AIEEE 2010 Solved Paper

The standard enthalpy of formation of is . If the enthalpy of formation of from its atoms is and that of is , the average bond enthalpy of N–H bond in is

The time for half life period of a certain reaction products is 1 hour. When the initial concentration of the reactant ‘A’, is , how much time does it take for its concentration to come from to if it is a zero order reaction ?

A solution containing is passed through a cation exchanger. The chloride ions obtained in solution were reated with excess of to give . The formula of the complex is (At. Mass of Ag = 108 u)

Consider the reaction : The rate equation for this reaction is Which of these mechanisms is/are consistent with this rate equation ?

(A)


(B)

If of water is introduced into a flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ?
(Given : Vapour pressure of

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

If sodium sulphate is considered to be completely issociated into cations and anions in aqueous solution, the change in freezing point of water , when of sodium sulphate is dissolved in 1 kg of water, is

From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous , is

In the chemical reactions,

the compounds ‘A’ and ‘B’ respectively are

of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in HCl solution. The excess of the acid required solution for complete neutralization. The percentage of nitrogen in the compound is

The energy required to break one mole of bonds in is . The longest wavelength of light capable of breaking a single bond is

Ionisation energy of . The energy of the first stationary state (n = 1) of is

Consider the following bromides :

The correct order of reactivity is

Which one of the following has an optical isomer ?

On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa espectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane and 35 g of octane will be (molar mass of and of

The main product of the following reaction is

Three reactions involving are given below:
(i)
(ii)
(iii)
In which of the above does

In aqueous solution the ionization constants for carbonic acid are: and

Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

The correct order of increasing basicity of the given conjugate bases is

The correct sequence which shows decreasing order of the ionic radii of the elements is

Solubility product of silver bromide is . The quantity of potassium bromide (molar mass taken as ) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is

The Gibbs energy for the decomposition of at is as follows :

The potential difference needed for electrolytic reduction of at is at least

At the solubility product of is . At which pH, will ions start precipitating in the form of from a solution of ions ?

Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

Out of the following, the alkene that exhibits optical isomerism is

Biuret test is not given by

The correct order of values with negative sign for the four successive elements Cr, Mn, Fe and Co is

The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

For a particular reversible reaction at temperature and were found to be both . If is the temperature at equilibrium, the reaction would be spontaneous when

A rectangular loop has a sliding connector PQ of length and resistance and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents and are

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose is the time taken for the energy stored in the capacitor to reduce to half its initial value and is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio will be

Directions: Questions contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions.

Directions: Questions contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements

Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is and the maximum kinetic energy of the photoelectrons is When the ultraviolet light is replaced by Xrays,both and increase.

Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

A ball is made of a material of density where with and representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position ?

A particle is moving with velocity , where K is a constant. The general equation for its path is

Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX’ is given by

In the circuit shown below, the key K is closed at t = 0. The current through the battery is

The figure shows the position – time (x – t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

Directions : Following Questions are based on the following paragraph.
A nucleus of mass M + Dm is at rest and decays into two daughter nuclei of equal mass each. Speed of light is c.

The binding energy per nucleon for the parent nucleus is and that for the daughter nuclei is . Then

Directions : Following Questions are based on the following paragraph.

A nucleus of mass M + Dm is at rest and decays into two daughter nuclei of equal mass each. Speed of light is c.

The speed of daughter nuclei is

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 – particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field at the centre O is

The combination of gates shown below yields

A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is

If a source of power 4 kW produces photons/second, the radiation belong to a part of the spectrum called

The respective number of significant figures for the numbers and are

In a series LCR circuit and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by . On taking out the inductor from the circuit the current leads the voltage by . The power dissipated in the LCR circuit is

Let there be a spherically symmetric charge distribution with charge density varying as upto r = R, and for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D is

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of with each other. When suspended in a liquid of density , the angle remains the same. If density of the material of the sphere is , the dielectric constant of the liquid is

Two conductors have the same resistance at but their temperature coefficients of resistance are and . The respective temperature coefficients of their series and parallel combination are nearly

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ‘P’ is such that it sweeps out a length , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ‘P’ when t = 2 s is nearly

Two fixed frictionless inclined plane making an angle and with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ?

For a particle in uniform circular motion the acceleration at a point P(R, q) on the circle of radius R is (here q is measured from the x–axis)

An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

As the beam enters the medium, it will

An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

The initial shape of the wave front of the beam is

An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

The speed of light in the medium is

A small particle of mass m is projected at an angle q with the x-axis with an initial velocity in the x-y plane as shown in the figure. At a time the angular momentum of the particle is

The equation of a wave on a string of linear mass density is given by . The tension in the string is

Let and let , where , then

Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number such that x > 0. Which of the following statements is the negation of the statement P ?

Let and . Then vector satisfying and is

The equation of the tangent to the curve , , that is parallel to the x-axis, is

Solution of the differential equation is

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and is

If two tangents drawn from a point P to the parabola are at right angles, then the locus of P is

If the vectors and are mutually orthogonal, then

Consider the following relations:

R = {(x, y) | x, y are real numbers and x = wy for some rational number w};

m, n, p and q are integers such that n, and . Then

Let be defined by If f has a local minimum at x = -1, then a possible value of k is

The number of non-singular matrices, with four entries as 1 and all other entries as 0, is

Statement-1: (Assertion) and Statement-2: (Reason)
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}.

Statement – 1: The probability that the chosen numbers when arranged in some order will form an AP is .

Statement – 2: If the four chosen numbers from an AP, then the set of all possible values of common difference is

Statement-1: (Assertion) and Statement-2: (Reason)
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x – y + z = 5.

Statement-2: The plane x – y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).

Statement-1: (Assertion) and Statement-2: (Reason)
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let and

Statement-1:
Statement-2: and

Statement-1: (Assertion) and Statement-2: (Reason)
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let A be a matrix with non-zero entries and let , where I is identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.

Statement-1: Tr(A) = 0
Statement-2: |A| = 1

Statement-1: (Assertion) and Statement-2: (Reason)
Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Let be a continuous function defined by .
Statement-1: , for some
. Statement-2: for all

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

If a and b are the roots of the equation then

The number of complex numbers z such that equals

A line AB in three-dimensional space makes angles and with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle with the positive z-axis, then equals

The line L given by passes through the point (13, 32). The line K is parallel to L and has the equation . Then the distance between L and K is

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the minute. If and are in A.P. with common difference -2, then the time taken by him to count all notes is

Let f: be a positive increasing function with Let f: be a positive increasing function with Then

Let p(x) be a function defined on R such that for all and .Then p(x) dx equals

Let be a differentiable function with and . Let Then g’(0) =

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Consider the system of linear equations:



The system has

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

The circle intersects the line at two distinct points if