JEE Main 2005 Previous Year Question Paper with Solutions

Which of the following factors may be regarded as the main cause of lanthanide contraction?

Hydrogen ion concentration in in a solution of will be

Consider an endothermic reaction, with the activation energies and for the backward and forward reactions, respectively. In general

Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

Which of the following compounds shows optical isomerism?

Of the following sets which one does NOT contain isoelectronic species?

Heating an aqueous solution of aluminium chloride to dryness will give

In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-

The best reagent to convert pent-3-en-2-ol into pent -3-en-2-one is

If the bond dissociation energies of and (all diatomic molecules) are in the ratio of 1:1:0.5 and for the formation of is . The bond dissociation energy of will be

A schematic plot of versus inverse of temperature for a reaction is shown below

Which types of isomerism is shown by 2,3-dichlorobutane?

An ionic compound has a unit cell consisting of ions at the corners of a cube and ions on the centres of the faces of the cube. The empirical formula for this compound would be

An organic compound having molecular mass 60 is found to contain and while rest is oxygen. On heating it gives along with a solid residue. The solid residue give violet colour with alkaline copper sul

The solubility product of a salt having general formula , in water is: . The concentration of ions in the aqueous solution of the salt is

Which of the following oxides is amphoteric in character?

Electrolyte: Calculate Using appropriate molar conductance's of the electrolytes listed above at infinite dilution in at

Equimolar solutions in the same solvent have

Calomel on reaction with ammonium hydroxide gives

The photon of hard gamma radiation knocks a proton out of nucleus to form

Tertiary alkyl halides are practically inert to substitution by mechanism because of

For the reaction , at When and are compared at , it is found that

The oxidation state of chromium in the final product formed the reaction between and acidified potassium dichromate solution is :

The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous acid is

An amount of solid is placed in a flask already containing ammonia gas at a certain temperature and . Pressure. Ammonium hydrogen sulphide decomposes to yield and gases in the flask. When the decompos

In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same energy in the absence of magnetic and electric fields?(A) (B) (C) (D) (E)

If we consider that , in place of , mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of the substance will

Heating mixture of and will give

Lattice energy of an ionic compounds depends upon

In which of the following arrangements the order is NOT according to the property indicated against it?

The reactionis fastest when is

The correct order of the thermal stability of hydrogen halides is

-cresol reacts with chloroform in alkaline medium to give the compound which adds hydrogen cyanide to form, the compound . The latter on acidic hydrolysis gives chiral carboxylic acid. The structure o

Hydrogen bomb is based on the principle of

Acid catalyzed hydration of alkenes except ethene leads to the formation of

Alkyl halides react with dialkyl copper reagents to give

The value of the 'spin only' magnetic moment for one of the following configurations is . The correct one is

Two solutions of a substance (non electrolyte) are mixed in the following manner. of first solution of second solution. What is the molarity of the final mixture?

Elimination of bromine from 2-bromobutane results in the formation of-

What is the conjugate base of ?

Aluminium oxide may be electrolysed at to furnish aluminium metal (Atomic mass amu; 1 Faraday Coulombs). The cathode reaction is To prepare of aluminium metal by this method would require

The IUPAC name of the coordination compound is

Among the following acids which has the lowest value?

Which one of the following species is diamagnetic in nature?

can be taken as the time taken for the concentration of a reactant to drop to of its initial value. If the rate constant for a first order reaction is , the can be written as

The highest electrical conductivity of the following aqueous solutions is of

In silicon dioxide

Reaction of cyclohexanone with dimethylamine in the presence of catalytic amount of an acid forms a compound if water during the reaction is continuously removed. The compound formed is generally know

Due to the presence of an unpaired electron, free radicals are:

For a spontaneous reaction the , equilibrium constant and will be respectively

The decreasing order of nucleophilicity among the nucleophiles (A) (B) (C) (D) is

A reaction involving two different reactants can never be

Which one of the following methods is neither meant for the synthesis nor for separation of amines?

The lanthanide contraction is responsible for the fact that

Benzene and toluene form nearly ideal solutions. At , the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at for a solution containing of b

Consider the reaction: carried out at constant temperature and pressure. If and are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

The oxidation state of in is

Pick out the isoelectronic structure from the following :(i) (ii) (iii) (iv)

The exothermic formation of is represented by the equation: Which of the following will increase the quantity of in an equilibrium mixture of and ?

