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AIEEE 2007

Exam Held on Sun Apr 29 2007 09:30:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

In the reaction<br><br> 2Al(s) + 6HCl(aq) $$\to$$ 2Al<sup>3+</sup> (aq) + 6Cl<s...
The density (in g mL<sup>-1</sup>) of a 3.60 M sulphuric acid solution that is 2...
Which of the following sets of quantum numbers represents the highest energy of ...
Which of the following species exhibits the diamagnetic behaviour?
The charge/size ratio of a cation determines its polarizing power. Which one of ...
In which of the following ionization processes, the bond order has increased and...
Which of the following hydrogen bonds is the strongest?
In conversion of lime-stone to lime, <br> CaCO<sub>3</sub>(s) $$\to$$ CaO(s) + C...
Identify the correct statement regarding a spontaneous process
The first and second dissociation constants of an acid H<sub>2</sub>A are 1.0 $$...
In a sautrated solution of the sparingly soluble strong electrolyte AgIO<sub>3</...
The pK<sub>a</sub> of a weak acid (HA) is 4.5. The pOH of an aqueous buffered so...
Presence of a nitro group in a benzene ring
Which one of the following conformation of cyclohexane is chiral?
The compound formed as a result of oxidation of ethyl benzene by KMnO<sub>4 </su...
Which of the following reactions will yield 2, 2-dibromopropane?
The reaction of toluene with Cl<sub>2</sub> in presence of FeCl<sub>3</sub> give...
A 5.25 % solution of a substance is isotonic with a 1.5% solution of urea (molar...
A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at...
Equal masses of methane and oxygen are mixed in an empty container at 25<sup>o</...
The equivalent conductances of two strong electrolytes at infinite dilution in H...
The cell, Zn | Zn<sup>2+</sup> (1M) || Cu<sup>2+</sup> (1M) | Cu($$E_{cell}^o$$ ...
The energies of activation for forward and reverse reactions for A<sub>2</sub> +...
Consider the reaction, 2A + B $$\to$$ products. When concentration of B alone wa...
A radioactive element gets spilled over the floor of a room. Its half-life perio...
Which of the following nuclear reactions will generate an isotope?
Identify the incorrect statement among the following
Regular use of which of the following fertilizer increases the acidity of soil? ...
Identify the incorrect statement among the following
The actinoids exhibits more number of oxidation states in general than the lanth...
Which one of the following has a square planar geometry?
Which of the following is the correct order of decreasing S<sub>N</sub>2 reactiv...
In the following sequence of reactions, <br> CH<sub>3</sub>CH<sub>2</sub>OH $$\b...
Which one of the following is the strongest base in aqueous solution?
In the chemical reaction,<br> CH<sub>3</sub>CH<sub>2</sub>NH<sub>2</sub> + CHCl<...
The secondary structure of a protein refers to
Assuming that water vapour is an ideal gas, the internal energy change $$\left( ...
<img class="question-image" src="https://imagex.cdn.examgoal.net/uMZOloedoQ1yYDH...
Which of the following molecules is expected to rotate the plane of plane - pola...
The stability of dihalides of $$Si,Ge,Sn$$ and $$Pb$$ increases steadily in the ...

