Solved papers for JEE Main & Advanced AIEEE Solved Paper-2009

AIEEE Solved Paper-2009 Total Questions - 90

1) Direction: Q. No. 1 The question contains Statement-I and Statement-II of the four Choices given after the statements, choose the one that best describe the two statements. STATEMENT-1 For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connected point P to point Q. STATEMENT-2 The net work done by a conservative force on an object moving along a closed loop is zero. AIEEE Solved Paper-2009

A)

Statement - 1 is True, Statement - 2 is False.

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 the correct explanation for Statement-1.

D)

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

View Answer
2) There is a plot of binding energy per nucleon\[{{E}_{b}},\]against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions: (i) \[A+B\to C+\varepsilon \] (ii) \[C\to A+B+\varepsilon \] (iii) \[D+E\to F+\varepsilon \] (iv) \[F\to D+E+\varepsilon \] Where \[\varepsilon \] is the energy released? In which reaction is e positive? AIEEE Solved Paper-2009

A)

(i) and (iv)

B)

(i) and (iii)

C)

(ii) and (iv)

D)

(ii) and (iii).

View Answer
3) A p-n junction (4) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit. The current (I) in the resistor (R) can be shown by: AIEEE Solved Paper-2009

A)

B)

C)

D)

View Answer
4) The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform. Output is: AIEEE Solved Paper-2009

A)

B)

C)

D)

View Answer
5) If\[x,\text{ v}\]and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time? AIEEE Solved Paper-2009

A)

\[{{a}^{2}}{{T}^{2}}+4{{\pi }^{2}}{{v}^{2}}\]

B)

\[aT/x\]

C)

       \[aT+2\pi n\]

D)

       \[aT/v.\]

View Answer
6) In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of\[45{}^\text{o}\]with the x-axis meets the experimental curve at P. The coordinates of P will be AIEEE Solved Paper-2009

A)

(2f, 2f)

B)

\[\left( \frac{f}{2},\frac{f}{2} \right)\]

C)

       \[(f,\text{ }f)\]

D)

       \[(4f,\text{ }4f).\]

View Answer
7)   A thin uniform rod of length l and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is \[\omega \]. Its centre of mass rises to a maximum height of AIEEE Solved Paper-2009

A)

\[\frac{1}{3}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]

B)

\[\frac{1}{6}\frac{\ell \omega }{g}\]

C)

       \[\frac{1}{2}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]

D)

       \[\frac{1}{6}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}\]

View Answer
8) Let\[p(r)=\frac{Q}{\pi {{R}^{4}}}r\]be the charge density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance\[{{r}_{1}}\]from the centre of sphere, the magnitude of electric field is AIEEE Solved Paper-2009

A)

0

B)

\[\frac{Q}{4\pi {{\varepsilon }_{0}}r_{1}^{2}}\]

C)

       \[\frac{Qr_{1}^{2}}{4\pi {{\varepsilon }_{0}}{{R}^{4}}}\]

D)

       \[\frac{Qr_{1}^{2}}{3\pi {{\varepsilon }_{0}}{{R}^{4}}}\]

View Answer
9)   The transition from the state\[n=4\]to\[n=3\]in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from: AIEEE Solved Paper-2009

A)

\[2\to 1\]

B)

\[3\to 2\]

C)

       \[4\to 2\]

D)

       \[5\to 4\]

View Answer
10) One kg of a diatomic gas is at a pressure of \[8\times {{10}^{4}}N/{{m}^{2}}.\] The density of the gas is\[4\text{ }kg/{{m}^{3}}\]. What is the energy of the gas due to its thermal motion? AIEEE Solved Paper-2009

A)

\[3\times {{10}^{4}}J\]

B)

\[5\times {{10}^{4}}J\]

C)

       \[6\times {{10}^{4}}J\]

D)

       \[7\times {{10}^{4}}J.\]

View Answer
11) STATEMENT - 1 The temperature dependence of resistance is usually given as\[R={{R}_{0}}(1+\alpha \,\,\Delta t)\]. The resistance of a wire changes from\[100\,\Omega \]to \[150\,\Omega \] when its temperature is increased from\[27{}^\text{o}C\]to\[227{}^\text{o}C.\] This implies that\[\alpha =2.5\]\[\times {{10}^{3}}/{}^\text{o}C.\] STATEMENT - 2 \[R={{R}_{0}}(1+\alpha \text{ }\Delta t)\]is valid only when the change in the temperature DT is small and\[\Delta R=(R{{R}_{0}})<<{{R}_{0}}.\] AIEEE Solved Paper-2009

A)

Statement - 1 is True, Statement - 2 is False.

