AIEEE 2011

Paper was held on
Sun, May 1, 2011 9:30 AM

## Chemistry

A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at
680 nm, the other is at :

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Which one of the following order represents the correct sequence of the increasing basic nature of the
given oxides ?

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Among the following the maximum covalent character is shown by the compound :

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The hybridization of orbitals of N atom in $$NO_3^-$$, $$NO_2^+$$ and $$NH_4^+$$ are respectively :

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The structure of IF7 is :

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'a’ and `b’ are van der Waals’ constants for gases. Chlorine is more easily liquefied than ethane because

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The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a
volume of 10 dm3 to

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A vessel at 1000 K contains CO2 with a pressure of 0.5 atm. Some of the CO2 is converted into CO on
the addition of grap

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Identify the compound that exhibits tautomerism.

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Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the
presence of :

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In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre
positions. If

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A 5.2 molal aqueous solution of methyl alcohol, CH3OH, is supplied. What is the mole fraction of methyl
alcohol in the s

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Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be
added to 4 kg of wat

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The degree of dissociation ($$\alpha$$ ) of a weak electrolyte, AxBy is related to van’t Hoff factor (i) by the expressi

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The reduction potential of hydrogen half cell will be negative if :

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The rate of a chemical reaction doubles for every 10oC rise of temperature. If the temperature is raised
by 50oC , the r

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Which of the following statement is wrong?

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Which of the following statements regarding sulphur is incorrect?

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Boron cannot form which one of the following anions?

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In context of the lanthanoids, which of the following statements is not correct?

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Which of the following facts about the complex [Cr (NH3)6 ]Cl3 is wrong?

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The magnetic moment (spin only) of [NiCl4]2− is

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Phenol is heated with a solution of mixture of KBr and KBrO3. The major product obtained in the above
reaction is

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Which of the following reagents may be used to distinguish between phenol and benzoic acid ?

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Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the
products contains sodium

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The strongest acid amongst the following compounds is :

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Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above
reaction is

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Silver Mirror test is given by which one of the following compounds ?

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The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

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Outer electronic configuration of Gd (Atomic no : 64) is -

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The outer electron configuration of $$Gd$$ (Atomic No. $$64$$) is :

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## Mathematics

If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:

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Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots

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If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals :

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These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these po

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Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is

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The coefficient of $${x^7}$$ in the expansion of $${\left( {1 - x - {x^2} + {x^3}} \right)^6}$$ is

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A man saves ₹ 200 in each of the first three months of his service. In each of the subsequent months his saving increase

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The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respect

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The two circles x2 + y2 = ax, and x2 + y2 = c2 (c > 0) touch each other if :

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Equation of the ellipse whose axes of coordinates and which passes through the point $$(-3,1)$$ and has eccentricity $$\

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$${{{d^2}x} \over {d{y^2}}}$$ equals:

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For $$x \in \left( {0,{{5\pi } \over 2}} \right),$$ define $$f\left( x \right) = \int\limits_0^x {\sqrt t \sin t\,dt.} $

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

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Let $$A$$ and $$B$$ be two symmetric matrices of order $$3$$.
Statement - 1 : $$A(BA)$$ and $$(AB)$$$$A$$ are symmetri

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The number of values of $$k$$ for which the linear equations
$$4x + ky + 2z = 0,kx + 4y + z = 0$$ and $$2x+2y+z=0$$ pos

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The value of $$\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$$ is

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The area of the region enclosed by the curves $$y = x,x = e,y = {1 \over x}$$ and the positive $$x$$-axis is :

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Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The va

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If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :

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Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one

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If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement

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If the angle between the line $$x = {{y - 1} \over 2} = {{z - 3} \over \lambda }$$ and the plane
$$x+2y+3z=4$$ is $${\c

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The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\ov

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Statement - 1 : The point $$A(1,0,7)$$ is the mirror image of the point
$$B(1,6,3)$$ in the line : $${x \over 1} = {{y

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If $$\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)$$ and $$\overrightarrow b =

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The domain of the function f(x) = $${1 \over {\sqrt {\left| x \right| - x} }}$$ is

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$$\mathop {\lim }\limits_{x \to 2} \left( {{{\sqrt {1 - \cos \left\{ {2(x - 2)} \right\}} } \over {x - 2}}} \right)$$

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The value of $$p$$ and $$q$$ for which the function
$$f\left( x \right) = \left\{ {\matrix{
{{{\sin (p + 1)x + \sin x

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Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the s

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If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

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Let $R$ be the set of real numbers.
Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence

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Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three non-zero vectors which are pairwise

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## Physics

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circula

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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the
fountain is v, the

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An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :
$${{dv} \over {dt}} = - 2.5\sqrt v $$ w

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A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a

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A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$

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A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where

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Two bodies of masses $$m$$ and $$4$$ $$m$$ are placed at a distance $$r.$$ The gravitational potential at a point on the

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Work done in increasing the size of a soap bubble from a radius of $$3$$ $$cm$$ to $$5$$ $$cm$$ is nearly (Surface tensi

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Water is flowing continuously from a tap having an internal diameter $$8 \times {10^{ - 3}}\,\,m.$$ The water velocity a

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A Carnot engine operating between temperatures $${{T_1}}$$ and $${{T_2}}$$ has efficiency $${1 \over 6}$$. When $${T_2}$

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A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It i

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Three perfect gases at absolute temperatures $${T_1},\,{T_2}$$ and $${T_3}$$ are mixed. The masses of molecules are $${m

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$$100g$$ of water is heated from $${30^ \circ }C$$ to $${50^ \circ }C$$. Ignoring the slight expansion of the water, the

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Two particles are executing simple harmonic motion of the same amplitude $$A$$ and frequency $$\omega $$ along the $$x$$

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A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes

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The transverse displacement $$y(x, t)$$ of a wave on a string is given by $$y\left( {x,t} \right) = {e^{ - \left( {a{x^2

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The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distan

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Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a dist

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If a wire is stretched to make it $$0.1\% $$ longer, its resistance will:

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A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$

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A fully charged capacitor $$C$$ with initial charge $${q_0}$$ is connected to a coil of self inductance $$L$$ at $$t=0.$

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A boat is moving due east in a region where the earth's magnetic fields is $$5.0 \times {10^{ - 5}}$$ $$N{A^{ - 1}}\,{m^

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A resistor $$'R'$$ and $$2\mu F$$ capacitor in series is connected through a switch to $$200$$ $$V$$ direct supply. Acro

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Let $$x$$-$$z$$ plane be the boundary between two transparent media. Medium $$1$$ in $$z \ge 0$$ has a refractive index

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This question has a paragraph followed by two statements, Statement $$-1$$ and Statement $$-2$$. Of the given four alte

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A car is fitted with a convex side-view mirror of focal length $$20$$ $$cm$$. A second car $$2.8m$$ behind the first car

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Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :

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This question has Statement - $$1$$ and Statement - $$2$$. Of the four choices given after the statements, choose the on

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This question has Statement - $$1$$ and Statement - $$2$$. Of the four choices given after the statements, choose the on

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The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \righ

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