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

View Question 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

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

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

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

View Question 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

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

View Question The IUPAC name of neopentane is

View Question The alkene that exhibits geometrical isomerism is :

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

View Question Which of the following statements is incorrect regarding physisorptions ?

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

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

View Question 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

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

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

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

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

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

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

View Question Which of the following pairs represents linkage isomers ?

View Question Which of the following has an optical isomer ?

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

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

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

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

View Question The two functional groups present in a typical carbohydrate are

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

View Question The set representing the correct order of ionic radius is :

View Question ## Mathematics

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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(

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question ## Physics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

View Question
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

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

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

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

View Question