AIEEE 2005

Paper was held on
Thu, Apr 28, 2005 9:30 AM

## Chemistry

Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 m

View Question If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of

View Question Of the following sets which one does NOT contain isoelectronic species?

View Question In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same ener

View Question Which of the following oxides is amphoteric in character?

View Question In which of the following arrangements the order is NOT according to the property
indicated against it?

View Question Lattice energy of an ionic compounds depends upon

View Question Consider the reaction: N2 + 3H2 $$\to$$ 2NH3 carried out at constant temperature and
pressure. If $$\Delta H$$ and $$\De

View Question If the bond dissociation energies of XY, X2 and Y2 (all diatomic molecules) are in the ratio of 1:1:0.5 and $$\Delta H_f

View Question Consider an endothermic reaction, X $$\to$$ Y with the activation energies Eb and Ef
for the backward and forward reacti

View Question If $$\alpha$$ is the degree of dissociation of Na2SO4, the vant Hoff’s factor (i) used for
calculating the molecular mas

View Question The solubility product of a salt having general formula MX2, in water is: 4 $$\times$$ 10-12 . The
concentration of M2+

View Question The exothermic formation of ClF3 is represented by the equation:
Cl2 (g) + 3F2 (g) $$\leftrightharpoons$$ 2ClF3 (g); $$

View Question For the reaction
2NO2 (g) $$\leftrightharpoons$$ 2NO (g) + O2 (g), (Kc = 1.8 $$\times$$ 10-6 at 184oC) (R = 0.0831 kJ/(m

View Question What is the conjugate base of OH-?

View Question Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be :

View Question An amount of solid NH4HS is placed in a flask already containing ammonia gas at a
certain temperature and 0.50 atm. Pres

View Question Which one of the following species is diamagnetic in nature?

View Question Due to the presence of an unpaired electron, free radicals are:

View Question Reaction of one molecule of HBr with one molecule of 1,3-butadiene at 40oC gives
predominantly

View Question Of the five isomeric hexanes, the isomer which can give two monochlorinated
compounds is

View Question 2 methylbutane on reacting with bromine in the presence of sunlight gives mainly

View Question Acid catalyzed hydration of alkenes except ethene leads to the formation of

View Question Which types of isomerism is shown by 2,3-dichlorobutane?

View Question Benzene and toluene form nearly ideal solutions. At 20 oC, the vapour pressure of
benzene is 75 torr and that of toluene

View Question Equimolar solutions in the same solvent have

View Question For a spontaneous reaction the ∆G , equilibrium constant (K) and $$E_{cell}^o$$ will be respectively

View Question Aluminium oxide may be electrolysed at 1000oC to furnish aluminium metal (Atomic
mass = 27 amu; 1 Faraday = 96,500 Coulo

View Question The highest electrical conductivity of the following aqueous solutions is of :

View Question
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View Question Hydrogen bomb is based on the principle of

View Question A reaction involving two different reactants can never be

View Question The photon of hard gamma radiation knocks a proton out of $${}_{12}^{24}Mg$$ nucleus to form

View Question t1/4 can be taken as the time taken for the concentration of a reactant to drop to $$3 \over 4$$ of its initial value. I

View Question The lanthanide contraction is responsible for the fact that :

View Question Which of the following factors may be regarded as the main cause of lanthanide
contraction?

View Question The IUPAC name of the coordination compound K3[Fe(CN)6] is

View Question The oxidation state of Cr in [Cr(NH3)4Cl2]+ is :

View Question Which of the following compounds shows optical isomerism?

View Question The value of the ‘spin only’ magnetic moment for one of the following configurations
is 2.84 BM. The correct one is :

View Question Which one of the following cyano complexes would exhibit the lowest value of
paramagnetic behaviour?
(At. No. Cr = 24,

View Question Tertiary alkyl halides are practically inert to substitution by SN2 mechanism because of

View Question Elimination of bromine from 2-bromobutane results in the formation of-

View Question Alkyl halides react with dialkyl copper reagents to give

View Question The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one is

View Question Among the following acids which has the lowest pKa value?

