Solved papers for JEE Main & Advanced AIEEE Solved Paper-2010

AIEEE Solved Paper-2010 Total Questions - 90

1) Directions Q. No. 1 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The initial shape of the wavefront of the beam is - AIEEE Solved Paper-2010

A)

planar

B)

convex

C)

concave

D)

convex near the axis and concave near the periphery

View Answer
2) Directions Q. No. 2 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is ? AIEEE Solved Paper-2010

A)

maximum on the axis of the beam

B)

minimum on the axis of the beam

C)

the same everywhere in the beam

D)

directly proportional to the intensity I

View Answer
3) Directions Q. No. 3 are based on the following paragraph. An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\] where \[{{\mu }_{0}}\] and \[{{\mu }_{2}}\] are positive constants and \[I\] is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will - AIEEE Solved Paper-2010

A)

travel as a cylindrical beam

B)

diverge

C)

converge

D)

diverge near the axis and converge near the periphery

View Answer
4) Directions Q. No. 4 are based on the following paragraph. A nucleus of mass \[M+\Delta m\] is at rest and decays into two daughter nuclei of equal mass \[\frac{M}{2}\] each. Speed of light is c. The speed of daughter nuclei is ? AIEEE Solved Paper-2010

A)

\[c\sqrt[{}]{\frac{\Delta m}{M+\Delta m}}\]

B)

\[c\frac{\Delta m}{M+\Delta m}\]

C)

\[c\sqrt[{}]{\frac{2\Delta m}{M}}\]

D)

\[c\sqrt[{}]{\frac{\Delta m}{M}}\]

View Answer
5) Directions Q. No. 5 are based on the following paragraph. A nucleus of mass \[M+\Delta m\] is at rest and decays into two daughter nuclei of equal mass \[\frac{M}{2}\] each. Speed of light is c. The binding energy per nucleon for the parent nucleus is\[{{E}_{1}}\]and that for the daughter nuclei is\[{{E}_{2}}\]. Then ? AIEEE Solved Paper-2010

A)

\[{{E}_{1}}=2{{E}_{2}}\]

B)

\[{{E}_{2}}=2{{E}_{1}}\]

C)

\[{{E}_{1}}>{{E}_{2}}\]

D)

\[{{E}_{2}}>{{E}_{1}}\]

View Answer
6) Directions: Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is\[{{V}_{0}}\]and the maximum kinetic energy of the photoelectrons is\[{{K}_{max}}\]. When the ultraviolet light is replaced by X-rays, both\[{{V}_{0}}\]and\[{{K}_{max}}\] increase. Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because the range of frequencies present in the incident light. Directions: Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. AIEEE Solved Paper-2010

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 not the correct explanation of Statement-1.

D)

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

View Answer
7) Directions: Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement- 2: Principle of conservation of momentum holds true for all kinds of collisions. Directions: Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. AIEEE Solved Paper-2010

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 not the correct explanation of Statement-1.

D)

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

View Answer
8)   The figure shows the position - time (x - t) graph of one-dimensional motion of the body of mass 0.4 kg. The magnitude of each impulse is ? AIEEE Solved Paper-2010

A)

0.2 Ns

B)

0.4 Ns

C)

0.8 Ns

D)

1.6 Ns

View Answer
9) Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX? is given by - AIEEE Solved Paper-2010

A)

B)

C)

D)

View Answer
10)   A ball is made of a material of density \[\rho \] where \[{{\rho }_{oil}}<\rho <{{\rho }_{water}}\]with\[{{\rho }_{oil}}\]and\[{{\rho }_{water}}\] representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position? AIEEE Solved Paper-2010

A)



B)

C)

D)



View Answer
11)   A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field\[\overrightarrow{E}\]at the centre O is ? AIEEE Solved Paper-2010

A)

\[\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]

B)

\[\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]

C)

       \[-\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]

D)

       \[-\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}\]

View Answer
12)   A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is- AIEEE Solved Paper-2010

A)

0.25

B)

0.5

C)

       0.75

D)

       0.99

View Answer
13)   The respective number of significant figures for the numbers 23.023, 0.0003 and\[2.1\times {{10}^{3}}\] are - AIEEE Solved Paper-2010

A)

4, 4, 2

B)

       5, 1, 2    23.023 significant fig. 5 0.0003 significant fig. 1 \[2.1\times {{10}^{3}}\]significant fig. 2

C)

       5, 1, 5

D)

       5, 5, 2

View Answer
14)   The combination of gates shown below yields AIEEE Solved Paper-2010

A)

NAND gate

B)

OR gate

C)

NOT gate

D)

       XOR gate

View Answer
15)   If a source of power 4 kW produces\[{{10}^{20}}\]photons/second, the radiation belongs to a part of the spectrum called ? AIEEE Solved Paper-2010

A)

\[\gamma -\]rays

B)

       X-rays

C)

       ultraviolet rays

D)

       microwaves

View Answer
16)   A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be ? AIEEE Solved Paper-2010

A)

\[\frac{A-Z-4}{Z-2}\]

