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AIEEE 2004

Exam Held on Sat Apr 24 2004 09:30:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

6.02 $$\times$$ 10<sup>20</sup> molecules of urea are present in 100 ml of its s...
To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H<...
The ammonia evolved from the treatment of 0.30 g of an organic compound for the ...
Which of the following sets of quantum numbers is correct for an electron in 4f ...
Consider the ground state of Cr atom (Z = 24). The number of electrons with the ...
The wavelength of the radiation emitted when in a hydrogen atom electron falls f...
Which one of the following sets of ions represents the collection of isoelectron...
Which one of the following ions has the highest value of ionic radius?
Among Al<sub>2</sub>O<sub>3</sub>, SiO<sub>2</sub>, P<sub>2</sub>O<sub>3</sub> a...
The formation of the oxide ion O<sup>2-</sup>(g) requires first an exothermic an...
The correct order of bond angles (smallest first) in H<sub>2</sub>S, NH<sub>3</s...
The bond order in NO is 2.5 while that in NO<sup>+</sup> is 3. Which of the foll...
The states of hybridization of boron and oxygen atoms in boric acid (H<sub>3</su...
Which one of the following has the regular tetrahedral structure? <br> (Atomic ...
The maximum number of 90° angles between bond pair of electrons is observed in
As the temperature is raised from 20°C to 40°C, the average kinetic energy of ne...
In Van der Waals equation of state of the gas law, the constant ‘b’ is a measure...
An ideal gas expands in volume from 1$$\times$$10<sup>-3</sup> m<sup>3</sup> to ...
The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 k...
The conjugate base of H<sub>2</sub>PO<sub>4</sub><sup>-</sup> is
What is the equilibrium expression for the reaction <br> P<sub>4</sub> (s) + 5O<...
For the reaction, CO(g) + Cl<sub>2</sub>(g) $$\leftrightharpoons$$ COCl<sub>2</s...
The equilibrium constant for the reaction N<sub>2</sub>(g) + O<sub>2</sub>(g) $$...
The molar solubility (in ol L<sup>-1</sup>) of a sparingly soluble salt MX<sub>4...
One mole of magnesium nitride on the reaction with an excess of water gives
Which one of the following has the minimum boiling point?
Which one the following does not have sp<sup>2</sup> hybridized carbon?
Which of the following compound is not chiral?
Consider the acidity of the carboxylic acids:<br> (a) PhCOOH <br> (b) o – NO<su...
Which of the following will have meso-isomer also?
Identify the correct statements regarding enzymes
For which of the following parameters the structural isomers C<sub>2</sub>H<sub>...
Which of the following liquid pairs shows a positive deviation from Raoult’s law...
Which one of the following aqueous solutions will exhibit highest boiling point?...
Which one of the following statements is false?
In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to
Consider the following E<sup>o</sup> values <br> $$E_{F{e^{3 + }}/F{e^{2 + }}}^o...
The standard e.m.f of a cell, involving one electron change is found to be 0.591...
The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 ...
In a cell that utilises the reaction Zn(s) + 2H<sup>+</sup> (aq) $$\to$$ Zn2+(aq...
The $$E_{{M^{3 + }}/{M^{2 + }}}^o$$ values for Cr, Mn, Fe and Co are – 0.41, +1...
In a first order reaction, the concentration of the reactant decreases from 0.8 ...
The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]...
Consider the following nuclear reactions<br> $${}_{92}^{238}M \to {}_y^xN + {}_2...
The half – life of a radioisotope is four hours. If the initial mass of the isot...
Which one of the following ores is best concentrated by froth – floatation metho...
Which among the following factors is the most important in making fluorine the s...
Beryllium and aluminium exhibit many properties which are similar. But the two e...
Which one the following statement regarding helium is incorrect?
Excess of KI reacts with CuSO<sub>4</sub> solution and then Na<sub>2</sub>S<sub>...
Aluminium chloride exists as dimer, Al<sub>2</sub>Cl<sub>6</sub> in solid state ...
Cerium (Z = 58) is an important member of the lanthanoids. Which of the followin...
Which one of the following complexes in an outer orbital complex?
Coordination compound have great importance in biological systems. In this conte...
Which one the following has largest number of isomers? (R = alkyl group, en = et...
The coordination number of central metal atom in a complex is determined by
The correct order of magnetic moments (spin only values in B.M.) among is<br> (A...
Among the properties (a) reducing (b) oxidising (c) complexing, the set of prope...
The compound formed on heating chlorobenzene with chloral in the presence concen...
On mixing ethyl acetate with aqueous sodium chloride, the composition of the res...
Which of the following undergoes reaction with 50% sodium hydroxide solution to ...
Which one of the following reduced with zinc and hydrochloric acid to give the c...
Acetyl bromide reacts with excess of CH<sub>3</sub>MgI followed by treatment wit...
Which base is present in RNA but not in DNA?
Insulin production and its action in human body are responsible for the level of...
The smog is essentially caused by the presence of
The compound formed in the positive test for nitrogen with the Lassaigne solutio...
Which of the following is the strongest base ?
Amongst the following compounds, the optically active alkane having lowest molec...
Rate of the reaction <br><br><img class="question-image" src="https://imagex.cdn...
The $$IUPAC$$ name of the compound is <br><br><img class="question-image" src="...
What type of crystal defect is indicated in the diagram below? <br><br><img cla...
Among the following compounds which can be dehydrated very easily is
Of the following outer electronic configurations of atoms, the highest oxidation...
The soldiers of Napolean army while at Alps during freezing winter suffered a se...

