AIEEE 2008

Paper was held on
Sun, Apr 27, 2008 9:30 AM

## Chemistry

Which one of the following constitutes a group of the isoelectronic species?

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The ionization enthalpy of hydrogen atom is 1.312 × 106 J mol−1. The energy required to excite the
electron in the atom

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Which of the following pair of species have the same bond order?

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The bond dissociation energy of B - F in BF3 is 646 jJ mol-1 whereas that of C - F in CF4 is 515 kj mol-1. The correct r

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Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated
below:
$${1 \over 2}C{l_2

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Standard entropy of X2, Y2 and XY3 are 60, 40 and 50 JK−1
mol−1 , respectively. For the reaction,
$${1 \over 2} X_2$$

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The equilibrium constants KP1 and KP2 for the reactions X $$\leftrightharpoons$$ 2Y and Z $$\leftrightharpoons$$ P + Q,

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Four species are listed below
i. $$HCO_3^−$$
ii. $$H_3O^+$$
iii. $$HSO_4^−$$
iv. $$HSO_3F$$
Which one of the following

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For the following three reactions a, b and c, equilibrium constants are given:
a. CO (g) + H2O (g) $$\leftrightharpoons

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The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH, is 4.78. The pH of an aqueous
solution of the correspo

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In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following
is the correct s

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The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC
system of nomenclat

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Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so
obtained is diaz

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In the following sequence of reactions, the alkene affords the compound ‘B’
CH3 - CH = CH - CH3 $$\buildrel {{O_3}} \ov

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The hydrocarbon which can react with sodium in liquid ammonia is

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Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The
correct order of the

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In a compound atoms of element Y from ccp lattice and those of element X occupy 2/3rd of tetrahedral
voids. The formula

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The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose (C6H12O6) is added to 178.2 g of water at 20oC, t

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At 80oC, the vapour pressure of pure liquid ‘A’ is 520 mm Hg and that of pure liquid ‘B’ is 1000 mm Hg. If a mixture sol

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Given $$E_{C{r^{3 + }}/Cr}^o$$ = -0.72 V; $$E_{Fe^{2+}/Fe}^o$$ = -0.42V, The potential for the cell Cr | Cr3+ (0.1M) ||

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For a reaction $${1 \over 2}A \to 2B$$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the

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Which of the following factors is of no significance for roasting sulphide ores to the oxides and not
subjecting the sul

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Which one of the following is the correct statement?

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Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the
main reason being :

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In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $$\Delta _o$$ be the highest?

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The coordination number and the oxidation state of the element ‘E’ in the complex [E(en)2(C2O4)]NO2 (where (en) is ethyl

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The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction,
is

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Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid,
gives

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Identify the wrong statements in the following :

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Bakelite is obtained from phenol by reacting with

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$$\alpha$$-D-(+)-glucose and $$\beta$$-D-(+)-glucose are

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Among the following substituted silanes the one which will give rise to cross linked silicone polymer on
hydrolysis is :

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The electrophile, $${E^ \oplus }$$ attacks the benzene ring to generate the intermediate $$\sigma - $$complex. Of the f

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The absolute configuration of

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The treatment of $$C{H_3}MgX\,\,$$ with $$C{H_3}C \equiv C - H$$ produces

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Amount of oxalic acid present in a solution can be determined by its titration with $$KMn{O_4}$$ solution in the presen

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## Mathematics

The conjugate of a complex number is $${1 \over {i - 1}}$$ then that complex number is :

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Let R be the real line. Consider the following subsets of the plane $$R \times R$$ :
$$S = \left\{ {(x,y):y = x + 1\,\,

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STATEMENT - 1 : For every natural number $$n \ge 2,$$
$$${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \o

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The quadratic equations $${x^2} - 6x + a = 0$$ and $${x^2} - cx + 6 = 0$$ have one root in common. The other roots of th

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In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of diffe

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How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

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Statement - 1 : $$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.} $$
Stat

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The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the ter

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The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of

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The point diametrically opposite to the point $$P(1, 0)$$ on the circle $${x^2} + {y^2} + 2x + 4y - 3 = 0$$ is :

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The differential equation of the family of circles with fixed radius $$5$$ units and centre on the line $$y = 2$$ is :

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A focus of an ellipse is at the origin. The directrix is the line $$x=4$$ and the eccentricity is $${{1 \over 2}}$$. The

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A parabola has the origin as its focus and the line $$x=2$$ as the directrix. Then the vertex of the parabola is at :

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$$AB$$ is a vertical pole with $$B$$ at the ground level and $$A$$ at the top. $$A$$ man finds that the angle of elevati

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The value of $$cot\left( {\cos e{c^{ - 1}}{5 \over 3} + {{\tan }^{ - 1}}{2 \over 3}} \right)$$ is :

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Suppose the cubic $${x^3} - px + q$$ has three distinct real roots
where $$p>0$$ and $$q>0$$. Then which one of t

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How many real solutions does the equation
$${x^7} + 14{x^5} + 16{x^3} + 30x - 560 = 0$$ have?

