AIEEE 2010

Paper was held on
Sun, Apr 25, 2010 9:30 AM

## Chemistry

The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest
wavelength of light capable of

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Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is

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The correct sequence which shows decreasing order of the ionic radii of the elements is

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If 10–4 dm3 of water is introduced into a 1.0 dm3 flask to 300 K, how many moles of water are in the vapour phase when e

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The standard enthalpy of formation of NH3 is –46.0 kJ mol–1. If the enthalpy of formation of H2 from its atoms is –436 k

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For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is
the temperature at

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Three reactions involving $$H_2PO_4^−$$ are given below :
(i) H3PO4 + H2O $$\to$$ H3O+ + $$H_2PO_4^−$$
(ii) $$H_2PO_4^−$

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Solubility product of silver bromide is 5.0 $$\times$$ 10–13. The quantity of potassium bromide (molar mass taken as 120

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In aqueous solution the ionization constants for carbonic acid are
K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11
Select the corre

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At 25°C, the solubility product of Mg(OH)2 is 1.0 $$\times$$ 10–11. At which pH, will Mg2+ ions start precipitating in t

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Out of the following, the alkene that exhibits optical isomerism is

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The correct order of increasing basicity of the given conjugate bases (R = CH3) is

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One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular
mass of 44 u. The alken

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The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the
cation is 110 pm, th

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Percentages of free space in cubic close packed structure and in body centred packed structure are
respectively :

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If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous
solution, the change in

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On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two
liquid components (hepta

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The correct order of $$E_{{M^{2 + }}/M}^o$$ values with negative sign for the four successive elements Cr, Mn, Fe
and Co

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The Gibbs energy for the decomposition of Al2O3 at 500oC is as follows :
$${2 \over 3}A{l_2}{O_3}$$ $$\to$$ $${4 \over 3

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The time for half life period of a certain reaction A $$\to$$ products is 1 hour. When the initial
concentration of the

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Consider the reaction :
Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq)
The rate equation for this reaction is rate = k

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29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method
and the evolved ammonia w

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A solution containing 2.675g of CoCl3. 6NH3 (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chlor

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Which one of the following has an optical isomer ?
(en = ethylenediamine)

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From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous
ZnCl2, is

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Biuret test is not given by

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The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

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Consider the following bromides :
The correct order of $${S_N}1$$ reactive is

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The main product of the following reaction is
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $${C_6}{H_5}C{H_2}CH\lef

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In the chemical reactions,
the compounds $$'A'$$ and $$'B'$$ respectively are

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## Mathematics

Let $$\cos \left( {\alpha + \beta } \right) = {4 \over 5}$$ and $$\sin \,\,\,\left( {\alpha - \beta } \right) = {5 \ov

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The number of complex numbers z such that $$\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|$$ e

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If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2

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There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are take

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Let $${s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}$$,
$${{s_2} = \sum\limits_{j = 1}^{10} {}

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A person is to count 4500 currency notes. Let $${a_n}$$ denote the number of notes he counts in the $${n^{th}}$$ minute.

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The line $$L$$ given by $${x \over 5} + {y \over b} = 1$$ passes through the point $$\left( {13,32} \right)$$. The line

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The circle $${x^2} + {y^2} = 4x + 8y + 5$$ intersects the line $$3x - 4y = m$$ at two distinct points if :

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If two tangents drawn from a point $$P$$ to the parabola $${y^2} = 4x$$ are at right angles, then the locus of $$P$$ is

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Let $$f:\left( { - 1,1} \right) \to R$$ be a differentiable function with $$f\left( 0 \right) = - 1$$ and $$f'\left( 0

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For a regular polygon, let $$r$$ and $$R$$ be the radii of the inscribed and the circumscribed circles. A $$false$$ stat

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The equation of the tangent to the curve $$y = x + {4 \over {{x^2}}}$$, that
is parallel to the $$x$$-axis, is

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Let $$f:R \to R$$ be defined by
$$$f\left( x \right) = \left\{ {\matrix{
{k - 2x,\,\,if} & {x \le - 1} \cr