Mathematics

Let $$\alpha ,\,\beta $$ be such that $$\pi &lt; \alpha - \beta &lt; 3\pi $$....
If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a...
A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis....
Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ an...
If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then <br><br>$${{\left( {...
If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on
Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers ...
If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \...
If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $$...
How many ways are there to arrange the letters in the word GARDEN with vowels in...
Let $$S(K)$$ $$ = 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.$$ Then wh...
The coefficient of the middle term in the binomial expansion in powers of $$x$$ ...
The number of ways of distributing 8 identical balls in 3 distinct boxes so that...
The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 ...
Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common diff...
If $${S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \s...
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} +...
The sum of series $${1 \over {2\,!}} + {1 \over {4\,!}} + {1 \over {6\,!}} + ......
The equation of the straight line passing through the point $$(4, 3)$$ and makin...
Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2, 1} \right)$$ be vertices of...
If the sum of the slopes of the lines given by $${x^2} - 2cxy - 7{y^2} = 0$$ is ...
If one of the lines given by $$6{x^2} - xy + 4c{y^2} = 0$$ is $$3x + 4y = 0,$$ t...
A variable circle passes through the fixed point A (p, q) and touches x-axis. Th...
If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle o...
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y...
Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. ...
If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of inters...
The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$...
If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x &gt; 0,$$ then $${{{dy...
A person standing on the bank of a river observes that the angle of elevation of...
The sides of a triangle are $$\sin \alpha ,\,\cos \alpha $$ and $$\sqrt {1 + \si...
A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice...
A function $$y=f(x)$$ has a second order derivative $$f''\left( x \right) = 6\le...
If $$2a+3b+6c=0$$, then at least one root of the equation <br>$$a{x^2} + bx + ...
The normal to the curve x = a(1 + cos $$\theta $$), $$y = a\sin \theta $$ at $$'...
Let $$A = \left( {\matrix{ 1 &amp; { - 1} &amp; 1 \cr 2 &amp; 1 &amp; {...
Let $$A = \left( {\matrix{ 0 &amp; 0 &amp; { - 1} \cr 0 &amp; { - 1} &am...
If $${a_1},{a_2},{a_3},.........,{a_n},......$$ are in G.P., then the value of t...
If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \...
$$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to
$$\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r ...
The value of $$I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}...
The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is
If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {...
If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left...
The area of the region bounded by the curves <br>$$y = \left| {x - 2} \right|,x ...
The differential equation for the family of circle $${x^2} + {y^2} - 2ay = 0,$$ ...
Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$...
The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respect...
The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probabili...
A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$...
Distance between two parallel planes <br>$$\,2x + y + 2z = 8$$ and $$4x + 2y +...
Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ be such that $$...
A particles is acted upon by constant forces $$ 4\widehat i + \widehat j - 3\wi...
A line with direction cosines proportional to $$2,1,2$$ meets each of the lines ...
If $${\overrightarrow a ,\overrightarrow b ,\overrightarrow c }$$ are non-coplan...
The intersection of the spheres <br>$${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$$...
Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-...
If the straight lines <br>$$x=1+s,y=-3$$$$ - \lambda s,$$ $$z = 1 + \lambda s$$...
Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be thre...
The range of the function f(x) = $${}^{7 - x}{C_{x - 3}}$$ is
If $$f:R \to S$$, defined by <br>$$f\left( x \right) = \sin x - \sqrt 3 \cos x +...
The graph of the function y = f(x) is symmetrical about the line x = 2, then
The domain of the function <br>$$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x...
Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \...
If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over ...
Consider the following statements: <br>(a) Mode can be computed from histogram ...
In a series of 2n observations, half of them equal $$a$$ and remaining half equa...

