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

### done AIEEE Solved Paper-2009 Total Questions - 90

• question_answer1) 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.

• question_answer2) 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).

• question_answer3) 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)

• question_answer4) 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)

• question_answer5) 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)
$aT/v.$

• question_answer6) 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)
$(4f,\text{ }4f).$

• question_answer7)   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)
$\frac{1}{6}\frac{{{\ell }^{2}}{{\omega }^{2}}}{g}$

• question_answer8) 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)
$\frac{Qr_{1}^{2}}{3\pi {{\varepsilon }_{0}}{{R}^{4}}}$

• question_answer9)   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)
$5\to 4$

• question_answer10) 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)
$7\times {{10}^{4}}J.$

• question_answer11) 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.

• question_answer12) 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)
$\frac{{{\mu }_{0}}I}{4\pi }\left[ 2(b\_a)+\frac{\pi }{3}(a+b) \right]$

• question_answer13) 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$\frac{{{\mu }_{0}}I{{I}_{1}}}{24ab}(b-a)$

• question_answer14) 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.

• question_answer15) 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)
$2.24\times {{10}^{16}}J.$

• question_answer16) 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)
$1.68\text{ }eV.$

• question_answer17) 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.

• question_answer18) 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.

• question_answer19) 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)

• question_answer20) 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)
$-\frac{1}{\sqrt{2}}$

• question_answer21) 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)

• question_answer22) 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)
${{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)$

• question_answer23) 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.

• question_answer24) 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)
$\sqrt{2}R$

• question_answer25) 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.

• question_answer26) 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.

• question_answer27)  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)
$12{{e}^{-5t}}V$

• question_answer28) 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

• question_answer29) 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

• question_answer30) 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

• question_answer31) 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.

• question_answer32) 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)
$C{{H}_{3}}COOH$

• question_answer33) 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)
${{(C{{H}_{3}})}_{3}}\overline{C}>{{(C{{H}_{3}})}_{2}}\overline{C}H>{{C}_{6}}{{H}_{5}}\overline{C}{{H}_{2}}>\overline{C}C{{l}_{3}}$

• question_answer34) 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

• question_answer35) 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

• question_answer36) 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

• question_answer37) Which of the following statement is incorrect regarding physissorptions?     AIEEE  Solved  Paper-2009

A)
It occurs because of van der Waal?s forces.

B)

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

D)

• question_answer38) 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)
$C{{H}_{3}}CHC{{l}_{2}}$

• question_answer39) 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)
$3.84\times {{10}^{3}}m$

• question_answer40) 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%

• question_answer41) 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

• question_answer42) 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

• question_answer43) 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

• question_answer44) 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

• question_answer45) 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

• question_answer46) 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)
${{[CO{{(en)}_{2}}{{(N{{H}_{3}})}_{2}}]}^{3+}}$

• question_answer47) 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)
$8.1\times {{10}^{7}}M$

• question_answer48) 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)
$Xe{{F}_{6}}+RbF\to Rb[Xe{{F}_{7}}]$

• question_answer49)   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)
$O_{2}^{2-}$

• question_answer50) 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.

• question_answer51) 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

• question_answer52) 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.

• question_answer53) 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

• question_answer54) The IUPAC name of neopentane is:     AIEEE  Solved  Paper-2009

A)
2 - methylbutane

B)
2, 2 - dimethylpropane

C)
2 - methylpropane

D)
2, 2 - dimethylbutane

• question_answer55) 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)
$M{{g}^{2+}}>B{{e}^{2+}}>L{{i}^{+}}>N{{a}^{+}}$

• question_answer56) 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$CHO$

• question_answer57) 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$C{{F}_{4}}$

• question_answer58) 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$pH\text{ }C{{H}_{2}}OH$

• question_answer59) 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 $[Pt\text{ }B{{r}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}$

• question_answer60) 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${{H}_{2}}C=CH\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,=C{{H}_{2}}$

• question_answer61) 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

• question_answer62) 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

• question_answer63) 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

• question_answer64) 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

• question_answer65) 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

• question_answer66) 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)
$A\cap B=\phi$

• question_answer67) 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)

• question_answer68) 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)

• question_answer69) 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

• question_answer70) $\int\limits_{0}^{\pi }{[\cot x]dx,}$where [.] denotes the greatest integer function, is equal to   AIEEE  Solved  Paper-2009 v

A)
$\pi /2$

B)
1

C)
$-1$

D)
$-\pi /2$

• question_answer71) 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

• question_answer72) 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)
$\frac{4}{\log _{10}^{4}-\log _{10}^{3}}$

• question_answer73) 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

• question_answer74) 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)
$\frac{-6}{7},\frac{-3}{7},\frac{2}{7}$

• question_answer75) 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)
$2+\sqrt{2}$

• question_answer76) 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)
$\left( \frac{5}{3},0 \right)$

• question_answer77) 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

• question_answer78) 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)
$4{{x}^{2}}+64{{y}^{2}}=48$

• question_answer79) 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

• question_answer80) 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)
$yy''={{(y')}^{2}}$

• question_answer81) 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

• question_answer82) 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)
$\text{ }log2$

• question_answer83) 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

• question_answer84) 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

• question_answer85) 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)
$\frac{\sqrt{3}}{4}$

• question_answer86) 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

• question_answer87) 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

• question_answer88) 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

• question_answer89) 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

• question_answer90) 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