AIEEE 2012

Paper was held on
Sun, Apr 29, 2012 9:30 AM

## Chemistry

The electrons identified by quantum numbers n and l :
(a) n = 4, $$l$$ = 1
(b) n = 4, $$ l$$ = 0
(c) n = 3, $$l$$ = 2
(d

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The increasing order of the ionic radii of the given isoelectronic species is :

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Ortho–Nitrophenol is less soluble in water than p– and m– Nitrophenols because :

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In which of the following pairs the two species are not isostructural ?

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The compressibility factor for a real gas at high pressure is :

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The incorrect expression among the following is :

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The equilibrium constant (KC) for the reaction N2(g) + O2(g) $$\to$$ 2NO(g) at temperature T is 4 $$\times$$ 10–4. The v

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The pH of a 0.1 molar solution of the acid HQ is 3. The value of the ionization constant, Ka of this acid is :

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Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?

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Very pure hydrogen (99.9%) can be made by which of the following processes ?

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Which branched chain isomer of the hydrocarbon with molecular mass 72u gives only one isomer of
mono substituted alkyl h

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2–Hexyne gives trans–2–Hexene on treatment with :

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Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius
of the lith

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According to Freundlich adsorption isotherm, which of the following is correct ?

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The density of a solution prepared by dissolving 120 g of urea (mol. Mass = 60 u ) in 1000g of water is
1.15 g/mL. The m

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Kf for water is 1.86K kg mol–1. If your automobile radiator holds 1.0 kg of water, how many grams of
ethylene glycol (C2

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The standard reduction potentials for Zn2+/ Zn, Ni2+/ Ni, and Fe2+/ Fe are –0.76, –0.23 and –0.44 V respectively. The re

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For a first order reaction, (A) $$\to$$ products, the concentration of A changes from 0.1 M to 0.025 M in 40
minutes. Th

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Which method of purification is represented by the following equation :
Ti (s) + 2I2 (g) $$\buildrel {523K} \over
\long

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The molecule having smallest bond angle is :

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Iron exhibits + 2 and +3 oxidation states. Which of the following statements about iron is incorrect ?

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Which among the following will be named as dibromidobis (ethylene diamine) chromium(III) bromide ?

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How many chiral compounds are possible on monochlorination of 2–methyl butane ?

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What is DDT among the following?

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Iodoform can be prepared from all except :

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Which of the following compounds can be detected by Molisch’s test ?

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The species which can best serve as an initiator for the cationic polymerization is :

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Which one of the following statements is correct ?

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Aspirin is known as :

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In the given transformation, which of the following is the most appropriate reagent ?

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## Mathematics

In a $$\Delta PQR,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} $$ If $$3{\mkern 1mu} \sin {\mkern 1mu} P + 4{\mkern 1mu} \cos

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If $$z \ne 1$$ and $$\,{{{z^2}} \over {z - 1}}\,$$ is real, then the point represented by the complex number z lies :

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The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:

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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can b

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If $$n$$ is a positive integer, then $${\left( {\sqrt 3 + 1} \right)^{2n}} - {\left( {\sqrt 3 - 1} \right)^{2n}}$$ is

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Statement-1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) +.....+ (361 + 380 + 400) is 8000.

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If the line $$2x + y = k$$ passes through the point which divides the line segment joining the points $$(1, 1)$$ and $$(

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The length of the diameter of the circle which touches the $$x$$-axis at the point $$(1, 0)$$ and passes through the poi

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STATEMENT-1 : An equation of a common tangent to the parabola $${y^2} = 16\sqrt 3 x$$ and the ellipse $$2{x^2} + {y^2} =

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An ellipse is drawn by taking a diameter of thec circle $${\left( {x - 1} \right)^2} + {y^2} = 1$$ as its semi-minor axi

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Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \n

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A spherical balloon is filled with $$4500\pi $$ cubic meters of helium gas. If a leak in the balloon causes the gas to e

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A line is drawn through the point $$(1, 2)$$ to meet the coordinate axes at $$P$$ and $$Q$$ such that it forms a triang

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Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determina