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 the correct explanation for Statement - 1.

D)

Statement - 1 is False, Statement - 2 is True.

View Answer
12) Directions Q. Nos. 12 are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius =b) and DA (radius = a) of the loop are joined by the straight wires AB and CD. A steady current is flowing in the loop. Angle made by A B and CD at the origin O is 30°. Another straight thin wire with steady current flowing out of the plane of the paper is kept at the origin. The magnitude of the magnetic field (B) due to the loop ABCD at the origin (O) is AIEEE Solved Paper-2009

A)

zero

B)

\[\frac{{{\mu }_{0}}I(b-a)}{24ab}\]

C)

\[\frac{{{\mu }_{0}}I}{4\pi }\left[ \frac{b-a}{ab} \right]\]

D)

\[\frac{{{\mu }_{0}}I}{4\pi }\left[ 2(b\_a)+\frac{\pi }{3}(a+b) \right]\]

View Answer
13) Directions Q. Nos. 13 are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius =b) and DA (radius = a) of the loop are joined by the straight wires AB and CD. A steady current \[I\] is flowing in the loop. Angle made by A B and CD at the origin O is 30°. Another straight thin wire with steady current \[{{I}_{2}}\] flowing out of the plane of the paper is kept at the origin. Due to the presence of the current \[{{I}_{1}}\] at the origin: AIEEE Solved Paper-2009

A)

the forces on AB and DC are zero

B)

the forces on AD and BC are zero

C)

the magnitude of the net force on the loop is given by\[\frac{{{I}_{1}}I}{4\pi }{{\mu }_{0}}\left[ 2(b-a)+\frac{\pi }{3}(a+b) \right]\]

D)

the magnitude of the net force on the loop is given by\[\frac{{{\mu }_{0}}I{{I}_{1}}}{24ab}(b-a)\]

View Answer
14) A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is: AIEEE Solved Paper-2009

A)

393.4 nm

B)

885.0 nm

C)

                       442.5 nm

D)

776.8 nm.

View Answer
15) Two points P and Q are maintained at the potentials of 10V and -4V, respectively. The work done in moving 100 electrons from P to Q is AIEEE Solved Paper-2009

A)

\[9.60\times {{10}^{17}}J\]

B)

\[9.60\times {{10}^{17}}J\]

C)

       \[2.24\times {{10}^{16}}J\]

D)

       \[2.24\times {{10}^{16}}J.\]

View Answer
16) The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is:(\[hc=\] \[1240\text{ }eV.nm\]) AIEEE Solved Paper-2009

A)

\[3.09\text{ }eV\]

B)

\[1.41\text{ }eV\]

C)

\[1.51\text{ }eV\]

D)

       \[1.68\text{ }eV.\]

View Answer
17) A particle has an initial velocity of\[3\hat{i}+4\hat{j}\]and an acceleration of\[0.4\hat{i}+0.3\hat{j}\]. It speed after 10 s is: AIEEE Solved Paper-2009

A)

10 units

B)

\[7\sqrt{2}\] units

C)

7 units

D)

       8.5 units.

View Answer
18) A motor cycle starts from rest and accelerates along a straight path at\[2m/{{s}^{2}}.\] At the straight point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (Speed of wound\[=330\text{ }m{{s}^{1}}\]) AIEEE Solved Paper-2009

A)

49 m

B)

(2) 98 m

C)

       147 m

D)

       196 m.

View Answer
19) Consider a rubber ball freely falling from a height\[h=4.9\text{ }m\]onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be: AIEEE Solved Paper-2009

A)

B)

C)

D)

View Answer
20) A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other tow corners. If the net electrical force on Q is zero, then Q/q equals: AIEEE Solved Paper-2009

A)

\[-2\sqrt{2}\]

B)

       -1

C)

       1

D)

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

View Answer
21) A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature \[\theta \] along the length\[x\]of the bar from its hot end is best described by which of the following figures? AIEEE Solved Paper-2009

A)

B)

C)

D)

View Answer
22) A transparent solid cylindrical rod has a refractive index of\[\frac{2}{\sqrt{3}}\].It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle \[\theta \] for which the light ray grazes along the wall of the rod is: AIEEE Solved Paper-2009

A)

\[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]

B)

       \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

C)

       \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]

D)

       \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]

View Answer
23) Three sound waves of equal amplitudes have frequencies\[(v1),v,(v+1).\]They superpose to give beats. The number of beats produced per second will be AIEEE Solved Paper-2009

A)

4

B)

                                      3

C)

       2

D)

       1.