B)

       \[\frac{A-Z-8}{Z-4}\]

C)

\[\frac{A-Z-4}{Z-8}\]

D)

       \[\frac{A-Z-12}{Z-4}\]

View Answer
17) Let there be a spherically symmetric charge distribution with charge density varying as\[\rho (r)={{\rho }_{0}}\left( \frac{5}{4}-\frac{r}{R} \right)\]up to\[r=R,\]and\[\rho (r)=0\]for\[r>R,\]where r is the distance from the origin. The electric field at a distance \[r(r<R)\]from the origin is given by ? AIEEE Solved Paper-2010

A)

\[\frac{{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)\]

B)

       \[\frac{4\pi {{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)\]

C)

       \[\frac{{{\rho }_{0}}r}{4{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)\]

D)

       \[\frac{4{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)\]

View Answer
18)   In a series LCR circuit\[R=200\,\,\Omega \]and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by\[30{}^\circ \]. On taking out the inductor from the circuit the current leads the voltage by \[30{}^\circ \]. The power dissipated in the LCR circuit is ? AIEEE Solved Paper-2010

A)

242 W

B)

       305 W

C)

210 W

D)

       Zero W

View Answer
19) In the circuit shown below, the key K is closed at\[t=0.\]the current through the battery is ? AIEEE Solved Paper-2010

A)

\[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]at \[t=0\]and \[\frac{V}{{{R}_{2}}}\]at\[t=\infty \]

B)

\[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\]at \[t=0\]and \[\frac{V}{{{R}_{2}}}\]at \[t=\infty \]

C)

\[\frac{V}{{{R}_{2}}}\]at\[t=0\]and \[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\]at\[t=\infty \]

D)

\[\frac{V}{{{R}_{2}}}\]at \[t=0\]and \[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\]at\[t=\infty \]

View Answer
20) A particle is moving with velocity ) \[\overrightarrow{v}=K(y\hat{i}+x\hat{j})\]where K is a constant. The general equation for its path is ? AIEEE Solved Paper-2010

A)

\[{{y}^{2}}={{x}^{2}}+constant\]

B)

\[y={{x}^{2}}+constant\]

C)

\[{{y}^{2}}=x+constant\]

D)

\[xy=constant\]

View Answer
21)   Let C be the capacitance of a capacitor discharging through a resistor R. Suppose\[{{t}_{1}}\]is the time taken for the energy stored in the capacitor to reduce to half its initial value and \[{{t}_{2}}\]is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio \[{{t}_{1}}/{{t}_{2}}\]will be ? AIEEE Solved Paper-2010

A)

2

B)

                       1

C)

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

D)

       \[\frac{1}{4}\]

View Answer
22) A rectangular loop has a sliding connector PQ of length\[l\]and resistance\[R\,\Omega \]and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents\[{{I}_{1}},{{I}_{2}}\]and I are ? AIEEE Solved Paper-2010

A)

\[{{I}_{1}}={{I}_{2}}=\frac{B/v}{6R},I=\frac{B/v}{3R}\]

B)

\[{{I}_{1}}=-{{I}_{2}}=\frac{B/v}{R},I=\frac{2B/v}{R}\]

C)

\[{{I}_{1}}={{I}_{2}}=\frac{B/v}{3R},I=\frac{2B/v}{3R}\]

D)

\[{{I}_{1}}={{I}_{2}}=I=\frac{B/v}{R}\]

View Answer
23)   The equation of a wave on a string of linear mass density\[0.04\text{ }kg\text{ }{{m}^{1}}\]is given by\[y=0.02\] (m) \[\sin \left[ 2\pi \left( \frac{t}{0.04(s)}-\frac{x}{0.50(m)} \right) \right]\].The tension in the string is ? AIEEE Solved Paper-2010

A)

6.25 N

B)

       4.0 N

C)

       12.5 N

D)

       0.5 N

View Answer
24) Two fixed frictionless inclined planes making an angle\[30{}^\circ \]and\[60{}^\circ \]with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B? AIEEE Solved Paper-2010

A)

\[4.9\text{ }m{{s}^{2}}\]in vertical direction

B)

\[4.9\text{ }m{{s}^{2}}\] in horizontal direction

C)

\[9.8\text{ }m{{s}^{2}}\]in vertical direction

D)

Zero

View Answer
25) For a particle in uniform circular motion, the acceleration\[\overrightarrow{a}\]at a point\[P(R,\text{ }\theta )\]on the circle of radius R is (Here\[\theta \]is measured from the x-axis) AIEEE Solved Paper-2010

A)

\[\frac{{{v}^{2}}}{R}\hat{i}+\frac{{{v}^{2}}}{R}\hat{j}\]

B)

       \[-\frac{{{v}^{2}}}{R}\cos \theta \hat{i}+\frac{{{v}^{2}}}{R}\sin \theta \hat{j}\]

C)

\[-\frac{{{v}^{2}}}{R}sin\theta \hat{i}+\frac{{{v}^{2}}}{R}\cos \theta \hat{j}\]