The structure of diborane contains

Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour?(At. No. )

2 methylbutane on reacting with bromine in the presence of sunlight gives mainly

If is the degree of dissociation of , the Van't Hoff's factor (i) used for calculating the molecular mass is

Of the five isomeric hexanes, the isomer which can give two monochlorinated compounds is

Amongst the following the most basic compound is

Reaction of one molecule of with one molecule of 1,3 -butadiene at gives predominantly

The normal to the curve at any point is such that

If and then is a polynomial of degree

The plane cuts the sphere in a circle of radius

Let and be the distinct roots of , then is equal to

Area of the greatest rectangle that can be inscribed in the ellipse

If and , then lies on

Let , be a function defined by ,then is both one-one and onto when is the interval

If , then is equal to

The value of for which the sum of the squares of the roots of the equation assume the least value is

If the roots of the equation be two consecutive integers, then equals

If the plane passes through the midpoint of the line joining the centres of the spheres and then a equals

If the cube roots of unity are then the roots of the equation , are

If the equation , has a positive root , then the equation has a positive root, which is

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

If and are two non-zero complex numbers such that , then is equal to

If the angel between the line and the plane is such that then value of is

In a triangle . If and are the roots of then

If , then the solution of the equation is

If both the roots of the quadratic equation are less than 5 , then lies in the interval

The parabolas and divide the square region bounded by the lines and the coordinate axes. If are respectively the areas of these parts numbered from top to bottom ; then is

equals

A random variable has Poisson distribution with mean 2 . Then equals

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

The value of , is

The area enclosed between the curve and the coordinate axes is

Let be observations such that and . Then a possible value of among the following is

A spherical iron ball in radius is coated with a layer of ice of uniform thickness that melts at a rate of . When the thickness of ice is , then the rate at which the thickness of ice decreases is

is equal to

If and then

The differential equation representing the family of curves , where , is a parameter, is of order and degree as follows:

The distance between the line , and the plane is

Suppose is differentiable at and , then equals

The value of integral, is

Let and two events such that and , where stands for complement of event . Then events and are

If the letter of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

A real valued function satisfies the functional equation where is given constant and is equal to

If , then the inverse of is

If is a real valued differentiable function satisfying and , then equals

Let be a non - negative continuous function such that the area bounded by the curve -axis and the ordinates and is . Then is

If the roots of the equation be two consecutive integers, then equals

The system of equations has infinite solutions, if is

The value of for which the sum of the squares of the roots of the equation assume the least value is

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

The angle between the lines and is

Let be differentiable for all . If and for , then

Let be a differentiable function having , . Then equals

If are in G.P., then the determinant is equal to

In a common base amplifier, the phase difference between the input signal voltage and output voltage is

A bullet fired into a fixed target loses half of its velocity after penetrating . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents

The intensity of gamma radiation from a given source is . On passing through of lead, it is reduced to . The thickness of lead which will reduce the intensity to will be

The function represents

When an unpolarized light of intensity is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

A magnetic needle is kept in a non-uniform magnetic field. It experiences

An annular ring with inner and outer radii and is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts

A system goes from to via two processes and as shown in figure. If and are the changes in internal energies in the processes and respectively, then

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force is applied at the point parallel to , such that the object has only the translational motion without rotation

The phase difference between the alternating current and is . Which of the following cannot be the constituent of the circuit?

One conducting tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field is perpendicular to the plane of the figure. If each tube moves t

Two point charges and are located at and respectively. The location of a point on the axis at which the net electric field due to these two point charges is zero is

The self inductance of the motor of an electric fan is . In order to impart maximum power at , it should be connected to a capacitance of

Two thin wire rings each having a radius are placed at a distance apart with their axes coinciding. The charges on the two rings are and . The potential difference between the centres of the two rings

A nuclear transformation is denoted by . Which of the following is the nucleus of element ?

A parallel plate capacitor is made by stacking equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is then the resultant capacitance is

A particle of mass is kept on the surface of a uniform sphere of mass and radius . Find the work to be done against the gravitational force between them to take the particle far away from the sphere (

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than is incident on it. The band gap in for the semiconductor is

If are non coplanar vectors and is a real number then

A gaseous mixture consists of of helium and of oxygen. The ratio of the mixture is

A coil of inductance and resistance is connected to a source of voltage . The current reaches half of its steady state value in

A smooth block is released at rest on a incline and then slides a distance . The time taken to slide is times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A photocell is illuminated by a small bright source placed away. When the same source of light is placed away, the number of electrons emitted by photo-cathode would

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

If is stress and is young's modulus of material of a wire, the energy stored in the wire per unit volume is

A parachutist after bailing out falls without friction. When parachute opens, it decelerates at . He reaches the ground with a speed of . At what height, did he bail out?