Physics

Which one of the following represents the correct dimensions of the coefficient ...
A ball is released from the top of a tower of height h meters. It takes T second...
If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \o...
A projectile can have the same range 'R' for two angles of projection. If T<sub>...
Which of the following statements is <b>FALSE</b> for a particle moving in a cir...
An automobile travelling with speed of 60 km/h, can brake to stop within a dista...
A ball is thrown from a point with a speed ν<sub>0</sub> at an angle of projecti...
Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging ov...
A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ wit...
A particle moves in a straight line with retardation proportional to its displac...
A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $...
A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j ...
A body of mass $$' m ',$$ acceleration uniformly from rest to $$'{v_1}'$$ in tim...
A particle is acted upon by a force of constant magnitude which is always perpen...
A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ -...
One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same...
A solid sphere is rotating in free space. If the radius of the sphere is increas...
A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height ...
If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in ...
The time period of an earth satellite in circular orbit is independent of
Suppose the gravitational force varies inversely as the n<sup>th</sup> power of ...
A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F....
If two soap bubbles of different radii are connected by a tube
Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\e...
One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with...
If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radi...
Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatu...
Which of the following statements is <b>correct</b> for any thermodynamic system...
The temperature of the two outer surfaces of a composite slab, consisting of two...
The bob of a simple pendulum executes simple harmonic motion in water with a per...
A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. Wh...
The total energy of particle, executing simple harmonic motion is
A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and ...
In forced oscillation of a particle the amplitude is maximum for a frequency $${...
The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^...
Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal c...
A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which...
Four charges equal to -$$Q$$ are placed at the four corners of a square and a c...
A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$...
The resistance of the series combination of two resistances is $$S.$$ When they ...
An electric current is passed through a circuit containing two wires of the same...
The total current supplied to the circuit by the battery is <img class="questio...
Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \ci...
In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one ...
Thermistors are usually made of
The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Cou...
The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the...
The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left...
A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire...
Curie temperature is the temperature above which
A current $$i$$ ampere flows along an infinitely long straight thin walled tube,...
A long wire carries a steady current. It is bent into a circle of one turn and t...
The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$...
The length of a magnet is large compared to its width and breadth. The time peri...
Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $...
The materials suitable for making electromagnets should have
Alternating current can not be measured by $$D.C.$$ ammeter because
In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components...
A coil having $$n$$ turns and resistance $$R\Omega $$ is connected with a galvan...
In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircl...
A metal conductor of length $$1$$ $$m$$ rotates vertically about one of its end...
In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the r...
A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $...
The angle of incidence at which reflected light is totally polarized for reflect...
An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a...
The maximum number of possible interference maximum for slit-separation equal to...
The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of l...
A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. Th...
According to Einstein's photoelectric equation, the plot of the kinetic energy o...
An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \ci...
The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and he...
A nucleus disintegrated into two nuclear parts which have their velocities in th...
When $$npn$$ transistor is used as an amplifer
For a transistor amplifier in common emitter configuration for load impedance of...
A piece of copper and another of germanium are cooled from room temperature to ...
The manifestation of band structure in solids is due to
When $$p$$-$$n$$ junction diode is forward biased then
A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism ...

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