View Answer
24) The height at which the acceleration due to gravity becomes\[\frac{g}{9}\](where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is: AIEEE Solved Paper-2009

A)

2R

B)

\[\frac{R}{\sqrt{2}}\]

C)

       R/2

D)

       \[\sqrt{2}R\]

View Answer
25) Two wires are made of the same material and have the same volume. However wire 1 has cross-section area A and wire 2 has cross- sectional area 3A. If the length of wire 1 increases by\[\Delta x\]on applying force F, how much force is needed to stretch wire 2 by the same amount? AIEEE Solved Paper-2009

A)

F

B)

                                       4F

C)

       6F

D)

       9F.

View Answer
26) In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree \[(=0.5{}^\text{o}),\]then the least count of the instrument is:

A)

one minute

B)

       half minute

C)

       one degree

D)

       half degree.

View Answer
27) An inductor of inductance\[L=400\text{ }mH\]and resistors of resistances\[{{R}_{1}}=2\text{ }\Omega \]and \[{{R}_{2}}=2\Omega \]are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is: AIEEE Solved Paper-2009

A)

\[6\text{ }{{e}^{5t}}V\]

B)

\[\frac{12}{t}{{e}^{-3t}}V\]

C)

\[6\left( 1-{{e}^{\frac{-t}{0.2}}} \right)V\]

D)

\[12{{e}^{-5t}}V\]

View Answer
28) Directions Q. Nos. 28 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. Assuming the gas to be ideal the work done on the gas in taking it from A to B is: AIEEE Solved Paper-2009

A)

200 R

B)

300 R

C)

400 R

D)

500 R

View Answer
29) Directions Q. Nos. 29 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. The work done on the gas is taking it from D to A is AIEEE Solved Paper-2009

A)

-414 R

B)

+414 R

C)

-690 R

D)

+690 R

View Answer
30) Directions Q. Nos. 30 are based on the following paragraph. Two moles of helium gas are taken over the cycle ABCDA, as shown in the p-T diagram. The net work done on the gas in the cycle ABCDA is AIEEE Solved Paper-2009

A)

zero

B)

276 R

C)

1076 R

D)

1904 R

View Answer
31) Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements is incorrect? AIEEE Solved Paper-2009

A)

Because of the large size of the Ln (III) ions the bonding in its compounds is predominantly ionic in character.

B)

The ionic sizes of Ln (III) decrease in general with increasing atomic number.

C)

Ln (III) compounds are generally colourless

D)

Ln (III) hydroxides are mainly basic in character.

View Answer
32) A liquid was mixed with ethanol and a drop of concentrated \[{{H}_{2}}S{{O}_{4}}\] was added. A compound with a fruity smell was formed. The liquid was: AIEEE Solved Paper-2009

A)

\[C{{H}_{3}}OH\]

B)

\[HCHO\]

C)

       \[C{{H}_{3}}COC{{H}_{3}}\]

D)

       \[C{{H}_{3}}COOH\]

View Answer
33) Arrange the carbanions,\[{{(C{{H}_{3}})}_{3}}\overline{C},\overline{C}C{{l}_{3}}{{(C{{H}_{3}})}_{2}}\] \[\overline{C}H,{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}},\] in order of their decreasing stability: AIEEE Solved Paper-2009

A)

\[{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}}>\overline{C}C{{l}_{3}}>{{(C{{H}_{3}})}_{3}}\overline{C}>{{(C{{H}_{3}})}_{2}}\overline{C}H\]

B)

\[{{(C{{H}_{3}})}_{2}}\overline{C}H>\overline{C}C{{l}_{3}}>{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}}>{{(C{{H}_{3}})}_{3}}\overline{C}\]

C)

\[\overline{C}C{{l}_{3}}>{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}}>{{(C{{H}_{3}})}_{2}}\overline{C}H>{{(C{{H}_{3}})}_{3}}\overline{C}\]

D)

\[{{(C{{H}_{3}})}_{3}}\overline{C}>{{(C{{H}_{3}})}_{2}}\overline{C}H>{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}}>\overline{C}C{{l}_{3}}\]

View Answer
34) The alkene that exhibits geometrical isomerism is: AIEEE Solved Paper-2009

A)

propene

B)

                       2-methyl propene

C)

2-butene

D)

       2-methyl-2-butene

View Answer
35) In which of the following arrangements, the sequence is not strictly according to the property written against it? AIEEE Solved Paper-2009

A)

\[C{{O}_{2}}>Si{{O}_{2}}<Sn{{O}_{2}}<Pb{{O}_{2}}:\]increasing oxidizing power

B)

\[HF<HCl<HBr<HI:\]increasing acid strength

C)

\[N{{H}_{3}}<P{{H}_{3}}<As\text{ }{{H}_{3}}<Sb{{H}_{3}}:\]increasing basic strength

D)

\[B<C<O<N:\]increasing first ionization enthalpy

View Answer
36) The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is: AIEEE Solved Paper-2009

A)

benzoic acid

B)

salicylaldehyde

C)

       salicylic acid

D)

       phthalic acid

View Answer
37) Which of the following statement is incorrect regarding physissorptions? AIEEE Solved Paper-2009

A)

It occurs because of van der Waal?s forces.

