AIEEE 2009

Paper was held on
Mon, Apr 27, 2009 9:30 AM

## Chemistry

Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 103 ms−1
(Mass of proton = 1.67 $$\tim

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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

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In which of the following arrangements, the sequence is not strictly according to the property written against it

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Using MO theory, predict which of the following species has the shortest bond length?

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On the basis of the following thermochemical data : ($$\Delta _fG^oH^+_{(aq)}$$ = 0)
H2O(l) $$\to$$ H+(aq) + OH-(aq); $

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Solid Ba(NO3)2 is gradually dissolved in a 1.0 $$\times$$ 10-4 M Na2CO3 solution. At what concentration of Ba2+ will a p

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Arrange the carbanions, $${(C{H_3})_3}\overline C $$, $$\overline C C{l_3}$$ , $${(C{H_3})_2}\overline C H$$, $${C_6}{H

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The IUPAC name of neopentane is

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The alkene that exhibits geometrical isomerism is :

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The number of stereoisomers possible for a compound of the molecular formula
CH3 - CH = CH - CH(OH) - Me is :

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Which of the following statements is incorrect regarding physisorptions ?

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Copper crystallizes in fcc with a unit cell length of 361 pm. What is the radius of copper atom?

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A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following
statements is correct r

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Two liquids X and Y form an ideal solution. At 300K, vapour pressure of the solution containing 1 mol
of X and 3 mol of

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Given : $$E_{F{e^{3 + }}/Fe}^o$$ = -0.036V; $$E_{F{e^{2 + }}/Fe}^o$$ = -0.439 V
The value of standard electrode potenti

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In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is
CH3OH(l) + 3/2O2 $$\to$$

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The half life period of a first order chemical reaction is 6.93 minutes. The time required for the
completion of 99% of

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Which one of the following reactions of Xenon compounds is not feasible?

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In context with the transition elements, which of the following statements is incorrect ?

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Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the
following statements

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Which of the following pairs represents linkage isomers ?

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Which of the following has an optical isomer ?

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The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is :

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A liquid was mixed with ethanol and a drop of concentrated H2SO4 was added. A compound with a
fruity smell was formed. T

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In Cannizzaro reaction given below
2PhCHO $$\buildrel {\mathop {:OH}\limits^{\left( - \right)} } \over
\longrightarr

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Which of the following on heating with aqueous KOH, produces acetaldehyde ?

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The two functional groups present in a typical carbohydrate are

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Buna-$$N$$ synthetic rubber is a copolymer of :

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The set representing the correct order of ionic radius is :

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## Mathematics

Let A and B denote the statements
A: $$\cos \alpha + \cos \beta + \cos \gamma = 0$$
B: $$\sin \alpha + \sin \beta

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If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :

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If the roots of the equation $$b{x^2} + cx + a = 0$$ imaginary, then for all real values of $$x$$, the expression $$3{b^

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From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row

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The remainder left out when $${8^{2n}} - {\left( {62} \right)^{2n + 1}}$$ is divided by 9 is :

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The sum to infinite term of the series $$1 + {2 \over 3} + {6 \over {{3^2}}} + {{10} \over {{3^3}}} + {{14} \over {{3^4}

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The shortest distance between the line $$y - x = 1$$ and the curve $$x = {y^2}$$ is :

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The lines $$p\left( {{p^2} + 1} \right)x - y + q = 0$$ and $$\left( {{p^2} + 1} \right){}^2x + \left( {{p^2} + 1} \right

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Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance o

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If $$P$$ and $$Q$$ are the points of intersection of the circles
$${x^2} + {y^2} + 3x + 7y + 2p - 5 = 0$$ and $${x^2} +

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The ellipse $${x^2} + 4{y^2} = 4$$ is inscribed in a rectangle aligned with the coordinate axex, which in turn is inscri

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Let $$y$$ be an implicit function of $$x$$ defined by $${x^{2x}} - 2{x^x}\cot \,y - 1 = 0$$. Then $$y'(1)$$ equals

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Let $$f\left( x \right) = x\left| x \right|$$ and $$g\left( x \right) = \sin x.$$
Statement-1: gof is differentiable at

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Given $$P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d$$ such that $$x=0$$ is the only
real root of $$P'\,\left(

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Let $$A$$ be a $$\,2 \times 2$$ matrix
Statement - 1 : $$adj\left( {adj\,A} \right) = A$$
Statement - 2 :$$\left| {adj\,

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Let $$a, b, c$$ be such that $$b\left( {a + c} \right) \ne 0$$ if
$$\left| {\matrix{
a & {a + 1} & {a - 1} \

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The area of the region bounded by the parabola $${\left( {y - 2} \right)^2} = x - 1,$$ the tangent of the parabola at th

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$$\int\limits_0^\pi {\left[ {\cot x} \right]dx,} $$ where $$\left[ . \right]$$ denotes the greatest integer function, i