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Let $$f:R \to R$$ be a continuous function defined by
$$$f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}$$$
Stateme

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Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$
where $$I$$ is $$2 \times 2$$ ident

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Consider the system of linear equations;
$$$\matrix{
{{x_1} + 2{x_2} + {x_3} = 3} \cr
{2{x_1} + 3{x_2} + {x_3}

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The number of $$3 \times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is :

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Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x)=p'(1-x),$$ for all $$x \in \left[ {0,1} \right],p\left( 0

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The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x=0$$ and $$x = {{3\pi } \over

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Solution of the differential equation
$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x

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Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$
Statement - 1

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random with

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Statement-1 : The point $$A(3, 1, 6)$$ is the mirror image of the point $$B(1, 3, 4)$$ in the plane $$x-y+z=5.$$
Statem

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A line $$AB$$ in three-dimensional space makes angles $${45^ \circ }$$ and $${120^ \circ }$$ with the positive $$x$$-axi

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Let $$\overrightarrow a = \widehat j - \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j - \widehat k.$$

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If the vectors $$\overrightarrow a = \widehat i - \widehat j + 2\widehat k,\,\,\,\,\,\overrightarrow b = 2\widehat i +

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Let $$f:R \to R$$ be a positive increasing function with
$$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}}

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Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x >

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For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding
means are given to be 2 a

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Consider the following relations
$R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$;
$

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## Physics

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $$ \times $$ 10–3 are

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For a particle in uniform circular motion the acceleration $$\overrightarrow a $$ at a point P(R, θ) on the circle of ra

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A particle is moving with velocity $$\overrightarrow v = k\left( {y\widehat i + x\widehat j} \right)$$, where K is a co

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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $$U\left(

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Statement - 1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic colli

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Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $${30^ \circ }$$ w

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Two fixed frictionless inclined planes making an angle $${30^ \circ }$$ and $${60^ \circ }$$ with the vertical are shown

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A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the

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A ball is made of a material of density $$\rho $$ where $${\rho _{oil}}\, < \rho < {\rho _{water}}$$ with $${\rho

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The equation of a wave on a string of linear mass density $$0.04\,\,kg\,{m^{ - 1}}$$ is given by
$$$y = 0.02\left( m \r

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Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho

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A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\o

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Let $$C$$ be the capacitance of a capacitor discharging through a resistor $$R.$$ Suppose $${t_1}$$ is the time taken fo

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Two conductors have the same resistance at $${0^ \circ }C$$ but their temperature coefficients of resistance are $${\alp

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Two long parallel wires are at a distance $$2d$$ apart. They carry steady equal currents flowing out of the plane of the

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In a series $$LCR$$ circuit $$R = 200\Omega $$ and the voltage and the frequency of the main supply is $$220V$$ and $$50

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An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

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An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

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An initially parallel cylindrical beam travels in a medium of refractive index $$\mu \left( I \right) = {\mu _0} + {\mu

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A rectangular loop has a sliding connector $$PQ$$ of length $$l$$ and resistance $$R$$ $$\Omega $$ and it is moving with

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In the circuit shown below, the key $$K$$ is closed at $$t=0.$$ The current through the battery is

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Statement - $$1$$ : When ultraviolet light is incident on a photocell, its stopping potential is $${V_0}$$ and the max

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A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each.

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A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each.

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If a source of power $$4kW$$ produces $${10^{20}}$$ photons/second, the radiation belongs to a part of the spectrum call

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A radioactive nucleus (initial mass number $$A$$ and atomic number $$Z$$ emits $$3\,\alpha $$- particles and $$2$$ posit

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The combination of gates shown below yields

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The figure shows the position$$-$$time $$(x-t)$$ graph of one-dimensional motion of body of mass $$0.4$$ $$kg.$$ The mag

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A small particle of mass $$m$$ is projected at an angle $$\theta $$ with the $$x$$-axis with an initial velocity $${v_0}

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A point $$P$$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $$P$$ is s

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