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

View Question
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

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

View Question
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

View Question
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

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

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

View Question
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

View Question
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

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

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

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

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

View Question
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

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

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

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

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

View Question
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

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

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

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

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

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

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

View Question
Biuret test is not given by

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

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

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

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

View Question
## Mathematics

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

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

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

View Question
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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question
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

View Question
Solution of the differential equation
$$\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x{\pi \over 2}$$ is

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

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

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

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

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

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

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

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

View Question
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

View Question
## Physics

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

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

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

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

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

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

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

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

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

View Question
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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question
The combination of gates shown below yields

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

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

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

View Question