View Question Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of
an acid forms a compound if water du

View Question Amongst the following the most basic compound is

View Question Which one of the following methods is neither meant for the synthesis nor for
separation of amines?

View Question An organic compound having molecular mass 60 is found to contain C = 20%, H =
6.67% and N = 46.67% while rest is oxygen.

View Question In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-

View Question The decreasing order of nucleophilicity among the nucleophiles

View Question The reaction
is fastest when $$X$$ is

View Question A schematic plot of $$ln$$ $${K_{eq}}$$ versus inverse of temperature for a reaction is shown below
The reaction must

View Question $$p$$-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the c

View Question The oxidation state of chromium in the final product formed the reaction between $$K{\rm I}$$ and acidified potassium di

View Question On heating mixture of $$C{u_2}O$$ and $$C{u_2}S$$ will give :

View Question Calomel $$\left( {H{g_2}C{l_2}} \right)$$ on reaction with ammonium hydroxide gives :

View Question Pick out the isoelectronic structure from the following :
$$\eqalign{
& \left( i \right)\,\,\,\,\,\,C{H_3}^ + \

View Question ## Mathematics

If $${z_1}$$ and $${z_2}$$ are two non-zero complex numbers such that $$\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}

View Question If the cube roots of unity are 1, $$\omega \,,\,{\omega ^2}$$ then the roots of the equation $${(x - 1)^3}$$ + 8 = 0, ar

View Question If $$\,\omega = {z \over {z - {1 \over 3}i}}\,$$ and $$\left| \omega \right| = 1$$, then $$z$$ lies on :

View Question In a triangle $$PQR,\;\;\angle R = {\pi \over 2}.\,\,If\,\,\tan \,\left( {{P \over 2}} \right)$$ and $$ \tan \left( {{Q

View Question If both the roots of the quadratic equation $${x^2} - 2kx + {k^2} + k - 5 = 0$$ are less than 5, then $$k$$ lies in the

View Question If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, the

View Question If the coefficient of $${x^7}$$ in $${\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}$$ equals the coe

View Question If $$x$$ is so small that $${x^3}$$ and higher powers of $$x$$ may be neglected, then $${{{{\left( {1 + x} \right)}^{{3

View Question If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of $${{\rm{(1 + y )}}^m}$$ are in A

View Question If $$x = \sum\limits_{n = 0}^\infty {{a^n},\,\,y = \sum\limits_{n = 0}^\infty {{b^n},\,\,z = \sum\limits_{n = 0}^\inft

View Question The line parallel to the $$x$$ - axis and passing through the intersection of the lines $$ax + 2by + 3b = 0$$ and $$bx -

View Question If a vertex of a triangle is $$(1, 1)$$ and the mid points of two sides through this vertex are $$(-1, 2)$$ and $$(3, 2)

View Question If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = {p^2}$$ orthogonally, then the equ

View Question If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, =

View Question If the pair of lines $$a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$$ lie along diameters of a circle and divide the

View Question An ellipse has $$OB$$ as semi minor axis, $$F$$ and $$F$$' its focii and theangle $$FBF$$' is a right angle. Then the ec

View Question Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x$$. The locus of mid point of $$PQ$$ is

View Question The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a -

View Question Let $$f:R \to R$$ be a differentiable function having $$f\left( 2 \right) = 6$$,
$$f'\left( 2 \right) = \left( {{1 \o

View Question If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals

View Question If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$ then $$4{x^2} - 4xy\cos \alpha + {y^2}$$ is equal to :

View Question Area of the greatest rectangle that can be inscribed in the
ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}}

View Question A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$5

View Question If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is :

View Question The system of equations
$$\matrix{
{\alpha \,x + y + z = \alpha - 1} \cr
{x + \alpha y + z = \alpha - 1} \cr

View Question If $${a_1},{a_2},{a_3},........,{a_n},.....$$ are in G.P., then the determinant
$$$\Delta = \left| {\matrix{
{\log {

