IIT JEE 2008 Solutions

SECTION – I

Q. No. 1 : Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and / or record time for different number of oscillations. The observations are shown in the table.

Least count for length = 0.1 cm
Least count for time = 0.1 s

If are the percentage errors in g, i.e. for students I, II and III, respectively,

SECTION – I

Q. No. 2 : Figure shows three resistor configurations R1, R2 and R3 connected to 3V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

SECTION – I

Q. No. 3 : Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

SECTION – I

Q. No. 4 : Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is ). In the position of minimum deviation, the angle of refraction will be

SECTION – I

Q. No. 5 : An ideal gas is expanding such that . The coefficient of volume expansion of the gas is

SECTION – I

Q. No. 6 : A spherically symmetric gravitational system of particles has a mass density
Where is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance from the centre of the system is represented by

SECTION – II

Q. No. 7 :Two balls, having linear momenta undergo a collision in free space. There is no external force acting on the balls. Let be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of

SECTION – II

Q. No. 8 : Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

(A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy (B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy (C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into equal fragments (D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into equal fragments

SECTION – II

Q. No. 9 :A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is l. Choose the correct choice(s).

(A) The particle enters Region III only if its velocity
(B) The particle enters Region III only if its velocity
(C) Path length of the particle in Region II is maximum when velocity
(D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I

SECTION – II

Q. No. 10 : In a Young’s double slit experiment, the separation between the two slits is d and the wavelength of the light is . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

(A) If the screen will contain only one maximum
(B) If , at least one more maximum (besides the central maximum) will be observed on the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase.
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase

SECTION – III

Q. No. 11 :

STATEMENT -1: In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.

and

STATEMENT -2 : Resistance of a metal increases with increase in temperature.

SECTION – III

Q. No. 12 :

STATEMENT -1:An astronaut in an orbiting space station above the Earth experiences weightlessness.

and

STATEMENT -2: An object moving around the Earth under the influence of Earth’s gravitational force is in a state of ‘free-fall’

SECTION – III

Q. No. 13 :

STATEMENT -1:Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

And

STATEMENT -2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

SECTION – III

Q. No. 14 :

STATEMENT -1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

And

STATEMENT -2: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

SECTION – III

Paragraph for Question Nos. 15 to 17

A small spherical monoatomic ideal gas bubble is trapped inside a liquid of density (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is the height of the liquid is H and the atmospheric pressure is (Neglect surface tension).

Q. No. 15 : As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

SECTION – IV

Q. No. 16 : The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

SECTION – IV

Q. No. 17 : When the gas bubble is at height y from the bottom, its temperature is

SECTION – IV

Paragraph for Question Nos. 18 to 20

In a mixture of H – gas ( is singly ionized He atom), H atoms and ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to ions (by collisions). Assume that the Bohr model of atom is exactly valid.

Q. No. 18 : The quantum number n of the state finally populated in ions is

SECTION – IV

Q. No. 19 : The wavelength of light emitted in the visible region by ions after collisions with H atoms is

SECTION – IV

Q. No. 20 : The ratio of the kinetic energy of the n = 2 electron for the H atom to that of ion is

SECTION – IV

Paragraph for Question Nos. 21 to 23

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from to at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ()

Q. No. 21 : The speed of the block at point B immediately after it strikes the second incline is

SECTION – IV

Q. No. 22 :The speed of the block at point C, immediately before it leaves the second incline is

SECTION – IV

Q. No. 23 : If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

SECTION – I

Q. No. 24 :Consider the two curves Then

SECTION – I

Q. No. 25 : If , then

SECTION – I

Q. No. 26 : The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors such that . Then, the volume of the parallelopiped is

SECTION – I

Q. No. 27 : Let a and b be non-zero real numbers. Then the equation represents

SECTION – I

Q. No. 28 : Let , m and n are integers, and let p be the left hand derivative of |x – 1| at x = 1. If then

SECTION – I

Q. No. 29 : The total number of local maxima and local minima of the function is

SECTION – II

Q. No. 30 : A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then

SECTION – II

Q. No. 31 : Let and be the end points of the latus rectum of the ellipse The equations of parabolas with latus rectum PQ are

SECTION – II

Q. No. 32 : Let and for n = 1, 2, 3, ............ . Then

SECTION – II

Q. No. 33 : Let f(x) be a non-constant twice differentiable function defined on such that and . Then

vanishes at least twice on [0,1]

SECTION – III

This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Q. No. 34 : Let f and g be real valued functions defined on interval (-1,1) such that g”(x) is continuous, and



Statement – 1

Statement – 2

SECTION – III

Q. No. 35 : Consider three planes and . Let be the lines of intersection of the planes and , and and and , respectively.

Statement – 1 At least two of the lines and are non –parallel.

Statement – 2 The three planes do not have a common point.

SECTION – III

Q. No. 36 : Consider the system of equations and

Statement – 1 The system of equations has no solution for

Statement – 2

SECTION – III

Q. No. 37 : Consider the system of equations where .

Statement – 1 The probability that the system of equations has a unique solution is

Statement – 2 The probability that the system of equations has a solution is 1.

