ethyl methyl ketone

B)
Isopropyl alcohol

C)
3-Methyl-2-butanone

D)
Isobutyl alcohol

• question_answer59) In which of the following pairs the two species are not is structural?   AIEEE  Solved  Paper-2012

A)
$C{{O}_{3}}^{2-}$ and $N{{O}_{3}}^{-}$

B)
$PC{{l}_{4}}^{+}$and $SiC{{l}_{4}}$

C)
$P{{F}_{5}}$ and $Br{{F}_{5}}$

D)
$Al{{F}_{6}}^{3-}$ and $S{{F}_{6}}$

• question_answer60) In the given transformation, which the following is the most appropriate reagent?                AIEEE  Solved  Paper-2012

A)
$N{{H}_{2}}N{{H}_{2}},\overset{\Theta }{\mathop{O}}\,H$

B)
$Zn-Hg/HCl$

C)
$Na,Liq,N{{H}_{3}}$

D)
$NaB{{H}_{4}}$

• question_answer61) The equation ${{e}^{\sin x}}-{{e}^{-\sin x}}-4=0$ has:   AIEEE  Solved  Paper-2012

A)
infinite number of real roots

B)
no real roots

C)
exactly one real root

D)
exactly four real roots

• question_answer62) Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2\hat{b}$ and $\vec{d}=5\hat{a}-4\hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is:   AIEEE  Solved  Paper-2012

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

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

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

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

• question_answer63) A spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is:   AIEEE  Solved  Paper-2012

A)
$\frac{9}{7}$

B)
$\frac{7}{9}$

C)
$\frac{2}{9}$

D)
$\frac{9}{2}$

• question_answer64) Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + .... + (361 + 380 + 400) is 8000. Statement-2: $\sum\limits_{k=1}^{n}{({{k}^{3}}-{{(k-1)}^{3}}={{n}^{3}}}$, for any natural number n.   AIEEE  Solved  Paper-2012

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) The negation of the statement ?If I become a teacher, then I will open a school? is:   AIEEE  Solved  Paper-2012

A)
I will become a teacher and I will not open a school.

B)
Either I will not become a teacher or I will not open a school.

C)
Neither I will become a teacher nor I will open a school

D)
I will not become a teacher or I will open a school.

• question_answer66) If the integral $\int{\frac{5\tan x}{\tan x-2}dx=x+a\,\ell n\left| \sin x-2\cos x \right|+k}$, then a is equal to:   AIEEE  Solved  Paper-2012

A)
$-1$

B)
$-2$

C)
1

D)
2

• question_answer67) Statement-1: An equation of a common tangent to the parabola ${{y}^{2}}=16\sqrt{3}x$ and the ellipse $2{{x}^{2}}+{{y}^{2}}=4$ is $y=2x+2\sqrt{3}$. Statement-2: If the line $mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola ${{y}^{2}}=16\sqrt{3}x$ and the ellipse $2{{x}^{2}}+{{y}^{2}}=4$, then m satisfies${{m}^{4}}+2{{m}^{2}}=24$.   AIEEE  Solved  Paper-2012

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_answer68) Let $A=\left( \begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \\ \end{matrix} \right)$. If ${{\mu }_{1}}$ and ${{\mu }_{2}}$ are column matrices such that A{{u}_{1}}\left( \begin{align} & 1 \\ & 0 \\ & 0 \\ \end{align} \right) and A{{u}_{2}}\left( \begin{align} & 0 \\ & 1 \\ & 0 \\ \end{align} \right), then ${{u}_{1}}+{{u}_{2}}$ is equal to:   AIEEE  Solved  Paper-2012

A)
\left( \begin{align} & -1 \\ & 1 \\ & 0 \\ \end{align} \right)

B)
\left( \begin{align} & -1 \\ & 1 \\ & -1 \\ \end{align} \right)

C)
\left( \begin{align} & -1 \\ & -1 \\ & 0 \\ \end{align} \right)

D)
\left( \begin{align} & 1 \\ & -1 \\ & -1 \\ \end{align} \right)

