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

AIEEE Solved Paper-2012 Total Questions - 90

1) 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)

\[2SY\alpha \,\Delta T\]

View Answer
2) 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

View Answer
3) 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)

View Answer
4) 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 \[\vec{k}||\vec{B}\times \vec{E}\]

View Answer
5) 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)

\[\frac{2}{b}\]

View Answer
6) 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

View Answer
7) 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.

View Answer
8) 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

View Answer
9) 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%

View Answer
10) 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)

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

View Answer
11) 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)

View Answer
12) 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)

View Answer
13) 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

View Answer
14) 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%

View Answer
15) 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

View Answer
16) 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

View Answer
17) 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 \[N{{m}^{-1}}\]

View Answer
18) 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)

View Answer
19) 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

View Answer
20) 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

View Answer
21) 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

View Answer
22) 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

View Answer
23) 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

View Answer
24) 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)

\[1:1\]

View Answer
25) 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)

\[2f\]

View Answer
26) 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

View Answer
27) 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)

             \[\frac{({{m}_{1}}+{{m}_{2}}){{n}^{2}}{{h}^{2}}}{2{{m}_{1}}{{m}_{2}}{{r}^{2}}}\]

View Answer
28) 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

View Answer
29) 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.

View Answer
30) 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)

\[{{r}_{\alpha }}={{r}_{d}}>{{r}_{p}}\]

View Answer
31) 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)

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

View Answer
32) 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

View Answer
33) 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

View Answer
34) 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)

\[PC{{l}_{3}}\]

View Answer
35) 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

View Answer
36) 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)

\[K={{e}^{-\Delta {{G}^{o}}/RT}}\]

View Answer
37) 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

View Answer
38) 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)

\[BaLi\]

View Answer
39) 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)

\[N{{H}_{4}}N{{O}_{3}}\]

View Answer
40) 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)

\[X=Zn,\,Y=Ni\]

View Answer
41) 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

View Answer
42) 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

View Answer
43) 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)

\[1-pb/RT\]

View Answer
44) 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

View Answer
45) Aspirin is known as: AIEEE Solved Paper-2012

A)

Acetyl salicylic acid

B)

Phenyl salicylate

C)

Acetyl salicylate

D)

Methyl salicylic acid

View Answer
46) 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.

View Answer
47) How many chiral compounds are possible on monochlorination of 2- methyl butane? AIEEE Solved Paper-2012

A)

8

B)

2

C)

4

D)

6

View Answer
48) 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

View Answer
49) 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)

\[(a)<(c)<(b)<(d)\]

View Answer
50) 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

View Answer
51) 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.

View Answer
52) 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)

\[1\times {{10}^{-7}}\]

View Answer
53) 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

View Answer
54) \[{{K}_{f}}\] 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

View Answer
55) What is DDT among the following : AIEEE Solved Paper-2012

A)

Greenhouse gas

B)

A fertilizer

C)

Biodegradable pollutant

D)

Non-biodegradable pollutant

View Answer
56) 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)

\[{{K}^{+}},{{S}^{2-}},C{{a}^{2+}},C{{l}^{-}}\]

View Answer
57) \[2-\] 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)

\[LiAI{{H}_{4}}\]

View Answer
58) 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

View Answer
59) 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 \[S{{F}_{6}}\]

View Answer
60) 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)

\[NaB{{H}_{4}}\]

View Answer
61) 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

View Answer
62) 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)

\[\frac{\pi }{4}\]

View Answer
63) 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)

\[\frac{9}{2}\]

View Answer
64) 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.

View Answer
65) 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.

View Answer
66) 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

View Answer
67) 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.

View Answer
68) 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)

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

View Answer
69) 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

View Answer
70) 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

View Answer
71) 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)

\[\frac{3\pi }{4}\]

View Answer
72) 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)

\[x-2y+2z+5=0\]

View Answer
73) 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)

\[\frac{11}{5}\]

View Answer
74) 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.

View Answer
75) 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)

\[\ell n\,18\]

View Answer
76) 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.

View Answer
77) 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)

\[10\sqrt{2}\]

View Answer
78) 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

View Answer
79) 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 \[x=0\].

View Answer
80) 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

View Answer
81) 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)

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

View Answer
82) 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.

View Answer
83) 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)

\[-1\]

View Answer
84) 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)

\[g(x).\,g(\pi )\]

View Answer
85) 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)

\[\frac{5}{3}\]

View Answer
86) 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)

\[{{5}^{3}}\]

View Answer
87) 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)

\[{{x}^{2}}+4{{y}^{2}}=16\]

View Answer
88) 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.

View Answer
89) 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)

\[-\frac{1}{2}\]

View Answer
90) 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)

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

View Answer