D)

\[-\frac{{{v}^{2}}}{R}\cos \theta \hat{i}-\frac{{{v}^{2}}}{R}sin\theta \hat{j}\]

View Answer
26)   A small particle of mass m is projected at an angle\[\theta \]with the x-axis with an initial velocity \[{{v}_{0}}\] in the\[x-y\]plane as shown in the figure. At a time \[t<\frac{{{v}_{0}}\sin \theta }{g},\] the angular momentum of the particle is ? AIEEE Solved Paper-2010

A)

\[\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{i}\]

B)

\[-mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{j}\]

C)

\[mg{{v}_{0}}t\cos \theta \hat{k}\]

D)

       \[-\frac{1}{2}mg{{v}_{0}}{{t}^{2}}\cos \theta \hat{k}\]

View Answer
27)   Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of\[30{}^\circ \]with each other. When suspended in a liquid of density\[0.8\text{ }g\text{ }c{{m}^{3}},\] the angle remains the same. If density of the material of the sphere is\[1.6\text{ }g\text{ }c{{m}^{3}},\] the dielectric constant of the liquid is ? AIEEE Solved Paper-2010

A)

1

B)

4

C)

       3

D)

2

View Answer
28)   A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length\[s={{t}^{3}}+5,\]where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when\[t=2s\] is nearly. AIEEE Solved Paper-2010

A)

\[14\text{ }m/{{s}^{2}}\]

B)

                       \[13\text{ }m/{{s}^{2}}\]

C)

       \[12\text{ }m/{{s}^{2}}\]

D)

       \[7.2\text{ }m/{{s}^{2}}\]

View Answer
29)   The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]where a and b are constants and\[x\]is the distance between the atoms. If the dissociation energy of the molecule is \[D=[U(x=\infty )-{{U}_{at\,equilibrium}}],D\]is ? AIEEE Solved Paper-2010

A)

\[\frac{{{b}^{2}}}{6a}\]

B)

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

C)

       \[\frac{{{b}^{2}}}{12a}\]

D)

       \[\frac{{{b}^{2}}}{4a}\]

View Answer
30)   Two conductors have the same resistance at \[0{}^\circ C\]but their temperature coefficients of resistance are\[{{\alpha }_{1}}\]and\[{{\alpha }_{2}}\]. the respective temperature coefficients of their series and parallel combinations are nearly ? AIEEE Solved Paper-2010

A)

\[\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2},\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2}\]

B)

\[\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2},{{\alpha }_{1}}+{{\alpha }_{2}}\]

C)

\[{{\alpha }_{1}}+{{\alpha }_{2}},\frac{{{\alpha }_{1}}+{{\alpha }_{2}}}{2}\]

D)

\[{{\alpha }_{1}}+{{\alpha }_{2}},\frac{{{\alpha }_{1}}{{\alpha }_{2}}}{{{\alpha }_{1}}+{{\alpha }_{2}}}\]

View Answer
31) In aqueous solution the ionization constants for carbonic acid are\[{{K}_{1}}=4.2\times {{10}^{-7}}\]and \[{{K}_{2}}=4.8\times {{10}^{-11}}\]Selection the correct statement for a saturated 0.034 M solution of the carbonic acid. AIEEE Solved Paper-2010

A)

The concentration of\[{{H}^{+}}\]is double that of\[CO_{3}^{2-}\]

B)

The concentration of\[{{H}^{+}}\]is 0.034 M.

C)

The concentration of\[CO_{3}^{2-}\]is greater than that of\[HCO_{3}^{-}\]

D)

The concentration of\[{{H}^{+}}\]and\[HCO_{3}^{-}\]are approximately equal.

View Answer
32)   Solution product of silver bromide is\[5.0\times {{10}^{-13}}\]. The quantity of potassium bromide (molar mass taken as\[120\text{ }g\text{ }mo{{l}^{-1}}\]) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of \[AgBr\]is AIEEE Solved Paper-2010

A)

\[5.0\times {{10}^{-8}}g\]

B)

       \[1.2\times {{10}^{-10}}\]

C)

       \[1.2\times {{10}^{-9}}g\]

D)

       \[6.2\times {{10}^{-5}}\]

View Answer
33) The correct sequence which shows decreasing order of the ionic radii of the elements is AIEEE Solved Paper-2010

A)

\[{{O}^{2-}}>{{F}^{-}}>N{{a}^{+}}>A{{l}^{3+}}\]

B)

\[A{{l}^{3+}}>M{{g}^{2+}}>N{{a}^{+}}>{{F}^{-}}>{{O}^{2-}}\]

C)

\[N{{a}^{+}}>M{{g}^{2+}}>A{{l}^{3+}}>{{O}^{2-}}>{{F}^{-}}\]

D)

\[N{{a}^{+}}>{{F}^{-}}>M{{g}^{2+}}{{O}^{2-}}A{{l}^{3+}}\]

View Answer
34) In the chemical reactions. The compounds 'A' and 'B' respectively are AIEEE Solved Paper-2010