Average density of the earth

A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 - divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1

A fully charged capacitor has a capacitance . It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity and mass . If the temperature o

A mass moves with a velocity and collides in-elastically with another identical mass. After collision the mass moves with velocity in a direction perpendicular to the initial direction of motion. Find

A spherical ball of mass is stationary at the top of a hill of height . It rolls down a smooth surface to the ground, then climbs up another hill of height and finally rolls down to a horizontal base

A long capillary tube is dipped in water. The water rises up to . If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

The upper half of an inclined plane with inclination is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of

The relation between time and distance is where and are constants. The acceleration is

A particle is moving eastwards with a velocity of . In 10 seconds the velocity changes to northwards. The average acceleration in this time is

The block of mass moving on the frictionless horizontal surface collides with the spring of spring constant and compresses it by length . The maximum momentum of the block after collision is

An energy source will supply a constant current into the load if its internal resistance is

Two simple harmonic motions are represented by the equations and . The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

The figure shows a system of two concentric spheres of radii and are kept at temperatures and , respectively. The radial rate of flow of heat in a substance between the two concentric spheres is propo

The change in the value of at a height above the surface of the earth is the same as at a depth below the surface of earth. When both and are much smaller than the radius of earth, then which one of t

Two thin, long, parallel wires, separated by a distance carry a current of in the same direction. They will

In a full wave rectifier circuit operating from mains frequency, the fundamental frequency in the ripple would be

A body of mass is accelerated uniformly from rest to a speed in a time . The instantaneous power delivered to the body as a function of time is given by

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

In the circuit, the galvanometer shows zero deflection. If the batteries and have negligible internal resistance, the value of the resistor will be -

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out,

When two tuning forks (fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heated. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6

A thin glass (refractive index ) lens has optical power of in air. Its optical power in a liquid medium with refractive index will be

If is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

A circuit has a resistance of and an impedance of . The power factor of the circuit will be

If is the mid point of and is any point outside , then

If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor

Let and . Then depends on

Two sources of equal are connected to an external resistance . The internal resistance of the two sources are and . If the potential difference across the source having internal resistance is zero, th

The moment of inertia of a uniform semicircular disc of mass and radius about a line perpendicular to the plane of the disc through the center is

A charged particle of mass and charge travels on a circular path of radius that is perpendicular to a magnetic field . The time taken by the particle to complete one revolution is

In a potentiometer experiment the balancing with a cell is at length . On shunting the cell with a resistance of , the balancing length becomes . The internal resistance of the cell is

Which of the following is incorrect regarding the first law of thermodynamics?

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

A charged ball hangs from a silk thread , which makes angle with a large charged conducting sheet , as shown in the figure. The surface charge density of the sheet is proportional to

If a simple harmonic motion is represented by . its time period is

A car starting from rest accelerates at the rate through a distance , then continues at constant speed for time and then decelerates at the rate to come to rest. If the total distance traversed is , t

A block is kept on a frictionless inclined surface with angle of inclination . The incline is given an acceleration to keep the block stationary. Then is equal to

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is and the fish is 12 below the surface, the radius of this circle in is

Two point white dots are apart on a black paper. They are viewed by eye of pupil diameter . Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelengt

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity the

Let and be distinct non- negative numbers. If the vectors and lie in a plane, then is

The resistance of hot tungsten filament is about 10 times the cold resistance. What will be resistance of and lamp when not in use ?

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Consider a car moving on a straight road with a speed of . The distance at which car can be stopped is

Two concentric coils each of radius equal to are placed at right angles to each other. 3 ampere and 4 ampere are the currents flowing in each coil respectively . The magnetic induction in Weber at the

A particle of mass subjected to a force with . What will be its initial acceleration if it is released from a point away from the origin?

If radius of the nucleus is estimated to be fermi then the radius of nucleus is estimated to be nearly

For any vector , the value of is equal to

Starting with a sample of pure of it decays into in 15 minutes. The corresponding half life is

A body of mass while falling vertically downloads under gravity breaks into two-parts; a body of mass and a body of mass . The center of mass of bodies and taken together shifts compared to that of bo