B)

More easily liquiefiable gases are adsorbed readily

C)

Under high pressure it results into multi molecular layer on adsorbent surface

D)

Enthalpy of adsorption (DHadorption) is low and positive.

View Answer
38) Which of the following on heating with aqueous\[KOH,\]produces acetaldehyde? AIEEE Solved Paper-2009

A)

\[C{{H}_{3}}COCl\]

B)

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

C)

                                       \[C{{H}_{2}}ClC{{H}_{2}}Cl\]

D)

       \[C{{H}_{3}}CHC{{l}_{2}}\]

View Answer
39) In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. certainity with which the position of the electron can be located is \[h=6.6\times {{10}^{34}}kg\]\[{{m}^{2}}{{s}^{1}},\]mass of electron\[{{e}_{m}}=9.1\times {{10}^{31}}kg\]): AIEEE Solved Paper-2009

A)

\[1.52\times {{10}^{4}}m\]

B)

\[5.01\times {{10}^{3}}m\]

C)

                                       \[1.92\times {{10}^{3}}m\]

D)

       \[3.84\times {{10}^{3}}m\]

View Answer
40) In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is \[C{{H}_{3}}OH(l)+3/2{{O}_{2}}(g)\xrightarrow[{}]{{}}C{{O}_{2}}(g)+2{{H}_{2}}O(l)\] At 298 K standard Gibb?s energies of formation for\[C{{H}_{3}}OH(l),{{H}_{2}}O(l)\]and\[C{{O}_{2}}(g)\]are -166.2, - 237.2 and -394.4 kJ \[mo{{l}^{1}}\]respectively. If standard enthalpy of combustion of methanol is\[726\text{ }kJ\text{ }mo{{l}^{1}},\] efficiency of the fuel cell will be: AIEEE Solved Paper-2009

A)

80%

B)

87%

C)

90%

D)

       97%

View Answer
41) Two liquids X and Y form an ideal solution. At 300 K, vapour pressure of the solution containing 1 mol of X and 3 mol of Y is 550 mm Hg. At the same temperature, if 1 mol of Y is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mmHg) of X and Y in their pure states will be respectively: AIEEE Solved Paper-2009

A)

200 and 300

B)

300 and 400

C)

       400 and 600

D)

       500 and 600

View Answer
42) The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be\[(log2=0.301)\] AIEEE Solved Paper-2009

A)

230.3 minutes

B)

23.03 minute

C)

       46.06 minutes

D)

       460.6 minutes

View Answer
43) Given: \[E_{F{{e}^{3+}}/Fe}^{0}=-0.036V,E_{F{{e}^{2+}}/Fe}^{0}=-0.439V.\]The value of standard electrode potential for the change,\[Fe_{(aq)}^{3+}+{{e}^{-}}\to F{{e}^{2+}}(aq)\]will be: AIEEE Solved Paper-2009

A)

-0.072 V

B)

0.385 V

C)

       0.770V

D)

       -0.270V

View Answer
44) On the basis of the following thermo chemical data:\[(\Delta f\,{{G}^{o}}H_{(aq)}^{+}=0)\] \[{{H}_{2}}O(l)\xrightarrow[{}]{{}}{{H}^{+}}(aq)+O{{H}^{}}(aq);\]              \[\Delta H=57.32\text{ }kJ\] \[{{H}_{2}}O(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l);\] \[\Delta H=-286.20\,KJ\] The value of enthalpy of formation of\[O{{H}^{}}\]ion at\[25{}^\circ C\]is: AIEEE Solved Paper-2009

A)

-22.88 kJ

B)

-228.88 kJ

C)

       +228.88 kJ

D)

       -343.52 kJ

View Answer
45) Copper crystallizes in \[fcc\] with a unit cell length of 361 pm. What is the radius of copper atom? AIEEE Solved Paper-2009

A)

109 pm

B)

127 pm

C)

       157 pm

D)

       181 pm

View Answer
46) Which of the following has an optical isomer? AIEEE Solved Paper-2009