A)

nitrobenzene and chlorobenzene

B)

nitrobenzene and flurobenzene

C)

phenol and benzene

D)

benzene diazonium chloride and flurobenzene

View Answer
35) If\[{{10}^{-4}}d{{m}^{-3}}\]of water is introduced into a 1.0\[d{{m}^{-3}}\]flask at 300 K, how many moles of water are in in the vapour phase when equilibrium is established? (Given: Vapour pressure of \[{{H}_{2}}O\]at 300 is 3170 pa;\[R=8.314\text{ }J\text{ }{{K}^{-1}}mo{{l}^{-1}})\] AIEEE Solved Paper-2010

A)

\[1.27\times 10\text{ }mo{{l}^{-3}}\]

B)

\[5.56\times 10\text{ }mo{{l}^{-3}}\]

C)

\[1.53\times 10\text{ }mo{{l}^{-2}}\]

D)

\[4346\times 10\text{ }mo{{l}^{-2}}\]

View Answer
36)   From amongst the following alcohols the one that would react fastest with conc,\[HCl\]and anhydrous\[ZNC{{l}_{2}},\]is AIEEE Solved Paper-2010

A)

1- Butanol

B)

       2- Butanol

C)

2- Methylpropan -2-ol

D)

2- Methylpropanol

View Answer
37)   If sodium sulphate is considered to be completely dissociated into cations and anions in equeous solution, the change in freezing point of water\[(\Delta {{T}_{f}}),\], When 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is\[({{K}_{f}}=1.86K\text{ }Kg\text{ }mo{{l}^{-1}})\] AIEEE Solved Paper-2010

A)

0.0186 K

B)

       0.0372 K

C)

       0.0558 K

D)

       0.0744 K

View Answer
38)   Three reactions involving \[{{H}_{2}}Po_{4}^{-}\] are given below: AIEEE Solved Paper-2010

A)

(1)\[{{H}_{3}}P{{o}_{4}}+{{H}_{2}}O\to {{H}_{3}}{{O}^{+}}\to {{H}_{3}}{{O}^{+}}{{H}_{2}}Po_{4}^{-}\] (2) \[{{H}_{2}}Po_{4}^{-}+{{H}_{2}}O\to HPO_{4}^{2-}+{{H}_{3}}{{O}^{+}}\] (3) \[{{H}_{2}}Po_{4}^{-}+O{{H}^{-}}\to {{H}_{3}}P{{O}_{4}}+{{O}^{2-}}\] In which of the above does \[{{H}_{2}}PO_{4}^{-}\]act as an acid? (i) Only

B)

(ii) Only

C)

       (iii) and (ii)

D)

       (iii) only

View Answer
39) The main product of the following reaction is \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}CH(OH)CH{{(C{{H}_{3}})}_{2}}\xrightarrow[{}]{conc.\,{{H}_{2}}S{{O}_{4}}}?\] AIEEE Solved Paper-201

A)

B)

C)

D)

View Answer
40)   The energy required to break one mole of \[ClCl\]bonds in\[C{{l}_{2}}\]is \[242\text{ }kJ\text{ }mo{{l}^{-1}}\]. The longest wavelength of light capable of breaking a single\[ClCl\]bond is (\[C=3\times {{10}^{8}}m{{s}^{-1}}\]and\[{{N}_{A}}\text{=}6.02\times {{10}_{23}}\text{ }mo{{l}^{-1}}\]) AIEEE Solved Paper-2010

A)

494 nm

B)

                       594

C)

       640 nm

D)

       700 nm

View Answer
41)   29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl's method and the evolved ammonia was absorbed in 20 mL of\[0.1\text{ }M\text{ }HCl\]solution. The excess of the acid required 15 mL of 0.1 M\[NaOH\]solution for complete neutralization. The percentage of nitrogen in the compound is AIEEE Solved Paper-2010

A)

29.5

B)

                       59.0

C)

       47.4

D)

       23.7

View Answer
42) Ionisation energy of\[H{{e}^{+}}\]is \[19.6\times {{10}^{-18}}J\,ato{{m}^{-1}}\]. The energy of the first stationary state (\[n=1\]) of \[L{{i}^{2+}}\]is AIEEE Solved Paper-2010

A)

\[8.82\times {{10}^{-17}}J\text{ }ato{{m}^{-1}}\]

B)

\[4.41\times {{10}^{-16}}J\text{ }ato{{m}^{-1}}\]

C)

\[-4.41\times {{10}^{-17}}J\text{ }ato{{m}^{-1}}\]

D)

\[-2.2\times {{10}^{-15}}J\text{ }ato{{m}^{-1}}\]

View Answer
43)   On mixing, heptane and octane form an ideal solution At 373 K, the vapour pressures of the two liquid components (Heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0 g of heptane and 35 g of octane will be (molar mass of heptane\[=100\text{ }g\text{ }mo{{l}^{1}}\]and of octane \[=114\text{ }g\text{ }mo{{l}^{-1}}\]) AIEEE Solved Paper-2010

A)

144.5 kPa

B)

       72.0 kPa

C)

       36.1 kPa

D)

       96.2 kPa

View Answer
44) Which one of the following has an optical isomer? AIEEE Solved Paper-2010