• question_answer69) If n is a positive integer, then ${{\left( \sqrt{3}+1 \right)}^{2n}}-{{\left( \sqrt{3}-1 \right)}^{2n}}$ is:   AIEEE  Solved  Paper-2012

A)
an irrational number

B)
an odd positive integer

C)
an even positive integer

D)
a rational number other than positive integers

• question_answer70) If 100 times the 100th term of an AP with non zero common  difference equals the 50 times its 50th term, then the 150th term of this AP is :   AIEEE  Solved  Paper-2012

A)
-150

B)
150 times its 50th term

C)
150

D)
zero

• question_answer71) In a $\Delta PQR$, if $3\sin P+4\cos Q=6$ and $4\sin Q+3\cos P=1$, then the angle R is equal to:   AIEEE  Solved  Paper-2012

A)
$\frac{5\pi }{6}$

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

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

D)
$\frac{3\pi }{4}$

• question_answer72) A equation of a plane parallel to the plane $x-2y+2z-5=0$and at a unit distance from the origin is:     AIEEE  Solved  Paper-2012

A)
$x-2y+2z-3=0$

B)
$x-2y+2z+1=0$

C)
$x-2y+2z-1=0$

D)
$x-2y+2z+5=0$

• question_answer73) If the line $2x+y=k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals :   AIEEE  Solved  Paper-2012

A)
$\frac{29}{5}$

B)
5

C)
6

D)
$\frac{11}{5}$

• question_answer74) Let ${{x}_{1}},{{x}_{2}},\,....\,,{{x}_{n}}$ be n observations, and let $\overline{x}$ be their arithmetic mean and ${{\sigma }^{2}}$ be the variance Statement-1: Variance of $2{{x}_{1}},2{{x}_{2}},\,......,\,2{{x}_{n}}$ is $4{{\sigma }^{2}}$. Statement-2: Arithmetic mean $2{{x}_{1}},2{{x}_{2}},\,......,\,2{{x}_{n}}$ is $4\overline{x}$.   AIEEE  Solved  Paper-2012

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_answer75) The population p(t) at time t of a certain mouse species satisfies the differential equation$\frac{dp(t)}{dt}=0.5\,p(t)-450$If $p(0)=850$, then the time at which the population becomes zero is :   AIEEE  Solved  Paper-2012

A)
$2\,\ell n18$

B)
$\ell n\,9$

C)
$\frac{1}{2}\ell n\,18$

D)
$\ell n\,18$

• question_answer76) Let a, $b\in R$ be such that the function f given by $f(x)=\ell n\left| x \right|+b{{x}^{2}}+ax,\,x\ne 0$ has extreme values at $x=-1$ and $x=2$. Statement-1: f has local maximum at $x=-1$ and at $x=2$. Statement-2: $a=\frac{1}{2}$ and $b=\frac{-1}{4}$.   AIEEE  Solved  Paper-2012

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_answer77) The area bounded between the parabolas ${{x}^{2}}=\frac{y}{4}$ and ${{x}^{2}}=9y$ and the straight line $y=2$is:   AIEEE  Solved  Paper-2012

A)
$20\sqrt{2}$

B)
$\frac{10\sqrt{2}}{3}$

C)
$\frac{20\sqrt{2}}{3}$

D)
$10\sqrt{2}$

• question_answer78) Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:   AIEEE  Solved  Paper-2012

A)
880

B)
629

C)
630

D)
879

• question_answer79) If f : $R\to R$ is a function defined by $f(x)=[x]\cos \left( \frac{2x-1)}{2} \right)\pi$, where $[x]$ denotes the greatest integer function, then f is:   AIEEE  Solved  Paper-2012

A)
continuous for every real $x$.

B)
discontinuous only at $x=0$.

C)
discontinuous only at non-zero integral values of $x$.

D)
continuous only at $x=0$.

