AIEEE 2007

Paper was held on
Sun, Apr 29, 2007 9:30 AM

## Chemistry

In the reaction
2Al(s) + 6HCl(aq) $$\to$$ 2Al3+ (aq) + 6Cl-(aq) + 3H2(g)

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The density (in g mL-1) of a 3.60 M sulphuric acid solution that is 29% H2SO4 (molar mass = 98 g mol-1) by mass will be

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Which of the following sets of quantum numbers represents the highest energy of an atom?

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Which of the following species exhibits the diamagnetic behaviour?

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The charge/size ratio of a cation determines its polarizing power. Which one of the following
sequences represents the i

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In which of the following ionization processes, the bond order has increased and the magnetic
behaviour has changed?

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Which of the following hydrogen bonds is the strongest?

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In conversion of lime-stone to lime,
CaCO3(s) $$\to$$ CaO(s) + CO2 (g) the vales of ∆H° and ∆S° are +179.1 kJ mol−1
an

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Identify the correct statement regarding a spontaneous process :

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The first and second dissociation constants of an acid H2A are 1.0 $$\times$$ 10−5
and 5.0 $$\times$$ 10−10 respectivel

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In a sautrated solution of the sparingly soluble strong electrolyte AgIO3 (Molecular mass = 283) the
equilibrium which s

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The pKa of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of
the acid is ionized is

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Presence of a nitro group in a benzene ring

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Which one of the following conformation of cyclohexane is chiral?

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The compound formed as a result of oxidation of ethyl benzene by KMnO4 is :

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Which of the following reactions will yield 2, 2-dibromopropane?

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The reaction of toluene with Cl2 in presence of FeCl3 gives predominantly

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A 5.25 % solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol−1) in
the same solvent.

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A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour
pressure of propyl al

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Equal masses of methane and oxygen are mixed in an empty container at 25oC. The fraction of the
total pressure exerted b

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The equivalent conductances of two strong electrolytes at infinite dilution in H2O (where ions move
freely through a sol

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The cell, Zn | Zn2+ (1M) || Cu2+ (1M) | Cu($$E_{cell}^o$$ = 1.10V) was allowed to be completely discharged at 298 K. Th

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The energies of activation for forward and reverse reactions for A2 + B2 $$\leftrightharpoons$$ 2AB are 180 kJ mol−1
and

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Consider the reaction, 2A + B $$\to$$ products. When concentration of B alone was doubled, the half-life did not change.

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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial
activity is

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Which of the following nuclear reactions will generate an isotope?

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Identify the incorrect statement among the following :

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Regular use of which of the following fertilizer increases the acidity of soil?

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Identify the incorrect statement among the following :

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The actinoids exhibits more number of oxidation states in general than the lanthanoids. This is
because :

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Which one of the following has a square planar geometry?

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Which of the following is the correct order of decreasing SN2 reactivity?

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In the following sequence of reactions,
CH3CH2OH $$\buildrel {P + {I_2}} \over
\longrightarrow $$ A $$\mathrel{\mathop

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Which one of the following is the strongest base in aqueous solution?

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In the chemical reaction,
CH3CH2NH2 + CHCl3 + 3KOH $$\to$$ (A) + (B) + 3H2O, the compound (A) and (B) are respectively

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The secondary structure of a protein refers to

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Assuming that water vapour is an ideal gas, the internal energy change $$\left( {\Delta U} \right)$$ when $$1$$ mol of w

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Which of the following molecules is expected to rotate the plane of plane - polarized light?

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The stability of dihalides of $$Si,Ge,Sn$$ and $$Pb$$ increases steadily in the sequence :

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## Mathematics

If $$\,\left| {z + 4} \right|\,\, \le \,\,3\,$$, then the maximum value of $$\left| {z + 1} \right|$$ is :

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If the difference between the roots of the equation $${x^2} + ax + 1 = 0$$ is less than $$\sqrt 5 ,$$ then the set of po

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The sum of the series $${}^{20}{C_0} - {}^{20}{C_1} + {}^{20}{C_2} - {}^{20}{C_3} + .....\, - \,.....\, + {}^{20}{C_{10}

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In the binomial expansion of $${\left( {a - b} \right)^n},\,\,\,n \ge 5,$$ the sum of $${5^{th}}$$ and $${6^{th}}$$ term

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The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $$A \cup B \cup C

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The sum of series $${1 \over {2!}} - {1 \over {3!}} + {1 \over {4!}} - .......$$ upto infinity is

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In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common

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Let $$P = \left( { - 1,0} \right),\,Q = \left( {0,0} \right)$$ and $$R = \left( {3,3\sqrt 3 } \right)$$ be three point.

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Let A $$\left( {h,k} \right)$$, B$$\left( {1,1} \right)$$ and C $$(2, 1)$$ be the vertices of a right angled triangle wi

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If one of the lines of $$m{y^2} + \left( {1 - {m^2}} \right)xy - m{x^2} = 0$$ is a bisector of angle between the lines $

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Consider a family of circles which are passing through the point $$(-1, 1)$$ and are tangent to $$x$$-axis. If $$(h, k)$

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For the Hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ , which of the fol

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The equation of a tangent to the parabola $${y^2} = 8x$$ is $$y=x+2$$. The point on this line from which the other tange

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The normal to a curve at $$P(x,y)$$ meets the $$x$$-axis at $$G$$. If the distance of $$G$$ from the origin is twice the

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A tower stands at the centre of a circular park. $$A$$ and $$B$$ are two points on the boundary of the park such that $$

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If sin-1$$\left( {{x \over 5}} \right)$$ + cosec-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$, then the value