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The differential equation which represents the family of curves $$y = {c_1}{e^{{c_2}x}},$$ where $${c_1}$$ , and $${c_2}

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In a binomial distribution $$B\left( {n,p = {1 \over 4}} \right),$$ if the probability of at least one success is great

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One ticket is selected at random from $$50$$ tickets numbered $$00, 01, 02, ...., 49.$$ Then the probability that the su

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Let the line $$\,\,\,\,\,$$ $${{x - 2} \over 3} = {{y - 1} \over { - 5}} = {{z + 2} \over 2}$$ lie in the plane $$\,\,\,

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The projections of a vector on the three coordinate axis are $$6,-3,2$$ respectively. The direction cosines of the vecto

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If $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ are non-coplanar vectors and $$p,q$$ are real numbers, t

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Let $$f\left( x \right) = {\left( {x + 1} \right)^2} - 1,x \ge - 1$$
Statement - 1 : The set $$\left\{ {x:f\left( x \ri

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For real x, let f(x) = x3 + 5x + 1, then

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Statement-1 : $$ \sim \left( {p \leftrightarrow \sim q} \right)$$ is equivalent to $${p \leftrightarrow q}$$.
Statement

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If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is
equal to

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Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$
Statement - 2 : The sum of fir

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If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then :

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## Physics

In an experiment the angles are required to be measured using an instrument, 29 divisions of the
main scale exactly coin

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A particle has an initial velocity $$3\widehat i + 4\widehat j$$ and an acceleration of $$0.4\widehat i + 0.3\widehat j$

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A thin uniform rod of length $$l$$ and mass $$m$$ is swinging freely about a horizontal axis passing through its end. It

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The height at which the acceleration due to gravity becomes $${g \over 9}$$ (where $$g=$$ the acceleration due to gravit

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Two wires are made of the same material and have the same volume. However wire $$1$$ has cross-sectional area $$A$$ and

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Statement - 1: The temperature dependence of resistance is usually given as $$R = {R_0}\left( {1 + \alpha \,\Delta t} \r

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One $$kg$$ of a diatomic gas is at a pressure of $$8 \times {10^4}\,N/{m^2}.$$ The density of the gas is $$4kg/{m^3}$$.

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A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperat

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Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.
Assuming the gas to be

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Two moles of helium gas are taken over the cycle $$ABCD,$$ as shown in the $$P$$-$$T$$ diagram.
The work done on the g

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Two moles of helium gas are taken over the cycle $$ABCD$$, as shown in the $$P$$-$$T$$ diagram.
The net work done on t

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If $$x,$$ $$v$$ and $$a$$ denote the displacement, the velocity and the acceleration of a particle executing simple harm

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Three sound waves of equal amplitudes have frequencies $$\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$$ They sup

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A motor cycle starts from rest and accelerates along a straight path at $$2m/{s^2}.$$ At the starting point of the motor

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Let $$P\left( r \right) = {Q \over {\pi {R^4}}}r$$ be the change density distribution for a solid sphere of radius $$R$$

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(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that

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A charge $$Q$$ is placed at each of the opposite corners of a square. A charge $$q$$ is placed at each of the other two

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Two points $$P$$ and $$Q$$ are maintained at the potentials of $$10$$ $$V$$ and $$-4$$ $$V$$, respectively. The work don

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A current loop $$ABCD$$ is held fixed on the plane of the paper as shown in the figure. The arcs $$BC$$ (radius $$= b$$)

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A current loop $$ABCD$$ is held fixed on the plane of the paper as shown in the figure. The arcs $$BC$$ (radius $$= b$$)

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A mixture of light, consisting of wavelength $$590$$ $$nm$$ and an unknown wavelength, illuminates Young's double slit a

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In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for e

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An inductor of inductance $$L=400$$ $$mH$$ and resistors of resistance $${R_1} = 2\Omega $$ and $${R_2} = 2\Omega $$ are

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A transparent solid cylindrical rod has a refractive index of $${2 \over {\sqrt 3 }}.$$ It is surrounded by air. A light

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The transition from the state $$n=4$$ to $$n=3$$ in a hydrogen like atom result in ultra violet radiation. Infrared rad

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The surface of a metal is illuminated with the light of $$400$$ $$nm.$$ The kinetic energy of the ejected photoelectrons

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The above is a plot of binding energy per nucleon $${E_b},$$ against the nuclear mass $$M;A,B,C,D,E,F$$ correspond to

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The logic circuit shown below has the input waveforms $$'A'$$ and $$'B'$$ as shown. Pick out the correct output waveform

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A $$p$$-$$n$$ junction $$(D)$$ shown in the figure can act as a rectifier. An alternating current source $$(V)$$ is conn

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Consider a rubber ball freely falling from a height $$h=4.9$$ $$m$$ onto a horizontal elastic plate. Assume that the du

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