AIEEE 2004

Paper was held on
Sat, Apr 24, 2004 9:30 AM

## Chemistry

6.02 $$\times$$ 1020 molecules of urea are present in 100 ml of its solution. The concentration of urea solution is (Avo

View Question To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H3PO3), the volume of 0.1 M aqueous KOH so

View Question The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100

View Question Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

View Question Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 a

View Question The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, woul

View Question Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 1

View Question Which one of the following ions has the highest value of ionic radius?

View Question Among Al2O3, SiO2, P2O3 and SO2 the correct order of acid strength is

View Question The formation of the oxide ion O2-(g) requires first an exothermic and then an endothermic
step as shown below
O(g) + e

View Question The correct order of bond angles (smallest first) in H2S, NH3, BF3 and SiH4 is

View Question The bond order in NO is 2.5 while that in NO+ is 3. Which of the following statements is true for these two species?

View Question The states of hybridization of boron and oxygen atoms in boric acid (H3BO3) are respectively

View Question Which one of the following has the regular tetrahedral structure?
(Atomic nos : B = 5, S = 16, Ni = 28, Xe = 54)

View Question The maximum number of 90° angles between bond pair of electrons is observed in

View Question An ideal gas expands in volume from 1$$\times$$10-3 m3 to 1 $$\times$$ 10-2 m3 at 300 K against a constant pressure of 1

View Question The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1
respectively. The enthalpy of fo

View Question The conjugate base of H2PO4- is :

View Question What is the equilibrium expression for the reaction
P4 (s) + 5O2 $$\leftrightharpoons$$ P4O10 (s)?

View Question For the reaction, CO(g) + Cl2(g) $$\leftrightharpoons$$ COCl2(g) the $${{{K_p}} \over {{K_c}}}$$ is equal to :

View Question The equilibrium constant for the reaction N2(g) + O2(g) $$\leftrightharpoons$$ 2NO(g) at temperature T is
4 $$\times$$ 1

View Question The molar solubility (in ol L-1) of a sparingly soluble salt MX4 is "s". The corresponding solubility product is Ksp. 's

View Question Which one of the following has the minimum boiling point?

View Question Which one the following does not have sp2 hybridized carbon?

View Question Which of the following compound is not chiral?

View Question Consider the acidity of the carboxylic acids:
(a) PhCOOH
(b) o – NO2C6H4COOH
(c) p – NO2C6H4COOH
(d) m – NO2C6H4COOH

View Question Which of the following will have meso-isomer also?

View Question Identify the correct statements regarding enzymes

View Question For which of the following parameters the structural isomers C2H5OH and CH3OCH3 would
be expected to have the same value

View Question Which of the following liquid pairs shows a positive deviation from Raoult’s law?

View Question Which one of the following aqueous solutions will exhibit highest boiling point?

View Question Which one of the following statements is false?

View Question In a hydrogen – oxygen fuel cell, combustion of hydrogen occurs to :

View Question Consider the following Eo values
$$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = 0.77 V;
$$E_{S{n^{2 + }}/S{n}}^o$$ = -0.14 V
Under

View Question The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at 25oC.
The equilibrium constant of

View Question The limiting molar conductivities Λ° for NaCl, KBr and KCl are 126, 152 and 150 S cm2 mol-1 respectively. The Λ° for NaB

View Question In a cell that utilises the reaction Zn(s) + 2H+
(aq) $$\to$$ Zn2+(aq) + H2(g) addition of H2SO4 to cathode compartment,

View Question The $$E_{{M^{3 + }}/{M^{2 + }}}^o$$ values for Cr, Mn, Fe and Co are – 0.41, +1.57, + 0.77 and +1.97 V
respectively. Fo

View Question In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15
minutes. The time taken

View Question The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]. The correct
statement in relation to t

View Question Consider the following nuclear reactions
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ +

View Question The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the
mass remaining after

View Question Beryllium and aluminium exhibit many properties which are similar. But the two elements
differ in :

View Question Which one the following statement regarding helium is incorrect?

View Question Excess of KI reacts with CuSO4 solution and then Na2S2O3 solution is added to it. Which of the statements is incorrect f

View Question Cerium (Z = 58) is an important member of the lanthanoids. Which of the following
statements about cerium is incorrect?

View Question Which one of the following complexes in an outer orbital complex?

View Question Coordination compound have great importance in biological systems. In this context which of
the following statements is

View Question Which one the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

View Question The coordination number of central metal atom in a complex is determined by :

View Question The correct order of magnetic moments (spin only values in B.M.) among is :
(Atomic numbers: Mn = 25; Fe = 26, Co =27)

View Question Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN– ion
towards metal spe

View Question The compound formed on heating chlorobenzene with chloral in the presence concentrated
sulphuric acid is

View Question On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant
solution is

View Question Which of the following undergoes reaction with 50% sodium hydroxide solution to give the
corresponding alcohol and acid?