Mathematics

If $$\,\left| {z + 4} \right|\,\, \le \,\,3\,$$, then the maximum value of $$\l...
If the difference between the roots of the equation $${x^2} + ax + 1 = 0$$ is le...
The sum of the series $${}^{20}{C_0} - {}^{20}{C_1} + {}^{20}{C_2} - {}^{20}{C_3...
In the binomial expansion of $${\left( {a - b} \right)^n},\,\,\,n \ge 5,$$ the s...
The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, ...
The sum of series $${1 \over {2!}} - {1 \over {3!}} + {1 \over {4!}} - .......$$...
In a geometric progression consisting of positive terms, each term equals the su...
Let $$P = \left( { - 1,0} \right),\,Q = \left( {0,0} \right)$$ and $$R = \left( ...
Let A $$\left( {h,k} \right)$$, B$$\left( {1,1} \right)$$ and C $$(2, 1)$$ be th...
If one of the lines of $$m{y^2} + \left( {1 - {m^2}} \right)xy - m{x^2} = 0$$ is...
Consider a family of circles which are passing through the point $$(-1, 1)$$ and...
For the Hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\si...
The equation of a tangent to the parabola $${y^2} = 8x$$ is $$y=x+2$$. The point...
The normal to a curve at $$P(x,y)$$ meets the $$x$$-axis at $$G$$. If the distan...
A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points ...
If sin<sup>-1</sup>$$\left( {{x \over 5}} \right)$$ + cosec<sup>-1</sup>$$\left(...
The function $$f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right...
A value of $$c$$ for which conclusion of Mean Value Theorem holds for the functi...
If $$p$$ and $$q$$ are positive real numbers such that $${p^2} + {q^2} = 1$$, th...
If$$D = \left| {\matrix{ 1 &amp; 1 &amp; 1 \cr 1 &amp; {1 + x} &amp; 1 ...
Let $$A = \left| {\matrix{ 5 &amp; {5\alpha } &amp; \alpha \cr 0 &amp; ...
$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} $$ equals
Let $$F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),$$ w...
The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {...
The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ ...
Let $$I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx} $$ and $$J = \int\limi...
The differential equation of all circles passing through the origin and having t...
Two aeroplanes $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ bomb a target in successio...
A pair of fair dice is thrown independently three times. The probability of gett...
If a line makes an angle of $$\pi /4$$ with the positive directions of each of $...
If $$\widehat u$$ and $$\widehat v$$ are unit vectors and $$\theta $$ is the acu...
If $$(2,3,5)$$ is one end of a diameter of the sphere $${x^2} + {y^2} + {z^2} - ...
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow ...
Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=...
The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right...
Let $$f:R \to R$$ be a function defined by <br><br>$$f(x) = \min \left\{ {x + 1,...
The function $$f:R/\left\{ 0 \right\} \to R$$ given by <br><br>$$f\left( x \righ...
The average marks of boys in a class is 52 and that of girls is 42. The average ...

Physics

A particle is projected at $$60^\circ $$ to the horizontal with a kinetic energy...
The velocity of a particle is v = v<sub>0</sub> + gt + ft<sup>2</sup>. If its po...
A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a sprin...
A $$2$$ $$kg$$ block slides on a horizontal floor with a speed of $$4m/s.$$ It s...
A circular disc of radius $$R$$ is removed from a bigger circular disc of radius...
A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rol...
Angular momentum of the particle rotating with a central force is constant due t...
A Carnot engine, having an efficiency of $$\eta = 1/10$$ as heat engine, is use...
If $${C_p}$$ and $${C_v}$$ denote the specific heats of nitrogen per unit mass a...
For the given uniform square lamina $$ABCD$$, whose center is $$O,$$ <img class...
When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is...
One end of a thermally insulated rod is kept at a temperature $${T_1}$$ and the ...
A particle of mass $$m$$ executes simple harmonic motion with amplitude a and fr...
Two springs, of force constant $${k_1}$$ and $${k_2}$$ are connected to a mass $...
A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\...
The displacement of an object attached to a spring and executing simple harmonic...
A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decr...
An electric charge $${10^{ - 3}}\,\,\mu \,C$$ is placed at the origin $$(0,0)$$ ...
The potential at a point $$x$$ (measured in $$\mu \,m$$) due to some charges sit...
Charges are placed on the vertices of a square as shown. Let $$\overrightarrow E...
A parallel plate condenser with a dielectric of dielectric constant $$K$$ betwee...
If $${g_E}$$ and $${g_M}$$ are the accelerations due to gravity on the surfaces ...
A battery is used to charge a parallel plate capacitor till the potential differ...
The resistance of a wire is $$5$$ ohm at $${50^ \circ }C$$ and $$6$$ ohm at $${1...
A charged particle with charge $$q$$ enters a region of constant, uniform and mu...
A current $$I$$ flows along the length of an infinitely long, straight, thin wal...
A long straight wire of radius $$a$$ carries a steady current $$i.$$ The curren...
A charged particle moves through a magnetic field perpendicular to its direction...
Two identical conducting wires $$AOB$$ and $$COD$$ are placed at right angles to...
In an $$a.c.$$ circuit the voltage applied is $$E = {E_0}\,\sin \,\omega t.$$ Th...
An ideal coil of $$10H$$ is connected in series with a resistance of $$5\Omega $...
In a Young's double slit experiment the intensity at a point where the path diff...
Two lenses of power $$-15$$ $$D$$ and $$+5$$ $$D$$ are in contact with each othe...
If $${M_O}$$ is the mass of an oxygen isotope $${}_8{O^{17}}$$ , $${M_p}$$ and $...
In gamma ray emission from a nucleus
Photon of frequency $$v$$ has a momentum associated with it. If $$c$$ is the vel...
The half-life period of a ratio-active element $$X$$ is same as the mean life ti...
Which of the following transitions in hydrogen atoms emit photons of highest fre...
Carbon, silicon and germanium have four valence electrons each. At room temperat...
If in a $$p$$-$$n$$ junction diode, a square input signal of $$10$$ $$V$$ is app...

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