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Let $$A$$ be $$a\,2 \times 2$$ matrix with real entries. Let $$I$$ be the $$2 \times 2$$ identity matrix. Denote by tr$$

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Let $$a, b, c$$ be any real numbers. Suppose that there are real numbers $$x, y, z$$ not all zero such that $$x=cy+bz,$$

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Let $$A$$ be a square matrix all of whose entries are integers.
Then which one of the following is true?

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The value of $$\sqrt 2 \int {{{\sin xdx} \over {\sin \left( {x - {\pi \over 4}} \right)}}} $$ is

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The area of the plane region bounded by the curves $$x + 2{y^2} = 0$$ and $$\,x + 3{y^2} = 1$$ is equal to :

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The solution of the differential equation
$${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$

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A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the

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It is given that the events $$A$$ and $$B$$ are such that
$$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1

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The vector $$\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k$$ lies in the plane of the vectors

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The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\ove

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The line passing through the points $$(5,1,a)$$ and $$(3, b, 1)$$ crosses the $$yz$$-plane at the point $$\left( {0,{{1

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If the straight lines $$\,\,\,\,\,$$ $$\,\,\,\,\,$$ $${{x - 1} \over k} = {{y - 2} \over 2} = {{z - 3} \over 3}$$ $$\,\,

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Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”,
and r be the stat

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Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where
Y = { y $$ \in $$ N, y = 4x + 3 for some x $$ \in $$ N }

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Let $$f\left( x \right) = \left\{ {\matrix{
{\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr

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The statement $$p \to \left( {q \to p} \right)$$ is equivalent to

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The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following
gives possible val

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## Physics

The dimension of magnetic field in M, L, T and C (coulomb) is given as

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A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recor

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Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The
total number of di

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An athlete in the olympic games covers a distance of $$100$$ $$m$$ in $$10$$ $$s.$$ His kinetic energy can be estimated

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A block of mass $$0.50$$ $$kg$$ is moving with a speed of $$2.00$$ $$m{s^{ - 1}}$$ on a smooth surface. It strike anothe

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Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis pe

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This question contains Statement - $$1$$ and Statement - $$2$$. of the four choices given after the statements, choose t

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A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. G

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A spherical solid ball of volume $$V$$ is made of a material of density $${\rho _1}$$. It is falling through a liquid of

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The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of

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An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${

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A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mas

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A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the fol

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A jar is filled with two non-mixing liquids $$1$$ and $$2$$ having densities $${\rho _1}$$ and $${\rho _2}$$ respective

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While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condi

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A wave travelling along the $$x$$-axis is described by the equation $$y(x, t)=0.005$$ $$\cos \,\left( {\alpha \,x - \bet

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A parallel plate capacitor with air between the plates has capacitance of $$9$$ $$pF.$$ The separation between its plate

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A thin spherical shell of radius $$R$$ has charge $$Q$$ spread uniformly over its surface. Which of the following graphs

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Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.
The value of the unknown

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Consider a block of conducting material of resistivity $$'\rho '$$ shown in the figure. Current $$'I'$$ enters at $$'A'$

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Consider a block of conducting material of resistivity $$'\rho '$$ shown in the figure. Current $$'I'$$ enters at $$'A'$

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A $$5V$$ battery with internal resistance $$2\Omega $$ and a $$2V$$ battery with internal resistance $$1\Omega $$ are co

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Relative permittivity and permeability of a material $${\varepsilon _r}$$ and $${\mu _r},$$ respectively. Which of the f

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A horizontal overhead powerline is at height of $$4m$$ from the ground and carries a current of $$100A$$ from east to we

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Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $$A=$$ $$10\,\,c{m^2}$

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An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment dista

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In an experiment, electrons are made to pass through a narrow slit of width $$'d'$$ comparable to their de Broglie wavel

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A student measures the focal length of a convex lens by putting an object pin at a distance $$'u'$$ from the lens and me

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This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one t

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A working transistor with its three legs marked $$P,Q$$ and $$R$$ is tested using a multi-meter. No conduction is found

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Suppose an electron is attracted towards the origin by a force $${k \over r}$$ where $$'k'$$ is a constant and $$'r'$$ i

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Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by dif

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Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by dif

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In the circuit below, $$A$$ and $$B$$ represent two inputs and $$C$$ represents the output.
The circuit represents

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A body is at rest at $$x=0.$$ At $$t=0,$$ it starts moving in the positive $$x$$-direction with a constant acceleration.

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