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The function $$f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)$$ is an incresing function in

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A value of $$c$$ for which conclusion of Mean Value Theorem holds for the function $$f\left( x \right) = {\log _e}x$$ on

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If $$p$$ and $$q$$ are positive real numbers such that $${p^2} + {q^2} = 1$$, then the maximum value of $$(p+q)$$ is

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If $$D = \left| {\matrix{
1 & 1 & 1 \cr
1 & {1 + x} & 1 \cr
1 & 1 & {1 + y} \cr

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Let $$A = \left| {\matrix{
5 & {5\alpha } & \alpha \cr
0 & \alpha & {5\alpha } \cr
0 &

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$$\int {{{dx} \over {\cos x + \sqrt 3 \sin x}}} $$ equals

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Let $$F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),$$ where $$f\left( x \right) = \int\limits_l

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The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}}

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The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :

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Let $$I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx} $$ and $$J = \int\limits_0^1 {{{\cos x} \over {\sqrt x }}dx} .

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The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is :

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Two aeroplanes $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ bomb a target in succession. The probabilities of $${\rm I}$$ and

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A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $$9$$ twice is :

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If a line makes an angle of $$\pi /4$$ with the positive directions of each of $$x$$-axis and $$y$$-axis, then the angle

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If $$\widehat u$$ and $$\widehat v$$ are unit vectors and $$\theta $$ is the acute angle between them, then $$2\widehat

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If $$(2,3,5)$$ is one end of a diameter of the sphere $${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0,$$ then the coord

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Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b = \widehat i - \widehat j + 2\widehat

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Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha $$

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The largest interval lying in $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which the function
$$f\left( x \

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Let $$f:R \to R$$ be a function defined by
$$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$, then which of

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The function $$f:R/\left\{ 0 \right\} \to R$$ given by
$$f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}}$$
ca

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The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys
and girls combined is 50.

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## Physics

A particle is projected at $$60^\circ $$ to the horizontal with a kinetic energy K. The kinetic energy at the
highest po

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The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit tim

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A block of mass $$m$$ is connected to another block of $$mass$$ $$M$$ by a spring (massless) of spring constant $$k.$$ T

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A $$2$$ $$kg$$ block slides on a horizontal floor with a speed of $$4m/s.$$ It strikes a uncompressed spring, and compre

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A circular disc of radius $$R$$ is removed from a bigger circular disc of radius $$2R$$ such that the circumferences of

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A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rolls down (without slipping) an inclined p

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Angular momentum of the particle rotating with a central force is constant due to

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A Carnot engine, having an efficiency of $$\eta = 1/10$$ as heat engine, is used as a refrigerator . If the work done o

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If $${C_p}$$ and $${C_v}$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume

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For the given uniform square lamina $$ABCD$$, whose center is $$O,$$

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When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$

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One end of a thermally insulated rod is kept at a temperature $${T_1}$$ and the other at $${T_2}$$. The rod is composed

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A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energ

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Two springs, of force constant $${k_1}$$ and $${k_2}$$ are connected to a mass $$m$$ as shown. The frequency of oscillat

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A point mass oscillates along the $$x$$-axis according to the law $$x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$

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The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x = 2 \times {10^{

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A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decreases by a factor of

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An electric charge $${10^{ - 3}}\,\,\mu \,C$$ is placed at the origin $$(0,0)$$ of $$X-Y$$ co-ordinate system. Two point

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The potential at a point $$x$$ (measured in $$\mu \,m$$) due to some charges situated on the $$x$$-axis is given by $$V\

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Charges are placed on the vertices of a square as shown. Let $$\overrightarrow E $$ be the electric field and $$V$$ the

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A parallel plate condenser with a dielectric of dielectric constant $$K$$ between the plates has a capacity $$C$$ and is

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If $${g_E}$$ and $${g_M}$$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively a

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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to

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The resistance of a wire is $$5$$ ohm at $${50^ \circ }C$$ and $$6$$ ohm at $${100^ \circ }C.$$ The resistance of the wi

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A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarr

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A current $$I$$ flows along the length of an infinitely long, straight, thin walled pipe. Then

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A long straight wire of radius $$a$$ carries a steady current $$i.$$ The current is uniformly distributed across its cr

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A charged particle moves through a magnetic field perpendicular to its direction. Then

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Two identical conducting wires $$AOB$$ and $$COD$$ are placed at right angles to each other. The wire $$AOB$$ carries an

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In an $$a.c.$$ circuit the voltage applied is $$E = {E_0}\,\sin \,\omega t.$$ The resulting current in the circuit is $$

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An ideal coil of $$10H$$ is connected in series with a resistance of $$5\Omega $$ and a battery of $$5V$$. $$2$$ second

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In a Young's double slit experiment the intensity at a point where the path difference is $${\lambda \over 6}$$ ( $$\la

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Two lenses of power $$-15$$ $$D$$ and $$+5$$ $$D$$ are in contact with each other. The focal length of the combination i

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If $${M_O}$$ is the mass of an oxygen isotope $${}_8{O^{17}}$$ , $${M_p}$$ and $${M_N}$$ are the masses of a proton and

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In gamma ray emission from a nucleus

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Photon of frequency $$v$$ has a momentum associated with it. If $$c$$ is the velocity of light, the momentum is

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The half-life period of a ratio-active element $$X$$ is same as the mean life time of another ratio-active element $$Y.$

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Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

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Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statement

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If in a $$p$$-$$n$$ junction diode, a square input signal of $$10$$ $$V$$ is applied as shown
Then the output signal a

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