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AIEEE 2005

Exam Held on Thu Apr 28 2005 09:30:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

Two solutions of a substance (non electrolyte) are mixed in the following manner...
If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be th...
Of the following sets which one does NOT contain isoelectronic species?
In a multi-electron atom, which of the following orbitals described by the three...
Which of the following oxides is amphoteric in character?
In which of the following arrangements the order is NOT according to the propert...
Lattice energy of an ionic compounds depends upon
Which one of the following statements is NOT true about the effect of an increas...
Consider the reaction: N<sub>2</sub> + 3H<sub>2</sub> $$\to$$ 2NH<sub>3</sub> ca...
If the bond dissociation energies of XY, X<sub>2</sub> and Y<sub>2</sub> (all di...
Consider an endothermic reaction, X $$\to$$ Y with the activation energies E<sub...
If $$\alpha$$ is the degree of dissociation of Na<sub>2</sub>SO<sub>4</sub>, the...
The solubility product of a salt having general formula MX<sub>2</sub>, in water...
The exothermic formation of ClF<sub>3</sub> is represented by the equation: <br>...
For the reaction 2NO<sub>2</sub> (g) $$\leftrightharpoons$$ 2NO (g) + O<sub>2</s...
What is the conjugate base of OH<sup>-</sup>?
Hydrogen ion concentration in mol / L in a solution of pH = 5.4 will be
An amount of solid NH4<sub></sub>HS is placed in a flask already containing ammo...
Which one of the following species is diamagnetic in nature?
Based on lattice energy and other considerations which one of the following alka...
Which of the following statements in relation to the hydrogen atom is correct?
Due to the presence of an unpaired electron, free radicals are:
Reaction of one molecule of HBr with one molecule of 1,3-butadiene at 40<sup>o</...
Of the five isomeric hexanes, the isomer which can give two monochlorinated comp...
2 methylbutane on reacting with bromine in the presence of sunlight gives mainly...
Acid catalyzed hydration of alkenes except ethene leads to the formation of
Which types of isomerism is shown by 2,3-dichlorobutane?
The volume of a colloidal particle, V<sub>C</sub> as compared to the volume of a...
The disperse phase in colloidal iron (III) hydroxide and colloidal gold is posit...
An ionic compound has a unit cell consisting of A ions at the corners of a cube ...
Benzene and toluene form nearly ideal solutions. At 20 <sup>o</sup>C, the vapour...
Equimolar solutions in the same solvent have
For a spontaneous reaction the ∆G , equilibrium constant (K) and $$E_{cell}^o$$ ...
Aluminium oxide may be electrolysed at 1000<sup>o</sup>C to furnish aluminium me...
The highest electrical conductivity of the following aqueous solutions is of
<div style="overflow-x: auto;"> <style type="text/css"> .tg {border-collapse:co...
Hydrogen bomb is based on the principle of
A reaction involving two different reactants can never be
The photon of hard gamma radiation knocks a proton out of $${}_{12}^{24}Mg$$ nuc...
t<sub>1/4</sub> can be taken as the time taken for the concentration of a reacta...
During the process of electrolytic refining of copper, some metals present as im...
The correct order of the thermal stability of hydrogen halides (H – X) is
The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous ac...
Heating an aqueous solution of aluminium chloride to dryness will give
In silicon dioxide
The structure of diborane (B<sub>2</sub>H<sub>6</sub>) contains
The lanthanide contraction is responsible for the fact that
Which of the following factors may be regarded as the main cause of lanthanide c...
The IUPAC name of the coordination compound K<sub>3</sub>[Fe(CN)<sub>6</sub>] is...
The oxidation state of Cr in [Cr(NH<sub>3</sub>)<sub>4</sub>Cl<sub>2</sub>]<sup>...
Which of the following compounds shows optical isomerism?
The value of the ‘spin only’ magnetic moment for one of the following configurat...
Which one of the following cyano complexes would exhibit the lowest value of par...
Tertiary alkyl halides are practically inert to substitution by S<sub>N</sub>2 m...
Elimination of bromine from 2-bromobutane results in the formation of-
Alkyl halides react with dialkyl copper reagents to give
The best reagent to convert pent -3- en-2-ol into pent -3-en-2-one is
Among the following acids which has the lowest pK<sub>a</sub> value?
Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount...
Amongst the following the most basic compound is
Which one of the following methods is neither meant for the synthesis nor for se...
An organic compound having molecular mass 60 is found to contain C = 20%, H = 6....
Which of the following is a polyamide?
Which one of the following types of drugs reduces fever?
In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-
Which of the following is fully fluorinated polymer?
The decreasing order of nucleophilicity among the nucleophiles <br><br><img cla...
The reaction <br><br><img class="question-image" src="https://imagex.cdn.examgoa...
A schematic plot of $$ln$$ $${K_{eq}}$$ versus inverse of temperature for a reac...
$$p$$-cresol reacts with chloroform in alkaline medium to give the compound A wh...
The oxidation state of chromium in the final product formed the reaction between...
Heating mixture of $$C{u_2}O$$ and $$C{u_2}S$$ will give
Calomel $$\left( {H{g_2}C{l_2}} \right)$$ on reaction with ammonium hydroxide gi...
Pick out the isoelectronic structure from the following : <br><br>$$\eqalign{ ...

