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## AIEEE 2003

Exam Held on Sat Apr 26 2003 09:30:00 GMT+0000 (Coordinated Universal Time)
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## Chemistry

What volume of hydrogen gas at 273 K and 1 atm pressure will be consumed in obta...
25 ml of a solution of barium hydroxide on titration with a 0.1 molar solution o...
The number of d-electrons retained in Fe<sup>2+</sup> (At no of Fe = 26) ion is
The orbital angular momentum for an electron revolving in an orbit is given by $... Which one of the following groupings represents a collection of isoelectronic sp... In Bohr series of lines of hydrogen spectrum, the third line from the red end co... The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity o... According to the Periodic Law of elements, the variation in properties of elemen... Which one of the following is an amphoteric oxide? An ethar is more volatile than an alcohol having the same molecular formula. Thi... Which one of the following pairs of molecules will have permanent dipole moments... The pair of species having identical shapes for molecules of both species is Which one of the following compounds has the smallest bond angle in its molecule... According to the kinetic theory of gases, in an ideal gas, between two successiv... The internal energy change when a system goes from state A to B is 40 kJ/mole. I... In an irreversible process taking place at constant T and P and in which only pr... The enthalpy change for a reaction does not depend upon The correct relationship between free energy change in a reaction and the corres... If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respect... The solubility in water of a sparingly soluble salt AB<sub>2</sub> is 1.0 $$\tim... Which one of the following statements is not true? Consider the reaction equilibrium<br> 2 SO<sub>2</sub> (g) + O<sub>2</sub> (g) ... For the reaction equilibrium <br> N<sub>2</sub>O<sub>4</sub> (g)$$\leftrighthar... When rain is accompanied by a thunderstorm, the collected rain water will have a... In curing cement plasters water is sprinkled from time to time. This helps in The solubilities of carbonates decrease down the magnesium group due to a decrea... The substance not likely to contain CaCO<sub>3</sub> is Which one of the following process will produce hard water? The IUPAC name of CH<sub>3</sub>COCH(CH<sub>3</sub>)<sub>2</sub> is In the anion HCOO<sup>$$-$$</sup> the two carbon-oxygen bonds are found to be o... The general formula C<sub>n</sub>H<sub>2n</sub>O<sub>2</sub> could be for open c... On mixing a certain alkane with chlorine and irradiating it with ultravioletligh... Butene-1 may be converted to butane by reaction with Which one of the following characteristics is not correct for physical adsorptio... How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.... A pressure cooker reduces cooking time for food because In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.... If liquids A and B form an ideal solution Standard reduction electrode potentials of three metals A,B&amp;C are respective... For a cell reaction involving a two-electron change, the standard e.m.f. of the ... When during electrolysis of a solution of AgNO<sub>3</sub> 9650 coulombs of char... For the redox reaction Zn(s) + Cu<sup>2+</sup>(0.1 M) $$\to$$ Zn<sup>2+</sup>(1M... Several blocks of magnesium are fixed to the bottom of a ship to The radionucleide $${}_{90}^{234}Th$$ undergoes two successive $$\beta$$ -decays... The half-life of a radioactive isotope is three hours. If the initial mass of th... In respect of the equation k = Ae<sup>-E<sub>a</sub>/RT</sup> in chemical kineti... The rate law for a reaction between the substances A and B is given by Rate = k[... For the reaction system: <br><br>2NO(g) + O<sub>2</sub>(g) $$\to$$ 2NO<sub>2</s... Graphite is a soft solid lubricant extremely difficult to melt. The reason for t... Concentrated hydrochloric acid when kept in open air sometimes produces a cloud ... Which one of the following substances has the highest proton affinity? What may be expected to happen when phosphine gas is mixed with chlorine gas? For making good quality mirrors, plates of float glass are used. These are obtai... Glass is a What would happen when a solution of potassium chromate is treated with an exces... The atomic numbers of vanadium (V), Chromium (Cr), manganese (Mn) and iron (Fe) ... Which one of the following nitrates will leave behind a metal on strong heating?... Ammonia forms the complex ion [Cu(NH<sub>3</sub>)<sub>4</sub>]<sup>2+</sup> with... The radius of La<sup>3+</sup> (Atomic number of La = 57) is 1.06 Å. Which one of... One mole of the complex compound Co(NH<sub>3</sub>)<sub>5</sub>Cl<sub>3</sub>, g... In the coordination compound, K<sub>4</sub>[Ni(CN)<sub>4</sub>], the oxidation s... Bottles containing C<sub>6</sub>H<sub>5</sub>l and C<sub>6</sub>H<sub>5</sub>CH<... During dehydration of alcohols to alkenes by heating with conc. H<sub>2</sub>SO<... When CH<sub>2</sub> = CH - COOH is reduced with LiAlH<sub>4</sub>, the compound ... The correct order of increasing basic nature for the bases NH<sub>3</sub>, CH<su... Ethyl isocyanide on hydrolysis in acidic medium generates Which of the following could act as a propellant for rockets? Complete