A)

\[{{[CO{{(N{{H}_{3}})}_{3}}Cl]}^{+}}\]

B)

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

C)

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

D)

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

View Answer
47) Solid\[Ba{{(N{{O}_{3}})}_{2}}\]is gradually dissolved in a 1.0 \[\times {{10}^{4}}M\text{ }N{{a}_{2}}C{{O}_{3}}\]solution. At what concentration of\[B{{a}^{2+}}\]will a precipitate being to form? (\[{{K}_{sp}}\]for\[Ba\text{ }C{{O}_{3}}=5.1\times {{10}^{9}}\]): AIEEE Solved Paper-2009

A)

\[4.1\times {{10}^{5}}M\]

B)

\[5.1\times {{10}^{5}}M\]

C)

       \[8.1\times {{10}^{8}}M\]

D)

       \[8.1\times {{10}^{7}}M\]

View Answer
48) Which one of the following reactions of Xenon compounds is not feasible? AIEEE Solved Paper-2009

A)

\[Xe{{O}_{3}}+6HF\to Xe{{F}_{6}}+3{{H}_{2}}O\]

B)

\[3Xe{{F}_{4}}+6{{H}_{2}}O\to 2Xe+Xe{{O}_{3}}+12\text{ }HF+\] \[1.5{{O}_{2}}\]

C)

\[2Xe{{F}_{2}}+2{{H}_{2}}O\to 2Xe+4HF+{{O}_{2}}\]

D)

\[Xe{{F}_{6}}+RbF\to Rb[Xe{{F}_{7}}]\]

View Answer
49)   Using MO theory predict which of the following species has the shortest bond length? AIEEE Solved Paper-2009

A)

\[O_{2}^{2+}\]

B)

\[O_{2}^{+}\]

C)

       \[O_{2}^{-}\]

D)

       \[O_{2}^{2-}\]

View Answer
50) In context with the transition elements, which of the following statements is incorrect? AIEEE Solved Paper-2009

A)

In addition to the normal oxidation states, the zero oxidation state is also shown by these elements in complexes.

B)

In the highest oxidation states, the transition metal show basic character and form cationic complexes.

C)

In the highest oxidation states of the first five transition element (Sc to Mn), all the 4s and 3d electrons are used for bonding.

D)

Once the \[{{d}^{5}}\] configuration is exceeded, the tendency to involve all the 3d electrons in bonding decreases.

View Answer
51) Calculate the wavelength (in nanometer) associated with a proton moving at\[1.0\times {{10}^{3}}\]\[m{{s}^{1}}\](Mass of proton\[=1.67\times {{10}^{27}}kg\] and h\[=6.63\times {{10}^{34}}Js\]): AIEEE Solved Paper-2009

A)

0.032 nm

B)

0.40 nm

C)

       2.5 nm

D)

       14.0 nm

View Answer
52) A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statement is correct regarding the behaviour of the solution? AIEEE Solved Paper-2009

A)

The solution formed is an ideal solution

B)

The solution is non-ideal, showing +ve deviation from Raoult?s Law

C)

The solution is non-ideal, showing -ve deviation from Raoult?s Law

D)

n-heptane shows +ve deviation while ethanol shows -ve deviation from Raoult?s Law.

View Answer
53) The number of stereoisomers possible for a compound of the molecular formula\[C{{H}_{3}}CH\] \[=CHCH(OH)Me\] is: AIEEE Solved Paper-2009

A)

3

B)

2

C)

       4

D)

       6

View Answer
54) The IUPAC name of neopentane is: AIEEE Solved Paper-2009

A)

2 - methylbutane

B)

2, 2 - dimethylpropane

C)

2 - methylpropane

D)

2, 2 - dimethylbutane

View Answer
55) The set representing the correct order of ionic radius is: AIEEE Solved Paper-2009

A)

\[L{{i}^{+}}>B{{e}^{2+}}>N{{a}^{+}}>M{{g}^{2+}}\]

B)

\[N{{a}^{+}}>L{{i}^{+}}>M{{g}^{2+}}>B{{e}^{2+}}\]

C)

\[L{{i}^{+}}>N{{a}^{+}}>M{{g}^{2+}}>B{{e}^{2+}}\]

D)

\[M{{g}^{2+}}>B{{e}^{2+}}>L{{i}^{+}}>N{{a}^{+}}\]

View Answer
56) The two functional groups present in a typical carbohydrate are: AIEEE Solved Paper-2009

A)

\[OH\] and \[COOH\]

B)

\[CHO\]and\[COOH\]

C)

\[>C=O\] and \[OH\]

D)

\[OH\] and\[CHO\]