View Question If $${a^2} + {b^2} + {c^2} = - 2$$ and
f$$\left( x \right) = \left| {\matrix{
{1 + {a^2}x} & {\left( {1 + {b^2}

View Question $$\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \right)}^2}}}} \right\}}^2}\,\,dx} $$ is

View Question If $${I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}

View Question The area enclosed between the curve $$y = {\log _e}\left( {x + e} \right)$$ and the coordinate axes is :

View Question The parabolas $${y^2} = 4x$$ and $${x^2} = 4y$$ divide the square region bounded by the lines $$x=4,$$ $$y=4$$ and the c

View Question Let $$f(x)$$ be a non - negative continuous function such that the area bounded by the curve $$y=f(x),$$ $$x$$-axis and

View Question The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\,\,a > 0,} $$ is

View Question The value of integral, $$\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \sqrt x }}} dx $$ is

View Question The differential equation representing the family of curves $${y^2} = 2c\left( {x + \sqrt c } \right),$$ where $$c>0,

View Question If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solution of the equation is :

View Question Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consult

View Question A random variable $$X$$ has Poisson distribution with mean $$2$$.
Then $$P\left( {X > 1.5} \right)$$ equals :

View Question Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},$$ $$P\left( {A \cap B}

View Question If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then :

View Question Let $$a, b$$ and $$c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\,\,\w

View Question The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :

View Question For any vector $${\overrightarrow a }$$ , the value of $${\left( {\overrightarrow a \times \widehat i} \right)^2} + {\

View Question If non zero numbers $$a, b, c$$ are in $$H.P.,$$ then the straight line $${x \over a} + {y \over b} + {1 \over c} = 0$$

View Question Let $$f:( - 1,1) \to B$$, be a function defined by
$$f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$,
then

View Question A real valued function f(x) satisfies the functional equation
f(x - y) = f(x)f(y) - f(a - x)f(a + y)
where a is given co

View Question A function is matched below against an interval where it is supposed to be
increasing. Which of the following pairs is i

View Question Suppose $$f(x)$$ is differentiable at x = 1 and
$$\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) =

View Question Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then
$$\mathop {\lim }\limits_{x \to \alp

View Question If $$f$$ is a real valued differentiable function satisfying
$$\left| {f\left( x \right) - f\left( y \right)} \right|$$

View Question If in a frequency distribution, the mean and median are 21 and 22 respectively, then
its mode is approximately :

View Question Let x1, x2,...........,xn be n observations such that
$$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a
possibl

View Question If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers, then $${b^2} - 4c$$ equals

View Question The value of $$a$$ for which the sum of the squares of the roots of the equation $${x^2} - \left( {a - 2} \right)x - a

View Question Let $R=\{(3,3),(6,6),(9,9),(12,12),(6,12)$, $(3,9),(3,12),(3,6)\}$ be a relation on the set $A=\{3,6,9,12\}$. The relati

View Question A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of $2 \mathrm{~cm} / \ma

View Question ## Physics

Out of the following pair, which one does NOT have identical dimensions is

View Question A car starting from rest accelerates at the rate f through a distance S, then continues
at constant speed for time t and

View Question The relation between time t and distance x is t = ax2 + bx where a and b are constants.
The acceleration is

View Question A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the velocity
changes to 5 m/s northwards. The ave

View Question A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parachute opens, it decelerates at $$2\,\,m/{

View Question A bullet fired into a fixed target loses half of its velocity after penetrating $$3$$ $$cm.$$ How much further it will p

View Question A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides a distance $$'d'$$. The time taken to s

View Question A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. What will be its initial acceleration if

View Question Consider a car moving on a straight road with a speed of $$100$$ $$m/s$$. The distance at which car can be stopped is $$

View Question An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular sp

View Question The upper half of an inclined plane with inclination $$\phi $$ is perfectly smooth while the lower half is rough. A body

View Question A body of mass $$m$$ is accelerated uniformly from rest to a speed $$v$$ in a time $$T.$$ The instantaneous power delive

View Question A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of height $$100$$ $$m$$. It rolls down a smoo