hydrolysis of cellulose gives Nylon threads are made of Which one of the following statements is correct? Among the following four structures $$i$$ to $$iv,$$ <br><br><img src="https://i... The reduction in atomic size with increase in atomic number is a characteristic... The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe),... The reaction of chloroform with alcoholic $$KOH$$ and p-toluidine forms The reason for double helical structure of $$DNA$$ is operation of A red solid is insolvable in water. However it becomes soluble if some $$K{\rm I... ## Mathematics If$$z$$and$$\omega $$are two non-zero complex numbers such that$$\left| {z\... Let $${Z_1}$$ and $${Z_2}$$ be two roots of the equation $${Z^2} + aZ + b = 0$$,... If $${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$$ then If the sum of the roots of the quadratic equation $$a{x^2} + bx + c = 0$$ is equ... The value of '$$a$$' for which one root of the quadratic equation $$\left( {{a... The number of real solutions of the equation$${x^2} - 3\left| x \right| + 2 = 0... The real number $$x$$ when added to its inverse gives the minimum value of the s... If $$x$$ is positive, the first negative term in the expansion of $${\left( {1 +... The number of ways in which 6 men and 5 women can dine at a round table if no tw... The number of integral terms in the expansion of$${\left( {\sqrt 3 + \root 8 \... A student is to answer 10 out of 13 questions in an examination such that he mus... If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time... The sum of the serier $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}}........ A square of side a lies above the$$x$$-axis and has one vertex at the origin. T... If the pair of straight lines$${x^2} - 2pxy - {y^2} = 0$$and$${x^2} - 2qxy - ... If $${x_1},{x_2},{x_3}$$ and $${y_1},{y_2},{y_3}$$ are both in G.P. with the sam... Locus of centroid of the triangle whose vertices are $$\left( {a\cos t,a\sin t} ... If the equation of the locus of a point equidistant from the point$$\left( {{a_... If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, +... The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 1... The normal at the point$$\left( {bt_1^2,2b{t_1}} \right)$$on a parabola meets t... The foci of yhe ellipse$${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$a... If$$f\left( y \right) = {e^y},g\left( y \right) = y;y &gt; 0$$and <br>$$... If $$f\left( x \right) = {x^n},$$ then the value of <p>$$f\left( 1 \right) - {{... Let$$f\left( x \right)$$be a polynomial function of second degree. If$$f\lef... The sum of the radii of inscribed and circumscribed circles for an $$n$$ sided r... In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$, <br>$$... If in a$$\Delta ABCa{\cos ^2}\left( {{C \over 2}} \right) + {\cos ^2}\left... The trigonometric equation $${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$ has a solution... If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where$...
If $$A = \left[ {\matrix{ a &amp; b \cr b &amp; a \cr } } \right]$$ ...
If $$1,$$ $$\omega ,{\omega ^2}$$ are the cube roots of unity, then <p>$$\Delt... If the system of linear equations <br>$$x + 2ay + az = 0;x + 3by + bz = 0;...
The area of the region bounded by the curves $$y = \left| {x - 1} \right|$$ and ...
Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)... If$$f\left( {a + b - x} \right) = f\left( x \right)$$then$$\int\limits_a^b {x...
The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx... The solution of the differential equation <br><br>$$\left( {1 + {y^2}} \right) ...
The degree and order of the differential equation of the family of all parabolas...
Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) =... The mean and variance of a random variable$$X$$having binomial distribution ar... Five horses are in a race. Mr. A selects two of the horses at random and bets on... Let$$\overrightarrow u = \widehat i + \widehat j,\,\overrightarrow v = \wideh...
The vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k\,\,\&amp; \,\,\o... The shortest distance from the plane$$12x+4y+3z=327$$to the sphere$${x^2} + {...
The two lines $$x=ay+b,z=cy+d$$ and $$x = a'y + b',z = c'y + d'$$ will be perpen...
The lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and...
$$\overrightarrow a \,,\overrightarrow b \,,\overrightarrow c$$ are $$3$$ vect...
The radius of the circle in which the sphere <br>$${x^2} + {y^2} + {z^2} + 2x -... A tetrahedron has vertices at$$O(0,0,0), A(1,2,1) B(2,1,3)$$and$$C(-1,1,2).$$... If$$\left| {\matrix{ a &amp; {{a^2}} &amp; {1 + {a^3}} \cr b &amp; {{b^...
Consider points $$A, B, C$$ and $$D$$ with position <br>vectors $$7\widehat i -... If$$\overrightarrow u \,,\overrightarrow v $$and$$\overrightarrow w $$are th... Two systems of rectangular axes have the same origin. If a plane cuts then at di... The function$$f\left( x \right) = \log \left( {x + \sqrt {{x^2} + 1} } \ri...
A function $$f$$ from the set of natural numbers to integers defined by $$f\lef... If$$f:R \to R$$satisfies$$f$$(x + y) =$$f$$(x) +$$f$$(y), for all x, y$$ \...
Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log ...$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \ov...
The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec ... If$$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left...