A)

\[{{[Zn{{(en)}_{2}}]}^{2+}}\]

B)

\[{{[Zn(en){{(N{{H}_{3}})}_{2}}]}^{2+}}\]

C)

\[{{[CO{{(en)}_{3}}]}^{3+}}\]

D)

\[{{[CO{{({{H}_{2}}O)}_{4}}(en)]}^{3+}}\]

View Answer
45)   Consider the following bromides The correct order of\[{{S}_{N}}1\]reactivity is AIEEE Solved Paper-2010

A)

\[A>B>C\]

B)

       \[B>C>A\]

C)

       \[B>A>C\]

D)

       \[C>B>A\]

View Answer
46)   One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is- AIEEE Solved Paper-2010

A)

ethene

B)

                       propene

C)

1-butene

D)

       2-butene

View Answer
47)   Consider the reaction: \[C{{l}_{2}}(aq)+{{H}_{2}}S(aq)\to S(s)+2{{H}^{+}}(aq)+2C{{l}^{-}}(aq)\] The rate equation for this reaction is Rate\[=k[C{{l}_{2}}][{{H}_{2}}S]\] Which of these mechanisms is/are consistent with this rate equation? (A) \[\begin{align} & C{{l}_{2}}+{{H}_{2}}S\to {{H}^{+}}+C{{l}^{-}}+C{{l}^{-}}+H{{S}^{-}}(slow) \\ & Cl+H{{S}^{-}}\to {{H}^{+}}+C{{l}^{-}}+S(fast) \\ \end{align}\] (B) \[\begin{align} & {{H}_{2}}S\Leftrightarrow {{H}^{+}}+H{{S}^{-}}(fast\text{ }equilibrium) \\ & C{{l}_{2}}+H{{S}^{-}}\to 2C{{l}^{-}}+{{H}^{+}}+S(slow) \\ \end{align}\] AIEEE Solved Paper-2010

A)

A only

B)

B only

C)

       Both A and B

D)

Neither A nor B

View Answer
48) The Gibbs energy for the decomposition of \[A{{l}_{2}}{{O}_{3}}\]at\[500{}^\circ C\]is as follows: \[\frac{2}{3}A{{l}_{2}}{{O}_{3}}\to \frac{4}{3}Al+{{O}_{2}},\]                                        \[{{\Delta }_{r}}G=+966\,kJ\,mo{{l}^{-1}}\] The potential difference needed for electrolytic reduction of\[A{{l}_{2}}{{O}_{3}}\]at\[500{}^\circ C\]is at least AIEEE Solved Paper-2010

A)

5.0 V

B)

                       4.5 V

C)

       3.0 V

D)

       2.5 V

View Answer
49) The correct order of increasing basicity of the given conjugate bases\[(R=C{{H}_{3}})\]is AIEEE Solved Paper-2010

A)

\[RCO\overline{O}<HC\equiv \overline{C}<\overline{N}{{H}_{2}}<\overline{R}\]

B)

\[RCO\overline{O}<HC\equiv \overline{C}<\overline{R}<\overline{N}{{H}_{2}}\]

C)

\[\overline{R}<HC\equiv \overline{C}<RCO\overline{O}<\overline{N}{{H}_{2}}\]

D)

\[RCO\overline{O}<\overline{N}{{H}_{2}}<HC\equiv \overline{C}<\overline{R}\]

View Answer
50)   The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is AIEEE Solved Paper-2010

A)

144 pm

B)

288 pm

C)

       398 pm

D)

       618 pm

View Answer
51) Out of the following the alkene that exhibits optical isomerism is AIEEE Solved Paper-2010

A)

2-methyl-2-pentene

B)

3-methyl-2-pentene

C)

4-methyl-pentene

D)

3-methyl-1-pentene

View Answer
52)   For a particular reversible reaction at temperature T, \[\Delta H\] and\[\Delta S\]were found to be both +ve. If\[{{T}_{e}}\]is the temperature at equilibrium, the reaction would be spontaneous when AIEEE Solved Paper-2010

A)

\[T={{T}_{e}}\]

B)

\[{{T}_{e}}>T\]

C)

       \[T>{{T}_{e}}\]

D)

       \[{{T}_{e}}\]is 5 times T

View Answer
53)   Percentages of free space in cubic close packed structure and in body centered packed structure are respectively AIEEE Solved Paper-2010

A)

48% and 26%

B)

       30% and 26%

C)

       26% and 32%

D)

       32% and 48%

View Answer
54)   The polymer containing strong intermolecular forces e.g. hydrogen bonding, is AIEEE Solved Paper-2010

A)

natural rubber

B)

       Teflon

C)

nylon 6,6

D)

       polystyrene

View Answer
55) At\[25{}^\circ C,\] the solubility product of\[Mg{{(OH)}_{2}}\]is\[1.0\times {{10}^{-11}}\]. At which pH, will\[M{{g}^{2+}}\]ions start precipitating in the form of\[Mg{{(OH)}_{2}}\]from a solution of\[0.001\text{ }M\text{ }M{{g}^{2+}}\]ions ? AIEEE Solved Paper-2010