View Answer
57) The bond dissociation energy of\[BF\]in\[B{{F}_{3}}\]is\[646\text{ }kJ\text{ }mo{{l}^{1}}\] whereas that of\[CF\]in\[C{{F}_{4}}\]is\[515\text{ }kJ\text{ }mo{{l}^{1}}.\] The correct reason for higher\[B-F\]bond dissociation energy as compared to that of\[CF\]is: AIEEE Solved Paper-2009

A)

smaller size of B - atom as compared to that of C - atom

B)

stronger\[\sigma \]bond between B and F in\[B{{F}_{3}}\]as compared to that between C and F in\[C{{F}_{4}}\]

C)

significant\[p\pi -p\pi \]interaction between B and F in\[B{{F}_{3}}\]whreas there is no possibility of such interaction between C and F in\[C{{F}_{4}}\]

D)

lower degree of \[p\pi -p\pi \] interaction between B and F in\[B{{F}_{3}}\]than that between C and F in\[C{{F}_{4}}\]

View Answer
58) In Cannizzaro reaction given below \[2Ph\text{ }CHO\xrightarrow[{}]{:\overset{\text{O-}}{\mathop{OH}}\,}Ph\text{ }C{{H}_{2}}OH+pHC\overset{\bullet \,\bullet }{\mathop{O_{2}^{\text{O-}}}}\,\] The slowest step is: AIEEE Solved Paper-2009

A)

the attack of: \[O{{H}^{}}\]at the carboxyl group

B)

the transfer of hydride to the carbonyl group

C)

the abstraction of proton from the carboxylic group

D)

the deprotonation of\[pH\text{ }C{{H}_{2}}OH\]

View Answer
59) Which of the following pairs represents linkage isomers? AIEEE Solved Paper-2009

A)

\[[Cu{{(N{{H}_{3}})}_{4}}][Pt\text{ }C{{l}_{4}}]\]and \[[Pt{{(N{{H}_{3}})}_{4}}][CuC{{l}_{4}}]\]

B)

\[[Pd{{(P\text{ }P{{h}_{3}})}_{2}}{{(NCS)}_{2}}]\]and \[[Pd{{(P\text{ }P{{h}_{3}})}_{2}}{{(SCN)}_{2}}]\]

C)

\[[CO{{(N{{H}_{3}})}_{5}}\text{ }N{{O}_{3}}]S{{O}_{4}}\] and \[[CO{{(N{{H}_{3}})}_{5}}S{{O}_{4}}]N{{O}_{3}}\]

D)

\[[PtC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]B{{r}_{2}}\]and \[[Pt\text{ }B{{r}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}\]

View Answer
60) Buna-N synthetic rubber is a copolymer of: AIEEE Solved Paper-2009

A)

\[{{H}_{2}}C=CH-\overset{\begin{smallmatrix} Cl \\ | \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\] and \[{{H}_{2}}C=CHCH=C{{H}_{2}}\]

B)

\[{{H}_{2}}C=CHCH=C{{H}_{2}}\]and \[{{H}_{5}}{{C}_{6}}CH=C{{H}_{2}}\]

C)

\[{{H}_{2}}C=CHCN\] and \[{{H}_{2}}C=CHCH=C{{H}_{2}}\]

D)

\[{{H}_{2}}C=CHCN\] and\[{{H}_{2}}C=CH\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}\]

View Answer
61) Let a, b, c be such that\[b(a+c)\ne 0\]. If \[\left| \begin{matrix}    a & a+1 & a-1 \\    -b & b+1 & b-1 \\    c & c-1 & c+1 \\ \end{matrix} \right|+\left| \begin{matrix}    a+1 & b+1 & c-1 \\    a-1 & b-1 & c+1 \\    {{(-1)}^{n+2}}a & {{(-1)}^{n+1}}b & {{(-1)}^{n}}c \\ \end{matrix} \right|=0,\] then the value of n is AIEEE Solved Paper-2009

A)

zero

B)

any even integer

C)

any odd integer

D)

any integer

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62) If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ... , 1 + 100d from their mean is 255, then the d is equal to AIEEE Solved Paper-2009

A)

10.0

B)

                       20.0

C)

       10.1

D)

       20.2

View Answer
63) If the roots of the equation\[b{{x}^{2}}+cx+a=0\]be imaginary, then for all real values of\[x,\]the expression\[3{{b}^{2}}{{x}^{2}}+6bcx+2{{c}^{2}}\]is AIEEE Solved Paper-2009