Mathematics

If $${z_1}$$ and $${z_2}$$ are two non-zero complex numbers such that $$\,\left|...
If the cube roots of unity are 1, $$\omega \,,\,{\omega ^2}$$ then the roots of ...
If $$\,\omega = {z \over {z - {1 \over 3}i}}\,$$ and $$\left| \omega \right| =...
In a triangle $$PQR,\;\;\angle R = {\pi \over 2}.\,\,If\,\,\tan \,\left( {{P \o...
If both the roots of the quadratic equation $${x^2} - 2kx + {k^2} + k - 5 = 0$$ ...
If the letter of the word SACHIN are arranged in all possible ways and these wor...
The value of $$\,{}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}} {C_3}$$ is
If $$A = \left[ {\matrix{ 1 &amp; 0 \cr 1 &amp; 1 \cr } } \right]$$ ...
If the coefficient of $${x^7}$$ in $${\left[ {a{x^2} + \left( {{1 \over {bx}}} \...
If $$x$$ is so small that $${x^3}$$ and higher powers of $$x$$ may be neglected,...
If the coefficients of r<sup>th</sup>, (r+1)<sup>th</sup>, and (r + 2)<sup>th</s...
If $$x = \sum\limits_{n = 0}^\infty {{a^n},\,\,y = \sum\limits_{n = 0}^\infty ...
The sum of the series $$1 + {1 \over {4.2!}} + {1 \over {16.4!}} + {1 \over {64....
The line parallel to the $$x$$ - axis and passing through the intersection of th...
If a vertex of a triangle is $$(1, 1)$$ and the mid points of two sides through ...
A circle touches the x-axis and also touches the circle with centre at (0, 3) an...
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y...
If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\...
If the pair of lines $$a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$$ lie alo...
An ellipse has $$OB$$ as semi minor axis, $$F$$ and $$F$$' its focii and theangl...
The locus of a point $$P\left( {\alpha ,\beta } \right)$$ moving under the condi...
Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x...
The value of $$a$$ for which the sum of the squares of the roots of the equation...
Let $$f:R \to R$$ be a differentiable function having $$f\left( 2 \right) = 6$...
If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers,...
If in a $$\Delta ABC$$, the altitudes from the vertices $$A, B, C$$ on opposite ...
In a triangle $$ABC$$, let $$\angle C = {\pi \over 2}$$. If $$r$$ is the inradi...
If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$ then $$4{x^2} - 4x...
Area of the greatest rectangle that can be inscribed in the <br>ellipse $${{{x^...
The normal to the curve <br>$$x = a\left( {\cos \theta + \theta \sin \theta } ...
A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of unifo...
If the equation $${a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0...
If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is
The system of equations <p>$$\matrix{ {\alpha \,x + y + z = \alpha - 1} \c...
If $${a_1},{a_2},{a_3},........,{a_n},.....$$ are in G.P., then the determinant ...