SECTION – IV

This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Paragraph for Next 3 Question

Q. No. 38 : A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F respectively. The line PQ is given by the equation and the point D is Further, it is given that the origin and the centre of C are on the same side of the line PQ.

The equation of circle C is

SECTION – IV

Q. No. 39 : Points E and F are given by

SECTION – IV

Q. No. 40 :Equations of the sides QR, RP are

SECTION – IV

Paragraph for Next 3 Question

Q. No. 41 : Consider the functions defined implicitly by the equation on various intervals in the real line. If , the equation implicitly defines a unique real valued differentiable function . If the equation implicitly defines a unique real valued differentiable function satisfying .

If , then

SECTION – IV

Q. No. 42 : The area of the region bounded by the curve , the x-axis, and lines x = a and x = b, where , is

SECTION – IV

Q. No. 43 :

SECTION – IV

Paragraph for Next 3 Question

Q. No. 44 : Let A, B, C be three sets of complex numbers as defined below:

The number of elements in the set is

SECTION – IV

Q. No. 45 : Let z be any point in . Then lies b/w

SECTION – IV

Q. No. 46 : Let z be any point in and let w be any point satisfying . Then lies b/w

SECTION – I

Q. No. 47 : Hyperconjugation involves overlap of the following orbitals

SECTION – I

Q. No. 48 : The major product of the following reaction is

SECTION – I

Q. No. 49 : Aqueous solution of on reaction with gives

SECTION – I

Q. No. 50 : Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of

SECTION – I

Q. No. 51 : Under the same reaction conditions, initial concentration of of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio of the rate constants for first order and zero order of the reactions is

SECTION – I

Q. No. 52 : 2.5 mL of M weak monoacidic base is titrated with in water at . The concentration of at equivalence point is

SECTION – II

This section contains 4 multiple correct answers(s) type questions. Each question has 4 choices (A),(B),(C) and (D), out of which ONE OR MORE is/are correct.

Q. No. 53 : The correct statement(s) about the compound given below is(are)

(A) The compound is optically active. (B) The compound possesses centre of symmetry. (C) The compound possesses plane of symmetry. (D) The compound possesses axis of symmetry.

SECTION – II

Q. No. 54 : The correct statement(s) concerning the structures E, F and G is (are)

(A) E, F and G are resonance structures. (B) E, F and E, G are tautomers. (C) F and G are geometrical isomers. (D) F and G are diastereomers.

SECTION – II

Q. No. 55 : A solution of colourless salt H on boiling with excess NaOH produces a non–flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are)

(A)
(B)
(C)
(D)

SECTION – II

Q. No. 56 : A gas described by van der Waals equation

(A) behaves similar to an ideal gas in the limit of large molar volumes.
(B) behaves similar to an ideal gas in the limit of large pressures.
(C) is characterized by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature.
(D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally.

SECTION – III

This section contains 4 multiple correct answers(s) type questions. Each question has 4 choices (A),(B),(C) and (D), out of which ONE OR MORE is/are correct.

Q. No. 57 :
STATEMENT-1: Bromobenzene upon reaction with gives 1,4-dibromobenzene as the major product.

And

STATEMENT-2: In Bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.

SECTION – III

Q. No. 58 :
STATEMENT-1: compounds are stronger oxidizing agents than compounds.

and

STATEMENT-2: The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to ‘inert pair effect’.

SECTION – III

Q. No. 59 :
STATEMENT-1: The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of slope as the atomic number is increased.

And

STATEMENT-2: Proton–proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.

SECTION – III

Q. No. 60 :
STATEMENT-1: For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.

And

STATEMENT-2: At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

SECTION – IV

This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 61 to 63

Q. No. 61 : In the following reaction sequence, products I, J and L are formed. K represents a reagent.




The structure of the product I is

SECTION – IV

Q. No. 62 : The structures of compounds J and K, respectively, are

SECTION – IV

Q. No. 63 : The structure of product L is

SECTION – IV

Paragraph for Question Nos. 64 to 66

Q. No. 64 : There are some deposits of nitrates and phosphates in earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridization easily explains the ease of sigma donation capability of NH3 and PH3. Phosphine is a flammable gas and is prepared from white phosphorus.

Among the following, the correct statement is

SECTION – IV

Q. No. 65 : Among the following, the correct statement is

SECTION – IV

Q. No. 66 : White phosphorus on reaction with gives as one of the products. This is a

SECTION – IV

Paragraph for Question Nos. 67 to 69

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day–to–day life. One of its examples is the use of ethylene glycol and water mixture as anti–freezing liquid in the radiator of automobiles.

A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9.
Given: Freezing point depression constant of water
Freezing point depression constant of ethanol
Boiling point elevation constant of water
Boiling point elevation constant of ethanol
Standard freezing point of
Standard freezing point of
Standard boiling point of
Standard boiling point of
Vapour pressure of pure
Vapour pressure of pure

Molecular weight of
Molecular weight of
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non–volatile and non–dissociative.

Q. No. 67 : The freezing point of the solution M is

SECTION – IV

Q. No. 68 : The vapour pressure of the solution M is

SECTION – IV

Q. No. 69 : Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is