• question_answer80) If the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then k is equal to :   AIEEE  Solved  Paper-2012

A)
$-1$

B)
$\frac{2}{9}$

C)
$\frac{9}{2}$

D)
0

• question_answer81) Three numbers are chosen at random without replacement from {1, 2, 3, ..., 8}. The probability that their minimum is 3, given that their maximum is 6, is :   AIEEE  Solved  Paper-2012

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

B)
$\frac{1}{5}$

C)
$\frac{1}{4}$

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

• question_answer82) If $z\ne 1$ and $\frac{{{z}^{2}}}{z-1}$ is real, then the point represented by the complex number z lies :   AIEEE  Solved  Paper-2012

A)
either on the real axis or on a circle passing through the origin.

B)
on a circle with centre at the origin.

C)
either on the real axis or on a circle not passing through the origin.

D)
on the imaginary axis.

• question_answer83) Let P and Q be $3\times 3$ matrices $P\ne Q$. If ${{P}^{3}}={{Q}^{3}}$ and ${{P}^{2}}={{Q}^{2}}$, then determinant of $({{P}^{2}}={{Q}^{2}})$ is equal to :   AIEEE  Solved  Paper-2012

A)
$-2$

B)
1

C)
0

D)
$-1$

• question_answer84) If $g(x)=\int\limits_{0}^{x}{\cos 4t\,\,dt}$, then $g(x+\pi )$ equals   AIEEE  Solved  Paper-2012

A)
$\frac{g(x)}{g(\pi )}$

B)
$g(x)+g(\pi )$

C)
$g(x)-g(\pi )$

D)
$g(x).\,g(\pi )$

• question_answer85) The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is :   AIEEE  Solved  Paper-2012

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

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

C)
$\frac{6}{5}$

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

• question_answer86) Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is :   AIEEE  Solved  Paper-2012

A)
${{5}^{2}}$

B)
${{3}^{5}}$

C)
${{2}^{5}}$

D)
${{5}^{3}}$

• question_answer87) An ellipse is drawn by taking a diameter of the circle ${{(x-1)}^{2}}+{{y}^{2}}=1$ as its semi-minor axis and a diameter of the circle ${{x}^{2}}+{{(y-2)}^{2}}=4$ is semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is :   AIEEE  Solved  Paper-2012

A)
$4{{x}^{2}}+{{y}^{2}}=4$

B)
${{x}^{2}}+4{{y}^{2}}=8$

C)
$4{{x}^{2}}+{{y}^{2}}=8$

D)
${{x}^{2}}+4{{y}^{2}}=16$

• question_answer88) Consider the function, $f(x)=\left| x-2 \right|+\left| x-5 \right|,x\in R$. Statement-1: $f'(4)=0$ Statement-2: $f$ is continuous in [2, 5], differentiable in (2, 5) and $f(2)=f(5)$.   AIEEE  Solved  Paper-2012

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 corect explanation for Statement-1.

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

• question_answer89) A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. if the area of the triangle OPQ is least, then the slope of the line PQ is :   AIEEE  Solved  Paper-2012

A)
$-\frac{1}{4}$

B)
$-4$

C)
$-2$

D)
$-\frac{1}{2}$

• question_answer90) Let ABCD be a parallelogram such that $\overrightarrow{AB}=\vec{q},\,\,\overrightarrow{AD}=\vec{p}$ and $\angle BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\vec{r}$ is given by :   AIEEE  Solved  Paper-2012

A)
$\vec{r}=3\vec{q}-\frac{3(\vec{p}.\,\vec{q})}{(\vec{p}.\,\vec{p})}\vec{p}$

B)
$\vec{r}=-\vec{q}+\left( \frac{\vec{p}.\,\vec{q}}{\vec{p}.\,\vec{p}} \right)\vec{p}$

C)
$\vec{r}=\vec{q}-\left( \frac{\vec{p}.\,\vec{q}}{\vec{p}.\,\vec{p}} \right)\vec{p}$

D)
$\vec{r}=-3\vec{q}+\frac{3(\vec{p}.\,\vec{q})}{(\vec{p}.\,\vec{p})}\vec{p}$