View Question Which one of the following reduced with zinc and hydrochloric acid to give the corresponding
hydrocarbon?

View Question Acetyl bromide reacts with excess of CH3MgI followed by treatment with a saturated solution
of NH4Cl given

View Question Which base is present in RNA but not in DNA?

View Question Insulin production and its action in human body are responsible for the level of diabetes. This
compound belongs to whic

View Question The compound formed in the positive test for nitrogen with the Lassaigne solution of an
organic compound is

View Question Which of the following is the strongest base ?

View Question Amongst the following compounds, the optically active alkane having lowest molecular mass is

View Question Rate of the reaction
is fastest when $$Z$$ is

View Question The $$IUPAC$$ name of the compound is

View Question Among the following compounds which can be dehydrated very easily is

View Question Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

View Question ## Mathematics

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$.
If $$sin{\mkern 1mu} \alpha + \sin \be

View Question If $$u = \sqrt {{a^2}{{\cos }^2}\theta + {b^2}{{\sin }^2}\theta } + \sqrt {{a^2}{{\sin }^2}\theta + {b^2}{{\cos }^2}

View Question A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.
If the angle $$\beta \,$$, which it mak

View Question Let z and w be complex numbers such that $$\overline z + i\overline w = 0$$ and arg zw = $$\pi $$. Then arg z equals :

View Question If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then
$${{\left( {{x \over p} + {y \over q}} \right)} \over {\left

View Question If $$\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1$$, then z lies on :

View Question Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

View Question If $$\left( {1 - p} \right)$$ is a root of quadratic equation $${x^2} + px + \left( {1 - p} \right) = 0$$ then its ro

View Question If one root of the equation $${x^2} + px + 12 = 0$$ is 4, while the equation $${x^2} + px + q = 0$$ has equal roots,
t

View Question How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order

View Question The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$

View Question The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

View Question The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is

View Question Let $${{T_r}}$$ be the rth term of an A.P. whose first term is a and common difference is d. If for some positive intege

View Question The equation of the straight line passing through the point $$(4, 3)$$ and making intercepts on the co-ordinate axes who

View Question Let $$A\left( {2, - 3} \right)$$ and $$B\left( {-2, 1} \right)$$ be vertices of a triangle $$ABC$$. If the centroid of

View Question If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi $$, then the e

View Question If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus o

View Question Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diamet

View Question If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$

View Question The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$,

View Question If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is

View Question A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is

View Question Let $$A = \left( {\matrix{
1 & { - 1} & 1 \cr
2 & 1 & { - 3} \cr
1 & 1 & 1 \cr

View Question Let $$A = \left( {\matrix{
0 & 0 & { - 1} \cr
0 & { - 1} & 0 \cr
{ - 1} & 0 & 0 \c

View Question If $${a_1},{a_2},{a_3},.........,{a_n},......$$ are in G.P., then the value of the determinant
$$\left| {\matrix{
{\

View Question If $$\int {{{\sin x} \over {\sin \left( {x - \alpha } \right)}}dx = Ax + B\log \sin \left( {x - \alpha } \right), + C,}

View Question $$\int {{{dx} \over {\cos x - \sin x}}} $$ is equal to

View Question The value of $$I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx} $$

View Question The value of $$\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx} $$ is

View Question If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then

View Question If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {x

View Question The area of the region bounded by the curves
$$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :

View Question Solution of the differential equation $$ydx + \left( {x + {x^2}y} \right)dy = 0$$ is

View Question The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The pro

View Question A particle acted on by constant forces $$4\widehat i + \widehat j - 3\widehat k$$ and $$3\widehat i + \widehat j - \wide

View Question Let $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w $$ be such that $$\left| {\overrightarrow u } \right| = 1,

View Question A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-

View Question Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be non-zero vectors such that $$\left( {\overri

View Question If the straight lines
$$x=1+s,y=-3$$$$ - \lambda s,$$ $$z = 1 + \lambda s$$ and $$x = {t \over 2},y = 1 + t,z = 2 - t,$

View Question Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero vectors such that no two of t

View Question The range of the function f(x) = $${}^{7 - x}{P_{x - 3}}$$ is

View Question If $$f:R \to S$$, defined by
$$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$,
is onto, then the interval of $$S$$ is

View Question The graph of the function y = f(x) is symmetrical about the line x = 2, then

View Question The domain of the function
$$f\left( x \right) = {{{{\sin }^{ - 1}}\left( {x - 3} \right)} \over {\sqrt {9 - {x^2}} }}$$

View Question Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

View Question If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then

View Question Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of

View Question In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the
standard deviation of t

View Question Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is :

View Question ## Physics

Which one of the following represents the correct dimensions of the coefficient of viscosity?