A)

greater than 4ab

B)

less than 4ab

C)

greater than -4ab

D)

less than -4ab

View Answer
64) Let A and B denote the statements \[A:\text{ }cos\,\alpha +cos\beta +cos\,\gamma =0\] \[B:\text{ }sin\,\alpha +sin\,\beta +sin\,\gamma =0\] If\[cos(\beta \gamma )+cos(\gamma \alpha )+cos(\alpha \beta )=3/2,\] then AIEEE Solved Paper-2009

A)

A is true and B is false

B)

A is false and B is true

C)

both A and B are true

D)

both A and B are false

View Answer
65) The lines\[p({{p}^{2}}+1)xy+q=0\]and \[{{({{p}^{2}}+1)}^{2}}x+({{p}^{2}}+1)y+2q=0\]are perpendicular to a common line for AIEEE Solved Paper-2009

A)

no value of p

B)

exactly one value of p

C)

exactly two values of p

D)

more than two values of p

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66) If A, B and C are three sets such that \[A\cap B=A\cap C\]and\[A\cup B=A\cup C,\]then AIEEE Solved Paper-2009

A)

\[A=B\]

B)

\[A=C\]

C)

\[B=C\]

D)

       \[A\cap B=\phi \]

View Answer
67) If \[\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}\]are non-coplanar vectors and p, q are real numbers, then the equality\[[3\overrightarrow{u},\text{ }p\overrightarrow{v},p\overrightarrow{w}]-[p\overrightarrow{v},\overrightarrow{w},q\overrightarrow{u}]-[2\overrightarrow{w},q\overrightarrow{v},q\overrightarrow{u}]=0\]holds for AIEEE Solved Paper-2009

A)

exactly one value of (p, q)

B)

exactly two values of (p, q)

C)

more than two but not all values of (p, q)

D)

all values of (p, q)

View Answer
68) Let the line \[\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\]lie in the plane\[x+3y\alpha z+\beta =0.\]Then \[(\alpha ,\,\,\beta )\] equals AIEEE Solved Paper-2009

A)

(6, - 17)

B)

(-6, 7)

C)

(5, -15)

D)

(-5, 5)

View Answer
69) From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is AIEEE Solved Paper-2009

A)

less than 500

B)

at least 500 but less than 750

C)

at least 750 but less than 1000

D)

at least 1000

View Answer
70) \[\int\limits_{0}^{\pi }{[\cot x]dx,}\]where [.] denotes the greatest integer function, is equal to AIEEE Solved Paper-2009 v

A)

\[\pi /2\]

B)

1

C)

       \[-1\]

D)

       \[-\pi /2\]

View Answer
71) For real\[x,\]let\[f(x)={{x}^{3}}+5x+1,\]then AIEEE Solved Paper-2009

A)

f is one-one but not onto R

B)

f is onto R but not one-one

C)

f is one-one and onto R

D)

f is neither one-one nor onto R

View Answer
72) In a binomial distribution \[B\left( n,p=\frac{1}{4} \right),\]if the probability of at least one success is greater than or equal to\[\frac{9}{10}\], then n is greater than AIEEE Solved Paper-2009

A)

\[\frac{1}{\log _{10}^{4}-\log _{10}^{3}}\]

B)

\[\frac{1}{\log _{10}^{4}+\log _{10}^{3}}\]

C)

\[\frac{9}{\log _{10}^{4}-\log _{10}^{3}}\]

D)

\[\frac{4}{\log _{10}^{4}-\log _{10}^{3}}\]

View Answer
73) If P and Q are the points of intersection of the circles\[{{x}^{2}}+{{y}^{2}}+3x+7y+2p5=0\]and \[{{x}^{2}}+{{y}^{2}}+2x+2y{{p}^{2}}=0,\]then there is a circle passing through P, Q and (1, 1) for AIEEE Solved Paper-2009

A)

all values of p

B)

all except one value of p

C)

all except two values of p

D)

exactly one value of p

View Answer
74) The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction cosines of the vector are AIEEE Solved Paper-2009

A)

6, -3, 2

B)

\[\frac{6}{5},\frac{-3}{5},\frac{2}{5}\]

C)

\[\frac{6}{7},\frac{-3}{7},\frac{2}{7}\]

D)

       \[\frac{-6}{7},\frac{-3}{7},\frac{2}{7}\]

View Answer
75) If\[\left| Z-\frac{4}{z} \right|=2,\]then the maximum value of |Z| is equal to AIEEE Solved Paper-2009

A)

\[\sqrt{3}+1\]

B)

\[\sqrt{5}+1\]

C)

       2

D)

       \[2+\sqrt{2}\]

View Answer
76) Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) is equal to\[\frac{1}{3}\]. Then the circumcentre of the triangle ABC is at the point AIEEE Solved Paper-2009

