IIT JEE 2007 Question Paper

PART- III (PHYSICS)
Section – 1
Straight Objective Type

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Q. No. – 1. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

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Q. No. – 2. A magnetic field exists in the region and , in the region , where is a positive constant. A positive point charge moving with a velocity , where is a positive constant, enters the magnetic field at . The trajectory of the charge in this region can be like,

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Q. No. – 3. A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of with respect to the initial position. The object is

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Q. No. – 4. Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted Xrays is

Q. No. – 5. A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of Take (exact). The Young’s modulus obtained from the reading is

Q. No. – 6. Positive and negative point charges of equal magnitude are kept at , respectively. The work done by the electric field when another positive point charge is moved from to is

Q. No. – 7. In the experiment to determine the speed of sound using a resonance column,

Q. No. – 8. Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

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Q. No. – 9. A particle moves in the plane under the influence of a force such that its linear momentum is , where A and k are constants. The angle between the force and the momentum is

Section – II

This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2Q. No. – 10. STATEMENT-1: A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil. Because STATEMENT-2: In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

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Q. No. – 11.

STATEMENT-1: If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

because

STATEMENT-2:
The linear momentum of an isolated system remains constant.

Q. No. – 12.

STATEMENT-1: The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

because

STATEMENT-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

Q. No. – 13.

STATEMENT-1: A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

because

STATEMENT-2: For every action there is an equal and opposite reaction.

Section – III
Linked Comprehension Type

This section contains 2 paragraphs P14-16 and P17-19. Based upon each paragraph,

The figure shows a surface XY separating two transparent media, medium – 1 and medium -2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction. Q. No. – 14. Light travels as a

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Q. No. – 15. The phases of the light wave at c, d, e and f are and respectively. It is given that

Q. No. – 16. Speed of the light is

image:’savvica’

Paragraph for Question Nos. 17 to 19

Two trains A and B are moving with speeds and respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from to , as shown in the figure. The spread in the frequency (highest frequency − lowest frequency) is thus . The speed of sound in still air is . Q. No. – 17. The speed of sound of the whistle is

Q. No. – 18. The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by

Q. No. – 19. The spread of frequency as observed by the passengers in train B is

Section – IV
Matrix-Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

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Q. No. – 20. Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) The object moves on the x-axis under a conservative force in such a way that its “speed” and “position” satisfy , where and are positive constants.	(p) The object executes a simple harmonic motion.
(B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy , where k is a positive constant.	(q) The object does not change its direction.
(C) The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration.	(r) The kinetic energy of the object keeps on decreasing.
(D) The object is projected from the earth’s surface vertically upwards with a speed , where, is the mass of the earth and is the radius of the earth. Neglect forces from objects other than the earth.	(s) The object can change its direction only once.

Q. No. – 21. Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) Point P is situated midway between the wires. !{width:150px}	(p) The magnetic fields (B) at P due to the currents in the wires are in the same direction.
(B) Point P is situated at the midpoint of the line joining the centers of the circular wires, which have same radii. !{width:150px; height:100px}	(q) The magnetic fields (B) at P due to the currents in the wires are in opposite directions.
(C) Point P is situated at the midpoint of the line joining the centers of the circular wires, which have same radii. !{width:150px}	(r) There is no magnetic field at P.
(D) Point P is situated at the common center of the wires. !{width:150px; height:100px}	(s) The wires repel each other.

Q. No. – 22. Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) Bimetallic strip	(p) Radiation from a hot body
(B) Steam engine	(q) Energy conversion
(C) Incandescent lamp	(r) Melting
(D) Electric fuse	(s) Thermal expansion of solids

PART- III (CHEMISTRY)
Section – 1
Straight Objective Type

This section contains 9 multiple choice questions numbered 23 to 31. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

Q. No. – 23. Among the following, the least stable resonance structure is

24. For the process (l) (1 bar, 373 K) (1 bar, 373 K), the correct set of thermodynamic parameters is

Q. No. – 25. Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is

Q. No. – 26. Consider a reaction aG + bH Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is

Q. No. – 27. Among the following metal carbonyls, the C – O bond order is lowest in

Q. No. – 28. A positron is emitted from . The ratio of the atomic mass and atomic number of the resulting nuclide is

Q. No. – 29. Consider a titration of potassium dichromate solution with acidified Mohr’s salt solution using diphenylamine as indicator. The number of moles of Mohr’s salt required per mole of dichromate is

Q. No. – 30. The number of stereoisomers obtained by bromination of trans-2-butene is

Q. No. – 31. A solution of metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

Section – II
Assertion – Reason Type

This section 4 questions numbered 32 to 35. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason).

Q. No. – 32.

STATEMENT-1: Molecules that are not superimposable on their mirror images are chiral

because

STATEMENT-2: All chiral molecules have chiral centres.

Q. No. – 33.

STATEMENT-1: Alkali metals dissolves in liquid ammonia to give blue solution

because

STATEMENT-2: Alkali metals in liquid ammonia give solvated species of the type (M = alkali metals).

Q. No. – 34.

STATEMENT-1: Band gap in germanium is small.

because

STATEMENT-2: The energy spread of each germanium atomic energy level is infinitesimally small.