If $${a^2} + {b^2} + {c^2} = - 2$$ and <p>f$$\left( x \right) = \left| {\matri...
$$\int {{{\left\{ {{{\left( {\log x - 1} \right)} \over {1 + {{\left( {\log x} \...
If $${I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}...
The area enclosed between the curve $$y = {\log _e}\left( {x + e} \right)$$ and ...
The parabolas $${y^2} = 4x$$ and $${x^2} = 4y$$ divide the square region bounded...
Let $$f(x)$$ be a non - negative continuous function such that the area bounded...
The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\...
The value of integral, $$\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \s...
The differential equation representing the family of curves $${y^2} = 2c\left( {...
If $$x{{dy} \over {dx}} = y\left( {\log y - \log x + 1} \right),$$ then the solu...
Three houses are available in a locality. Three persons apply for the houses. Ea...
A random variable $$X$$ has Poisson distribution with mean $$2$$. <br>Then $$P\...
Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \righ...
If the angel $$\theta $$ between the line $${{x + 1} \over 1} = {{y - 1} \over 2...
If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then...
Let $$a, b$$ and $$c$$ be distinct non- negative numbers. If the vectors $$a\wid...
If the plane $$2ax-3ay+4az+6=0$$ passes through the midpoint of the line joining...
The distance between the line <br>$$\overrightarrow r = 2\widehat i - 2\wideha...
The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is
If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ are non coplanar...
For any vector $${\overrightarrow a }$$ , the value of $${\left( {\overrightarr...
Let $$\overrightarrow a \,\, = \,\,\widehat i - \widehat k,\,\,\,\,\,\overrighta...
If non zero numbers $$a, b, c$$ are in $$H.P.,$$ then the straight line $${x \ov...
The plane $$x+2y-z=4$$ cuts the sphere $${x^2} + {y^2} + {z^2} - x + z - 2 = 0$$...
Let $$f:( - 1,1) \to B$$, be a function defined by <br>$$f\left( x \right) = {\...
A real valued function f(x) satisfies the functional equation <br><br>f(x - y) =...
A function is matched below against an interval where it is supposed to be incre...
$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 ...
Suppose $$f(x)$$ is differentiable at x = 1 and <br><br>$$\mathop {\lim }\limits...
Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, t...
Let f be differentiable for all x. If f(1) = -2 and f'(x) $$ \ge $$ 2 for <br>x ...
If $$f$$ is a real valued differentiable function satisfying <br><br>$$\left| {f...
If in a frequently distribution, the mean and median are 21 and 22 respectively,...
Let x<sub>1</sub>, x<sub>2</sub>,...........,x<sub>n</sub> be n observations suc...
If the roots of the equation $${x^2} - bx + c = 0$$ be two consecutive integers,...
The value of $$a$$ for which the sum of the squares of the roots of the equatio...