A)

8

B)

       9

C)

                       10

D)

       11

View Answer
56) The correct order of\[E_{{{M}^{2+}}/M}^{o}\]values with negative sign for the four successive elements \[Cr,Mn,Fe\]and\[Co\]is AIEEE Solved Paper-2010

A)

\[Cr>Mn>Fe>Co\]

B)

\[Mn>Cr>Fe>Co\]

C)

\[Cr>Fe>Mn>Co\]

D)

\[Fe>Mn>Cr>Co\]

View Answer
57)   Biuret test is not given by AIEEE Solved Paper-2010

A)

proteins

B)

       carbohydrates

C)

polypeptides

D)

urea

View Answer
58)   The time for half life period of a certain reaction \[A\to \] Products is 1 hour. When the initial concentration of the reactant 'A', is 2.0 \[mol~{{L}^{-1}}\],how much time does it take for its concentration come from 0.50 to\[0.25\text{ }mol\text{ }{{L}^{-1}}\]if it is a zero order reaction? AIEEE Solved Paper-2010

A)

1 h

B)

                       4 h

C)

0.5 h

D)

       0.25 h

View Answer
59) A solution containing 2.675 g of\[COC{{l}_{3}}\]⋅ \[6N{{H}_{3}}\](molar mass\[=267.5\text{ }g\,mo{{l}^{-1}}\]) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of\[AgN{{O}_{3}}\]to give 4.78 g of\[AgCl\](molar mass\[=143.5\text{ }g\,mo{{l}^{-1}}\]). The formula of the complex is (At. mass of\[Ag=108\text{ }u\]) AIEEE Solved Paper-2010

A)

\[[COCl{{(N{{H}_{3}})}_{5}}]C{{l}_{2}}\]

B)

\[[CO{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}\]

C)

\[[COCl{{(N{{H}_{3}})}_{4}}]Cl\]

D)

\[[COC{{l}_{3}}{{(N{{H}_{3}})}_{3}}]\]

View Answer
60)   The standard enthalpy of formation of\[N{{H}_{3}}\]is\[-\,46.0\text{ }kJ\text{ }mo{{l}^{-1}}\]. If the enthalpy of formation of\[{{H}_{2}}\]from its atoms is\[-436\text{ }kJ\text{ }mo{{l}^{-1}}\]and that of\[{{N}_{2}}\]is\[-712\text{ }kJ\text{ }mo{{l}^{-1}}\], the average bond enthalpy of\[N-H\]bond in\[N{{H}_{3}}\]] AIEEE Solved Paper-2010

A)

\[-1102\text{ }kJ\text{ }mo{{l}^{-1}}\]

B)

\[-964\text{ }kJ\text{ }mo{{l}^{-1}}\]

C)

       \[+352\text{ }kJ\text{ }mo{{l}^{-1}}\]

D)

       \[+1056\text{ }kJ\text{ }mo{{l}^{-1}}\]

View Answer
61) Consider the following relations \[R=\{(x,y)|x,y\]are real numbers and\[x=wy\]for some rational number w}; \[S=\left\{ \left( \frac{m}{n},\frac{p}{q} \right) \right\}=|m,n,p\]and q are integers such that\[n,q\ne 0\]and\[qm=pn\}\]. Then -

A)

R is an equivalence relation but S is not an equivalence relation

B)

Neither R nor S is an equivalence relation

C)

S is an equivalence relation but R is not an equivalence relation

D)

R and S both are equivalence relations

View Answer
62)   The number of complex numbers z such that \[|z-1|=|z+1|=|z-i|\]equals - AIEEE Solved Paper-2010

A)

0

B)

                       1

C)

       2

D)

       \[\infty \]

View Answer
63)   If\[\alpha \]and\[\beta \]are the roots of the equation \[{{x}^{2}}x\]\[+1=0,\] then\[{{\alpha }^{2009}}+{{\beta }^{2009}}=\] AIEEE Solved Paper-2010

A)

-2

B)

-1

C)

1

D)

2

View Answer
64) Consider the system of linear equations : \[{{x}_{1}}+2{{x}_{2}}+{{x}_{3}}=3\] \[2{{x}_{1}}+3{{x}_{2}}+{{x}_{3}}=3\] \[3{{x}_{1}}+5{{x}_{2}}+2{{x}_{3}}=1\] The system has AIEEE Solved Paper-2010

A)

Infinite number of solutions

B)

Exactly 3 solutions

C)

a unique solution

D)

No solution

View Answer
65)   There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is - AIEEE Solved Paper-2010

A)

3

B)

36

C)

66

D)

       108

View Answer
66)   Let\[f:(1,1)\to R\]be a differentiable function with\[f(0)=1\]and\[f'(0)=1.\]Let\[~g(x)=\] \[=[f{{(2f(x)+2]}^{2}}\]Then\[g'(0)=\] AIEEE Solved Paper-2010

A)

4

B)

-4

C)

0

D)