A)

(0, 0)

B)

\[\left( \frac{5}{4},0 \right)\]

C)

       \[\left( \frac{5}{2},0 \right)\]

D)

       \[\left( \frac{5}{3},0 \right)\]

View Answer
77) The remainder left out when\[{{8}^{2n}}{{(62)}^{2n+1}}\] is divided by 9 is AIEEE Solved Paper-2009

A)

0

B)

                       2

C)

7

D)

       8

View Answer
78) The ellipse\[{{x}^{2}}+4{{y}^{2}}=4\]is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is AIEEE Solved Paper-2009

A)

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

B)

\[{{x}^{2}}+12{{y}^{2}}=16\]

C)

                       \[4{{x}^{2}}+48{{y}^{2}}=48\]

D)

       \[4{{x}^{2}}+64{{y}^{2}}=48\]

View Answer
79) The sum to infinity of the series \[1+\frac{2}{3}+\frac{6}{{{3}^{2}}}+\frac{10}{{{3}^{3}}}\frac{14}{{{3}^{4}}}+....\]is

A)

2

B)

                       3

C)

                       4

D)

       6

View Answer
80) The differential equation which represents the family of curves\[y={{c}_{1}}{{e}^{{{C}_{2}}x}},\]where\[{{c}_{1}}\]and \[{{c}_{2}}\]are arbitrary constants, is AIEEE Solved Paper-2009

A)

\[y'={{y}^{2}}\]

B)

       \[y''=y'y\]

C)

       \[yy''=y'\]

D)

       \[yy''={{(y')}^{2}}\]

View Answer
81) One ticket is selected at random from 50 tickets numbered 00, 01, 02, ... , 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals AIEEE Solved Paper-2009

A)

1/14

B)

                       1/7

C)

                                       5/14

D)

       1/50

View Answer
82) Let y be an implicit function of x defined by \[{{x}^{2x}}2{{x}^{x}}coty1=0.\]Then y?(1) equals AIEEE Solved Paper-2009

A)

-1

B)

1

C)

       \[log\text{ }2\]

D)

       \[\text{ }log2\]

View Answer
83) The area of the region bounded by the parabola\[{{(y2)}^{2}}=x1,\]the tangent to the parabola at the point (2, 3) and the x-axis is

A)

3

B)

                       6

C)

       9

D)

       12

View Answer
84) Given\[P(x)={{x}^{4}}+a{{x}^{3}}+cx+d\]such that\[x=0\]is the only real root of\[P'(x)=0\]. If \[P(1)<P(1),\]then in the interval [-1, 1]. AIEEE Solved Paper-2009

A)

P(-1) is the minimum and P(1) is the maximum of P

B)

P(-1) is not minimum but P(1) is the maximum of P

C)

P(-1) is the minimum but P(1) is not the maximum of P

D)

neither P(-1) is the minimum nor P(1) is the maximum of P

View Answer
85) The shortest distance between the line \[yx=1\]and the curve\[x={{y}^{2}}\]is AIEEE Solved Paper-2009

A)

\[\frac{3\sqrt{2}}{8}\]

B)

                       \[\frac{2\sqrt{3}}{8}\]

C)

       \[\frac{3\sqrt{2}}{5}\]

D)

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

View Answer
86) Directions: Questions No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let \[f(x)={{(x+1)}^{2}}1,\text{ }x\ge 1\] Statement - 1: The set\[\{x:f(x)={{f}^{-1}}(x)\}\] \[=\{0,\text{ }1\}\]. Statement - 2: f is a bijection. AIEEE Solved Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement 1: The variance of first n even natural numbers is \[\frac{{{n}^{2}}-1}{4}\] Statement 2: The sum of first n natural numbers is \[\frac{n(n+1)}{2}\] and the sum of squares of first n natural numbers is\[\frac{n(n+1)(2n+1)}{6}\] AIEEE Solved Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement 1:\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is equivalent to\[p\leftrightarrow q\] Statement 2:\[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is a tautology AIEEE Solved Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a 2 × 2 matrix Statement 1: adj (adj A) = A Statement 2:\[|adj\text{ }A|=|A|\] AIEEE Solved Paper-2009

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 No. 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 have four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let\[f(x)=x|x|\]and\[g(x)=sinx\] Statement 1: gof is differentiable at\[x=0\]and its derivative is continuous at that point Statement 2: gof is twice differentiable at\[x=0\]

A)

(a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for statement-1

B)

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1.

C)

(c) Statement-1 is true, statement-2 is false.

D)

(d) Statement-1 is false, Statement-2 is true

View Answer