Physics

Out of the following pair, which one does NOT have identical dimensions is
A car starting from rest accelerates at the rate f through a distance S, then co...
The relation between time t and distance x is t = ax<sup>2</sup> + bx where a an...
A particle is moving eastwards with a velocity of 5 m/s. In 10 seconds the veloc...
A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parac...
A bullet fired into a fixed target loses half of its velocity after penetrating ...
A smooth block is released at rest on a $${45^ \circ }$$ incline and then slides...
A particle of mass 0.3 kg subjected to a force $$F=-kx$$ with $$k=15$$ $$N/m$$. ...
Consider a car moving on a straight road with a speed of $$100$$ $$m/s$$. The di...
An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling wi...
The upper half of an inclined plane with inclination $$\phi $$ is perfectly smoo...
A body of mass $$m$$ is accelerated uniformly from rest to a speed $$v$$ in a ti...
A spherical ball of mass $$20$$ $$kg$$ is stationary at the top of a hill of he...
The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$...
A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity brea...
A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of ma...
The change in the value of $$g$$ at a height $$h$$ above the surface of the eart...
Average density of the earth
If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energ...
A $$20$$ $$cm$$ long capillary tube is dipped in water. The water rises up to $$...
A block is kept on a frictionless inclined surface with angle of inclination $$'...
The block of mass $$M$$ moving on the frictionless horizontal surface collides w...
A mass $$'m'$$ moves with a velocity $$'v'$$ and collides inelastically with ano...
A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen....
Which of the following is <b>incorrect</b> regarding the first law of thermodyna...
A T shaped object with dimensions shown in the figure, is lying on a smooth floo...
A system goes from $$A$$ to $$B$$ via two processes $$I$$ and $$II$$ as shown in...
The figure shows a system of two concentric spheres of radii $${r_1}$$ and $${r_...
The temperature-entropy diagram of a reversible engine cycle is given in the fig...
The function $${\sin ^2}\left( {\omega t} \right)$$ represents
Two simple harmonic motions are represented by the equations $${y_1} = 0.1\,\sin...
The bob of a simple pendulum is a spherical hollow ball filled with water. A plu...
If a simple harmonic motion is represented by $${{{d^2}x} \over {d{t^2}}} + \alp...
When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$...
An observer moves towards a stationary source of sound, with a velocity one-fift...
Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respect...
A parallel plate capacitor is made by stacking $$n$$ equally spaced plates conne...
Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ ap...
A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta ...
A fully charged capacitor has a capacitance $$'C'$$. It is discharged through a ...
Two thin, long, parallel wires, separated by a distance $$'d'$$ carry a current ...
A heater coil is cut into two equal parts and only one part is now used in the h...
In the circuit, the galvanometer $$G$$ shows zero deflection. If the batteries $...
Two voltmeters, one of copper and another of silver, are joined in parallel. Whe...
Two sources of equal $$emf$$ are connected to an external resistance $$R.$$ The...
A moving coil galvanometer has $$150$$ equal divisions. Its current sensitivity ...
The resistance of hot tungsten filament is about $$10$$ times the cold resistanc...
In a potentiometer experiment the balancing with a cell is at length $$240$$ $$...
An energy source will supply a constant current into the load if its internal re...
Two concentric coils each of radius equal to $$2$$ $$\pi $$ $$cm$$ are placed at...
A magnetic needle is kept in a non-uniform magnetic field. It experiences
A uniform electric field and a uniform magnetic field are acting along the same ...
A charged particle of mass $$m$$ and charge $$q$$ travels on a circular path of ...
The self inductance of the motor of an electric fan is $$10$$ $$H$$. In order to...
A coil of inductance $$300$$ $$mH$$ and resistance $$2\,\Omega $$ is connected t...
A circuit has a resistance of $$12$$ $$ohm$$ and an impedance of $$15$$ $$ohm$$....
The phase difference between the alternating current and $$emf$$ is $${\pi \ove...
A fish looking up through the water sees the outside world contained in a circul...
Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by...
A Young's double slit experiment uses a monochromatic source. The shape of the ...
A thin glass (refractive index $$1.5$$) lens has optical power of $$-5$$ $$D$$ i...
If $${I_0}$$ is the intensity of the principal maximum in the single slit diffra...
When an unpolarized light of intensity $${{I_0}}$$ is incident on a polarizing s...
One conducting $$U$$ tube can slide inside another as shown in figure, maintaini...
If radius of the $$\matrix{ {27} \cr {13} \cr } $$ $$Al$$ nucleus is...
Starting with a sample of pure $${}^{66}Cu,{7 \over 8}$$ of it decays into $$Zn$...
The electrical conductivity of a semiconductor increases when electromagnetic ra...
The intensity of gamma radiation from a given source is $$L$$. On passing throug...
If the kinetic energy of a free electron doubles, it's deBroglie wavelength chan...
A photocell is illuminated by a small bright source placed $$1$$ $$m$$ away. Whe...
In a full wave rectifier circuit operating from $$50$$ $$Hz$$ mains frequency, t...
A nuclear transformation is denoted by $$X\left( {n,\alpha } \right)\matrix{ ...
In a common base amplifier, the phase difference between the input signal voltag...
The diagram shows the energy levels for an electron in a certain atom. Which tra...

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