-2

View Answer
67) Let\[f:R\to R\]be a positive increasing function with \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{f(3x)}{f(x)}=1\].Then \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{f(2x)}{f(x)}=\] AIEEE Solved Paper-2010

A)

1

B)

                       \[\frac{2}{3}\]

C)

       \[\frac{3}{2}\]

D)

       3

View Answer
68) Let\[p(x)\]be a function defined on R such that \[p'(x)=p'(1x),\]for all\[x\in [0,1],p(0)=1\]and\[p(1)=41.\] Then \[\int\limits_{0}^{1}{p(x)}dx\]equals - AIEEE Solved Paper-2010

A)

\[\sqrt{41}\]

B)

                       21

C)

                       41

D)

       42

View Answer
69)   A person is to count 4500 currency notes. Let \[{{a}_{n}}\]denote the number of notes he counts in the\[{{n}^{th}}\]minute. If\[{{a}_{1}}={{a}_{2}}=....={{a}_{10}}=150\]and\[{{a}_{10}},{{a}_{11}},...\]are in an AP with common difference ? 2, then the time taken by him to count all notes is - AIEEE Solved Paper-2010

A)

24 minutes

B)

34 minutes

C)

       125 minutes

D)

       135 minutes

View Answer
70) The equation of the tangent to the curve\[y=x+\frac{4}{{{x}^{2}}},\]that is parallel to the x ? axis, is - AIEEE Solved Paper-2010

A)

y = 0

B)

y = 1

C)

       y = 2

D)

       y = 3

View Answer
71)   The area bounded by the curves\[y=cos\text{ }x\]and\[y=sin\text{ }x\]between the ordinates \[x=0\]and\[x=\frac{3\pi }{2}\]is - AIEEE Solved Paper-2010

A)

\[4\sqrt{2}-2\]

B)

       \[4\sqrt{2}+2\]

C)

       \[4\sqrt{2}-1\]

D)

       \[4\sqrt{2}+1\]

View Answer
72) Solution of the differential equation\[cos\text{ }x\text{ }dy=\] \[y(sin\text{ }xy)dx,\] \[0<x<\frac{\pi }{2}\]is - AIEEE Solved Paper-2010

A)

\[sec\text{ }x=(tan\text{ }x+c)y\]

B)

\[y\text{ }sec\text{ }x=tan\text{ }x+c\]

C)

\[y\text{ }tan\text{ }x=sec\text{ }x+c\]

D)

\[tan\text{ }x=(sec\text{ }x+c)y\]

View Answer
73)   Let\[\overrightarrow{a}=\hat{j}-\hat{k}\]and\[\overrightarrow{c}=\hat{i}-\hat{j}-\hat{k}\]Then the vector \[\overrightarrow{b}\]satisfying\[\overrightarrow{a}\times \overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\] and\[\overrightarrow{a}.\overrightarrow{b}=3\]is - AIEEE Solved Paper-2010

A)

\[-\hat{i}+\hat{j}-2\hat{k}\]

B)

       \[2\hat{i}-\hat{j}+2\hat{k}\]

C)

\[\hat{i}-\hat{j}-2\hat{k}\]

D)

       \[\hat{i}+\hat{j}-2\hat{k}\]

View Answer
74)   If the vectors \[\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k},\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}\]and \[\overrightarrow{c}=\lambda \hat{i}-\hat{j}+\mu \hat{k}\]are mutually orthogonal, then \[(\lambda ,\mu )=\] AIEEE Solved Paper-2010

A)

(-3, 2)

B)

(2, -3)

C)

(-2, 3)

D)

(3, -2)

View Answer
75)   If two tangents drawn from a point P to the parabola\[{{y}^{2}}=4x\]are at right angles, then the locus of P is AIEEE Solved Paper-2010

A)

\[x=1\]

B)

       \[2x+1=0\]

C)

       \[x=1\]

D)

       \[2x1=0\]

View Answer
76)   The line L given by \[\frac{x}{5}+\frac{y}{b}=1\]passes through the point (13, 32). The line K is parallel to L and has the equation \[\frac{x}{c}+\frac{y}{3}=1\].Then the distance between L and K is - AIEEE Solved Paper-2010

A)

\[\frac{23}{\sqrt{15}}\]

B)

       \[\sqrt{17}\]

C)

       \[\frac{17}{\sqrt{15}}\]

D)

       \[\frac{23}{\sqrt{17}}\]

View Answer
77) A line AB in three dimensional space makes angles\[45{}^\circ \]and\[120{}^\circ \]with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle\[\theta \]with the positive z-axis, then\[\theta \]equals - AIEEE Solved Paper-2010

A)

\[30{}^\circ \]

B)

\[45{}^\circ \]

C)

\[60{}^\circ \]

D)

\[75{}^\circ \]

View Answer
78) Let S be a non- empty subset of R. Consider the following statement: P: There is a rational number\[x\in S\]such that\[x>0\] Which of the following statements is the negation of the statement P? AIEEE Solved Paper-2010

A)

There is a rational number\[x\in S\]such that \[x\le 0\]