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Let $$A = \left( {\matrix{
1 & 0 & 0 \cr
2 & 1 & 0 \cr
3 & 2 & 1 \cr
} } \right

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If the $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,} $$ then $$a$$ is

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The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :

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If $$g\left( x \right) = \int\limits_0^x {\cos 4t\,dt,} $$ then $$g\left( {x + \pi } \right)$$ equals

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The population $$p$$ $$(t)$$ at time $$t$$ of a certain mouse species satisfies the differential equation $${{dp\left( t

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Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their

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Let $$\overrightarrow a $$ and $$\overrightarrow b $$ two unit vectors. If the vectors $$\,\overrightarrow c = \widehat

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A equation of a plane parallel to the plane $$x-2y+2z-5=0$$ and at a unit distance from the origin is :

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If the line $${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}$$ and $${{x - 3} \over 1} = {{y - k} \over 2} =

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Let $$ABCD$$ be a parallelogram such that $$\overrightarrow {AB} = \overrightarrow q ,\overrightarrow {AD} = \overrigh

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If $$f:R \to R$$ is a function defined by
$$f\left( x \right) = \left[ x \right]\cos \left( {{{2x - 1} \over 2}} \right)

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Consider the function, $$f\left( x \right) = \left| {x - 2} \right| + \left| {x - 5} \right|,x \in R$$
Statement - 1 : $

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The negation of the statement “If I become a teacher, then I will open a school” is

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Let x1, x2,........., xn be n observations, and let $$\overline x $$ be their arithematic mean and $${\sigma ^2}$$ be th

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Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y $$ \subseteq $$ X,

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## Physics

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference
applied across

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A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Ve

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A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy
can throw the same

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Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they mak

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This question has Statement $$1$$ and Statement $$2.$$ Of the four choices given after the Statements, choose the one th

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The mass of a spaceship is $$1000$$ $$kg.$$ It is to be launched from the earth's surface out into free space. The value

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A Carnot engine, whose efficiency is $$40\% $$, takes in heat from a source maintained at a temperature of $$500$$ $$K.$

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A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times {10^{ - 2}}\,\,N$

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Helium gas goes through a cycle $$ABCD$$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency

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A liquid in a beaker has temperature $$\theta \left( t \right)$$ at time $$t$$ and $${\theta _0}$$ is temperature of sur

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A wooden wheel of radius $$R$$ is made of two semicircular part (see figure). The two parts are held together by a ring

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If a simple pendulum has significant amplitude (up to a factor of $$1/e$$ of original ) only in the period between $$t =

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A cylindrical tube, open at both ends, has a fundamental frequency, $$f,$$ in air. The tube is dipped vertically in wate

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

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In a uniformly charged sphere of total charge $$Q$$ and radius $$R,$$ the electric field $$E$$ is plotted as function of

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Two electric bulbs marked $$25W$$ $$-$$ $$220$$ $$V$$ and $$100W$$ $$-$$ $$220V$$ are connected in series to a $$440$$ $

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Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic fi

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A charge $$Q$$ is uniformly distributed over the surface of non-conducting disc of radius $$R.$$ The disc rotates about

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A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. Whe

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In Young's double slit experiment , one of the slit is wider than other, so that amplitude of the light from one slit is

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An electromagnetic wave in vacuum has the electric and magnetic field $$\mathop E\limits^ \to $$and $$\mathop B\limits^

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An object $$2.4$$ $$m$$ in front of a lens forms a sharp image on a film $$12$$ $$cm$$ behind the lens. A glass plate $

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Hydrogen atom is excited from ground state to another state with principal quantum number equal to $$4.$$ Then the numbe

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A radar has a power of $$1kW$$ and is operating at a frequency of $$10$$ $$GHz.$$ It is located on a mountain top of hei

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Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutr

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A diatomic molecule is made of two masses $${m_1}$$ and $${m_2}$$ which are separated by a distance $$r.$$ If we calcula

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Truth table for system of four $$NAND$$ gates as shown in figure is:

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A particle of mass $$m$$ is at rest at the origin at time $$t=0.$$ It is subjected to a force $$F\left( t \right) = {F_0

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This question has Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best

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The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $$\tau $$ of t

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