Let $$f(a) = g(a) = k$$ and their n<sup>th</sup> derivatives <br>$${f^n}(a)$$, $... $$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \o... If$$f(x) = \left\{ {\matrix{ {x{e^{ - \left( {{1 \over {\left| x \right|}} +... In an experiment with 15 observations on $$x$$, then following results were avai... The median of a set of 9 distinct observations is 20.5. If each of the largest 4... ## Physics Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their... The physical quantities not having same dimensions are A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least ... A boy playing on the roof of a 10 m high building throws a ball with a speed of ... The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha ... A spring balance is attached to the ceiling of a lift. A man hangs his bag on th... A light spring balance hangs from the hook of the other light spring balance and... A marble block of mass$$2kg$$lying on ice when given a velocity of$$6$$... A block of mass$$M$$is pulled along a horizontal frictionless surface by a rop... A rocket with a lift-off mass$$3.5 \times {10^4}\,\,kg$$is blasted upwards wit... Consider the following two statements: <br>$$A.\,\,\,\,\,\,$$Linear moment... A spring of spring constant$$5 \times {10^3}\,N/m$$is stretched initially by ... A wire suspended vertically from one of its ends is stretched by attaching a wei... A body is moved along a straight line by a machine delivering a constant power. ... A particle performing uniform circular motion has angular frequency is doubled &... A circular disc$$X$$of radius$$R$$is made from an iron plate of thickness ... Let$$\overrightarrow F $$be the force acting on a particle having position ve... The time period of satellite of earth is$$5$$hours. If the separation between ... The escape velocity for a body projected vertically upwards from the surface of ... Two spherical bodies of mass$$M$$and$$5M$$&amp; radii$$R$$&amp;$$2R$$res... Three forces start acting simultaneously on a particle moving with velocity,$$\... A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary ... ''Heat cannot by itself flow from a body at lower temperature to a body at highe... During an adiabatic process, the pressure of a gas is found to be proportional t... Which of the following parameters does not characterize the thermodynamic state ... A carnot engine takes $$3 \times {10^6}$$ cal. of heat from a reservoir at $${62... According to Newton's law of cooling, the rate of cooling of a body is proportio... The earth radiates in the infra-red region of the spectrum. The spectrum is corr... A mass$$M$$is suspended from a spring of negligible mass. The spring is pulled... Two particles$$A$$and$$B$$of equal masses are suspended from two massless sp... The displacement of particle varies according to the relation <br>$$x=4\lef... The length of a simple pendulum executing simple harmonic motion is increased by... A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kine... A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tensi... The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by ... A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second wit... If the electric flux entering and leaving an enclosed surface respectively is $$... A sheet of aluminium foil of negligible thickness is introduced between the plat... A thin spherical conducting shell of radius$$R$$has a charge$$q.$$Another ch... The work done in placing a charge of$$8 \times {10^{ - 18}}$$coulomb on a cond... Three charges$$ - {q_1}, + {q_2}$$and$$ - {q_3}$$are placed as shown in the ... The length of a given cylindrical wire is increased by$$100\% $$. Due to the co... The length of a wire of a potentiometer is$$100cm$$, and the$$e.m.$$... The thermo$$e.m.f.$$of a thermo -couple is$$25\mu V/{}^ \circ C$$at roo... An ammeter reads upto$$1$$ampere. Its internal resistance is$$0.81ohm$$.... The nagative$$Zn$$pole of a Daniell cell, sending a constant current through a... A$$3$$volt battery with negligible internal resistance is connected in a circu... A$$220$$volt,$$1000$$watt bulb is connected across a$$110volt$$mains ... A thin rectangular magnet suspended freely has a period of oscillation equal to ... A particle of mass$$M$$and charge$$Q$$moving with velocity$$\overrightarrow... A particle of charge $$- 16 \times {10^{ - 18}}$$ coulomb moving with velocity ... A magnetic needle lying parallel to a magnetic field requires $$W$$ units of wor... The magnetic lines of force inside a bar magnet Two coils are placed close to each other. The mutual inductance of the pair of c... In an oscillating $$LC$$ circuit the maximum charge on the capacitor is $$Q$$. T... When the current changes from $$+ 2A$$ to $$-2A$$ in $$0.05$$ second, an $$e.m.... The core of any transformer is laminated so as to Consider telecommunication through optical fibres. Which of the following statem... To demonstrate the phenomenon of interference, we require two sources which emit... To get three images of a single object, one should have two plane mirrors at an ... The image formed by an objective of a compound microscope is A strip of copper and another of germanium are cooled from room temperature to ... Which of the following radiations has the least wavelength ? When a$${U^{238}}$$nucleus originally at rest, decays by emitting an alpha par... The difference in the variation of resistance with temperature in a metal and a ... A radioactive sample at any instant has its disintegration rate$$5000$$disinte... A nucleus with$$Z=92$$emits the following in a sequence:$$$\alpha ,{\beta ^ ...
Which of the following atoms has the lowest ionization potential ?
The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \righ... In the nuclear fusion reaction$$${}_1^2H + {}_1^3H \to {}_2^4He + n$$<br>giv... Which of the following cannot be emitted by radioactive substances during their ... In the middle of the depletion layer of a reverse- biased$$p$$-$$n$$junction, ... Two identical photo-cathodes receive light of frequencies$${f_1}$$and$${f_2}$...
If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the ener...

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