B)

There is no rational number\[x\in S\]such that \[x\le 0\]

C)

Every rational number\[x\in S\]satisfies \[x\le 0\]

D)

\[x\in S\]and\[x\le 0\] \[\Rightarrow \]\[x\]is not rational

View Answer
79)   Let \[\cos (\alpha +\beta )=\frac{4}{5}\]and let,\[sin(\alpha -\beta )=\frac{5}{13}\]where\[0\le \alpha ,\beta \le \frac{\pi }{4}\].Then tan\[2\alpha =\] AIEEE Solved Paper-2010

A)

\[\frac{25}{16}\]

B)

                       \[\frac{56}{33}\]

C)

\[\frac{19}{12}\]

D)

       \[\frac{20}{7}\]

View Answer
80) The circle\[{{x}^{2}}+{{y}^{2}}=4x+8y+5\]intersects the line\[3x4y=m\]at two distinct points if AIEEE Solved Paper-2010

A)

\[85<m<35\]

B)

\[35<m<15\]

C)

       \[15<m<65\]

D)

       \[35<m<85\]

View Answer
81)   For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is - AIEEE Solved Paper-2010

A)

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

B)

                       \[\frac{11}{2}\]

C)

       \[6\]

D)

       \[\frac{13}{2}\]

View Answer
82)   An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is - AIEEE Solved Paper-2010

A)

\[\frac{1}{3}\]

B)

                       \[\frac{2}{7}\]

C)

       \[\frac{1}{21}\]

D)

       \[\frac{2}{23}\]

View Answer
83) For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is - AIEEE Solved Paper-2010

A)

There is a regular polygon with \[\frac{r}{R}=\frac{1}{2}\]

B)

There is a regular polygon with \[\frac{r}{R}=\frac{1}{\sqrt{2}}\]

C)

There is a regular polygon with \[\frac{r}{R}=\frac{2}{3}\]

D)

There is a regular polygon with \[\frac{r}{R}=\frac{\sqrt{3}}{2}\]

View Answer
84)   The number of\[3\times 3\]non - singular matrices, with four entries as 1 and all other entries as 0, is - AIEEE Solved Paper-2010

A)

Less than 4

B)

       5

C)

       6

D)

at least 7

View Answer
85)   Let\[f:R\to R\]be defined by \[f(x)=\left\{ \begin{matrix}    k-2x, & if & x\le -1 \\    2x+3, & if & x>-1 \\ \end{matrix} \right.\] If\[f\]has a local minimum at\[x=1,\]then a possible value of k is AIEEE Solved Paper-2010

A)

1

B)

                                      0

C)

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

D)

       \[-1\]

View Answer
86) Directions: Questions number 86 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is\[\frac{1}{85}\] Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is \[(\pm 1,\pm 2,\pm 3,\pm 4,\pm 5\}\] Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. AIEEE Solved Paper-2010

A)

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

B)

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

C)

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

D)

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

View Answer
87) Directions: Questions number 87 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let \[{{S}_{1}}=\sum\limits_{j=1}^{10}{j{{(j-1)}^{10}}}{{C}_{j}},{{S}_{2}}=\sum\limits_{j=1}^{10}{{{j}^{10}}{{C}_{j}}}\]and \[{{S}_{3}}=\sum\limits_{j=1}^{10}{{{j}^{2}}^{10}{{C}_{j}}}\] Statement ? 1: \[{{S}_{3}}=55\times {{2}^{9}}.\] Statement ? 2:\[{{S}_{1}}=90\times {{2}^{8}}\]and\[{{S}_{2}}=10\times {{2}^{8}}.\] Statement ? 1 (Assertion) and Statement ? 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. AIEEE Solved Paper-2010

A)

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

B)

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

C)

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

D)

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

View Answer
88) Directions: Questions number 88 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement - 1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane\[xy+z=5.\] Statement - 2: The plane\[xy+z=5\]bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. AIEEE Solved Paper-2010

A)

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

B)

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

C)

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

D)

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

View Answer
89) Directions: Questions number 89 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let\[f:R\to R\]be a continuous function defined by \[f(x)=\frac{1}{{{e}^{x}}+2{{e}^{-x}}}\] Statement - 1: \[f(c)=\frac{1}{3},\]for some\[c\in R\]. Statement - 2: \[0<f(x)\le \frac{1}{2\sqrt{2}},\]for all \[x\in R\]. Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. AIEEE Solved Paper-2010

A)

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

B)

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

C)

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

D)

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

View Answer
90) Directions: Questions number 90 are Assertion - Reason type questions. Each of these questions contains two statements: Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a \[2\times 2\] matrix with non zero entries and let\[{{A}^{2}}=I,\]where I is\[2\times 2\]identity matrix. Define Tr(A) = sum of diagonal elements of A and \[|A|=\]determinant of matrix A. Statement - 1 : Tr(A) = 0 Statement - 2 : \[|A|=1\] Statement - 1 (Assertion) and Statement - 2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. AIEEE Solved Paper-2010

A)

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

B)

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

C)

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

D)

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

View Answer