View Question A ball is released from the top of a tower of height h meters. It takes T seconds to reach the
ground. What is the posit

View Question If $$\overrightarrow A \times \overrightarrow B = \overrightarrow B \times \overrightarrow A $$, then the angle beetw

View Question A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time
of flights in the two ca

View Question Which of the following statements is FALSE for a particle moving in a circle with a constant
angular speed?

View Question An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m.
If the car is going twice a

View Question A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point
and at the same instant p

View Question Two masses $${m_1} = 5kg$$ and $${m_2} = 4.8kg$$ tied to a string are hanging over a light frictionless pulley. What is

View Question A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of sta

View Question A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for an

View Question A uniform chain of length $$2$$ $$m$$ is kept on a table such that a length of $$60$$ $$cm$$ hangs freely from the edge

View Question A force $$\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$$ is ap

View Question A body of mass $$' m ',$$ acceleration uniformly from rest to $$'{v_1}'$$ in time $${T}$$. The instantaneous power deliv

View Question A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle,

View Question A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a m

View Question One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia ab

View Question A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the fol

View Question A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the

View Question If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mas

View Question The time period of an earth satellite in circular orbit is independent of

View Question Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circu

View Question A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

View Question If two soap bubbles of different radii are connected by a tube

View Question Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta $$ with a velocity $$v.$$ The retardi

View Question One mole of ideal monatomic gas $$\left( {\gamma = 5/3} \right)$$ is mixed with one mole of diatomic gas $$\left( {\gam

View Question If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio

View Question Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ vo

View Question Which of the following statements is correct for any thermodynamic system ?

View Question The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of therma

View Question The bob of a simple pendulum executes simple harmonic motion in water with a period $$t,$$ while the period of oscillati

View Question A particle at the end of a spring executes $$S.H.M$$ with a period $${t_1}$$. While the corresponding period for another

View Question The total energy of particle, executing simple harmonic motion is

View Question A particle of mass $$m$$ is attached to a spring (of spring constant $$k$$) and has a natural angular frequency $${\omeg

View Question The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin $$ $$\left( {100t + 20x +

View Question Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a f

View Question A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which is fixed, with a speed $$'v'$$. It appr

View Question Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the sys

View Question A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. T

View Question The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resist

View Question An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the

View Question The total current supplied to the circuit by the battery is

View Question Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is

View Question In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is

View Question Thermistors are usually made of

View Question The electrochemical equivalent of a metal is $${3.35109^{ - 7}}$$ $$kg$$ per Coulomb. The mass of the metal liberated at

View Question The thermo $$emf$$ of a thermocouple varies with temperature $$\theta $$ of the hot junction as $$E = a\theta + b{\the

View Question The Kirchhoff's first law $$\left( {\sum i = 0} \right)$$ and second law $$\left( {\sum iR = \sum E} \right),$$ where th

View Question A material $$'B'$$ has twice the specific resistance of $$'A'.$$ A circular wire made of $$'B'$$ has twice the diameter

View Question Curie temperature is the temperature above which

View Question A current $$i$$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any poin

View Question A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the c

View Question The magnetic field due to a current carrying circular loop of radius $$3$$ $$cm$$ at a point on the axis at a distance o

View Question The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration mag

View Question Two long conductors, separated by a distance $$d$$ carry current $${I_1}$$ and $${I_2}$$ in the same direction. They exe

View Question The materials suitable for making electromagnets should have

View Question Alternating current can not be measured by $$D.C.$$ ammeter because

View Question In an $$LCR$$ series $$a.c.$$ circuit, the voltage across each of the components, $$L,C$$ and $$R$$ is $$50V$$. The volt

View Question A coil having $$n$$ turns and resistance $$R\Omega $$ is connected with a galvanometer of resistance $$4R\Omega .$$ This

View Question In a uniform magnetic field of induction $$B$$ a wire in the form of a semicircle of radius $$r$$ rotates about the diam

View Question A metal conductor of length $$1$$ $$m$$ rotates vertically about one of its ends at angular velocity $$5$$ radians per

View Question In a $$LCR$$ circuit capacitance is changed from $$C$$ to $$2$$ $$C$$. For the resonant frequency to remain unchaged, th

View Question A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface

View Question The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index

View Question An electromagnetic wave of frequency $$v=3.0$$ $$MHz$$ passes from vacuum into a dielectric medium with permittivity $$

View Question The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-s

View Question The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emiss

View Question A radiation of energy $$E$$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

View Question According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a met

View Question An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The d

View Question The binding energy per nucleon of deuteron $$\left( {{}_1^2\,H} \right)$$ and helium nucleus $$\left( {{}_2^4\,He} \righ

View Question A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of

View Question The manifestation of band structure in solids is due to

View Question When $$p$$-$$n$$ junction diode is forward biased then

View Question A light ray is incident perpendicularly to one face of a $${90^ \circ }$$ prism and is totally internally reflected at t

View Question