View Question The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the pl

View Question A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass

View Question A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm

View Question The change in the value of $$g$$ at a height $$h$$ above the surface of the earth is the same as at a depth $$d$$ below

View Question Average density of the earth

View Question If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is

View Question A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$8$$ $$cm.$$ If the entire arrangement is

View Question A block is kept on a frictionless inclined surface with angle of inclination $$'\,\alpha \,'.$$ The incline is given an

View Question The block of mass $$M$$ moving on the frictionless horizontal surface collides with the spring of spring constant $$k$$

View Question A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with another identical mass. After collision the

View Question A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio $${{Cp} \over {{C_v}}}$$ of t

View Question Which of the following is incorrect regarding the first law of thermodynamics?

View Question A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $$'\,\,\overrightarrow F \,\,

View Question A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in figure. If $$\Delta {U_1}$$ and $$\Delt

View Question The figure shows a system of two concentric spheres of radii $${r_1}$$ and $${r_2}$$ are kept at temperatures $${T_1}$$

View Question The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

View Question The function $${\sin ^2}\left( {\omega t} \right)$$ represents

View Question Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \rig

View Question The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscilla

View Question If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$$ its time period is

View Question When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, so

View Question Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$

View Question A parallel plate capacitor is made by stacking $$n$$ equally spaced plates connected alternatively. If the capacitance b

View Question Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ apart with their axes coinciding. The char

View Question A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta $$ with a large charged conducting sheet

View Question A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a small coil of resistance wire embedded i

View Question Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current of $$'i'$$ $$A$$ in the same direction.

View Question A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

View Question In the circuit, the galvanometer $$G$$ shows zero deflection. If the batteries $$A$$ and $$B$$ have negligible internal

View Question Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge $$q$$ flows through the

View Question Two sources of equal $$emf$$ are connected to an external resistance $$R.$$ The internal resistance of the two sources

View Question A moving coil galvanometer has $$150$$ equal divisions. Its current sensitivity is $$10$$- divisions per milliampere and

View Question The resistance of hot tungsten filament is about $$10$$ times the cold resistance. What will be resistance of $$100$$ $$

View Question An energy source will supply a constant current into the load if its internal resistance is

View Question Two concentric coils each of radius equal to $$2$$ $$\pi $$ $$cm$$ are placed at right angles to each other. $$3$$ ampe

View Question A magnetic needle is kept in a non-uniform magnetic field. It experiences :

View Question A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an ele

View Question A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of radius $$r$$ that is perpendicular to a

View Question The self inductance of the motor of an electric fan is $$10$$ $$H$$. In order to impart maximum power at $$50$$ $$Hz$$,

View Question A coil of inductance $$300$$ $$mH$$ and resistance $$2\,\Omega $$ is connected to a source of voltage $$2$$ $$V$$. The c

View Question A circuit has a resistance of $$12$$ $$ohm$$ and an impedance of $$15$$ $$ohm$$. The power factor of the circuit will be

View Question The phase difference between the alternating current and $$emf$$ is $${\pi \over 2}.$$ Which of the following cannot be

View Question A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of w

View Question Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by eye of pupil diameter $$3$$ $$mm.$$ App

View Question A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen

View Question A thin glass (refractive index $$1.5$$) lens has optical power of $$-5$$ $$D$$ in air. Its optical power in a liquid med

View Question If $${I_0}$$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its int

View Question When an unpolarized light of intensity $${{I_0}}$$ is incident on a polarizing sheet, the intensity of the light which d

View Question One conducting $$U$$ tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes

View Question The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than $$248

View Question If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

View Question A photocell is illuminated by a small bright source placed $$1$$ $$m$$ away. When the same source of light is placed $${

View Question In a full wave rectifier circuit operating from $$50$$ $$Hz$$ mains frequency, the fundamental frequency in the ripple w

View Question A nuclear transformation is denoted by $$X\left( {n,\alpha } \right)\matrix{
7 \cr
3 \cr
} Li.$$ Which of th

View Question The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of

View Question