Q. No. – 35.

STATEMENT-1: Glucose gives a reddish-brown precipitate with Fehling’s solution.

because

STATEMENT-2: Reaction of glucose with Fehling’s solution gives CuO and gluconic acid.

Section – III
Linked Comprehension Type

This section contains 2 paragraphs 36-38 and 39-41. Based upon each paragraph, 3 multiple choice questions have to be answered.

Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicyladehydes as depicted below.

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Q. No. – 36. Which one of the following reagents is used in the above reaction?

Q. No. – 37. The electrophile in this reaction is

38. The structure of the intermediate I is

Paragraph for question Nos 39 to 41

Redox reactions play a pivotal role in chemistry and biology. The values of standard redox potential of two half-cell reactions decide which way the reaction is expected to proceed. A simple example is a Daniel cell in which zinc goes into solution and copper gets deposited. Given below are a set of half-cell reactions (acidic medium) along with their (V with respect to normal hydrogen electrode) values. Using this data obtain the correct explanations to Questions 39-41.

Q. No. – 39. Among the following, identify the correct statement.

Q. No. – 40. While is stable, is not stable in acid solution because

Q. No. – 41. Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of

Section – IV
Matrix-Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column-I have to be matched with statements (p, q, r, s) in Column-II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

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Q. No. – 42. Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I	Column II
(A)	(p) redox reaction
(B)	(q) one of the products has trigonal planar structure
(C)	(r) dimeric bridged tetrahedral metal ion
(D)	(s) disproportionation

Q. No. – 43. Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I	Column II
(A)	(p) gives precipitate with 2, 4-dinitrophenylhydrazine
(B)	(q) gives precipitate with
(C)	(r) is a nucleophile
(C)	(s) is involved in cyanohydrin formation

Q. No. – 44. Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) Simple cubic and face-centred cubic	(p) have these cell parameters and
(B) cubic and rhombohedral	(q) are two crystal systems
(C) cubic and tetragonal	(r) have only two crystallography angles of
(D) hexagonal and monoclinic	(s) belong to same crystal system

PART- III (MATHEMATICS)
Section – 1
Straight Objective Type
This section contains 9 multiple choice questions numbered 45 to 53.

Q. No. – 45. Let be unit vectors such that . Which one of the following is correct?

Q. No. 46. Let for and then equals

Q. No. – 47. equals

Q. No. – 48. The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

Q. No. – 49. If and , then all the values of lie on

Q. No. – 50. Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q. No. – 51. Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

Q. No. – 52. The differential equation determines a family of circles with

Q. No. – 53. Let denote the complement of an event . Let be pairwise independent events with and . Then equals

Section – II
Assertion − Reason Type

This section contains 4 questions numbered 54 to 57. Each question contains STATEMENT − 1 (Assertion) and STATEMENT -2 (Reason).

Q. No. – 54. Let for all real .

STATEMENT -1: For each real t, there exists a point c in such that .

because

STATEMENT -2: for each real .

Q. No. – 55. Consider the planes and .

STATEMENT -1: The parametric equations of the line of intersection of the given planes are ,


because

STATEMENT -2: The vectors is parallel to the line of intersection of the given planes.

Q. No. – 56. Lines and intersect the line at and , respectively. The bisector of the acute angle between and intersects at .

STATEMENT -1: The ratio equals .

because

STATEMENT -2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

Q. No. – 57.

STATEMENT -1: The curve is symmetric with respect to the line .

because

STATEMENT -2: A parabola is symmetric about its axis.

Section – III
Linked Comprehension Type

This section contains 2 paragraphs M58−60 and M61−63. Based upon each paragraph, 3 multiple choice questions have to be answered.

Paragraph for question Nos. 58 to 60

If a continuous f defined on the real line R, assumes positive and negative values in R then the equation f(x) = 0 has a root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum values is negative then the equation f(x) = 0 has a root in R.

Consider for all real x where k is a real constant.

Q. No. – 58. The line meets for at the equation f(x) = 0 has a root in R.

Q. No. – 59. The positive value of for which has only one root is

Q. No. – 60. For , the set of all values of k for which has two distinct roots is

Paragraph for Question Nos. 61 to 63

Let denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For ,

let and has arithmetic, geometric and harmonic means as respectively.

Q. No. – 61. Which one of the following statements is correct?

Q. No. – 62. Which of the following statements is correct?

Q. No. – 63. Which of the following statements is correct?

Section – IV
Matrix − Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A−p, A−s, B−q, B−r, C−p, C−q and D−s, then the correctly bubbled 4 × 4 matrix should be as follows:

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Q. No. – 64. Let

Match the conditions / expressions in Column I with statements in Column II and indicate your answers by darkening the appropriate bubbles in 4 × 4 matrix given in the ORS.

Column I	Column II
(A) If , then satisfies	(p)
(B) If , then satisfies	(q)
(C) If , then satisfies	(r)
(D) If , then satisfies	(s)

Q. No. – 65. Let be such that

Match the statements in Column I with the statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
|Column I|Column II| |(A) If and , then |(p) lies on the circle
|(B) If and , then |(q) lies on | |(C) If and , then |(r) lies on | |(D) If and , then |(s) lies on |

Q. No. – 66. Match the statements in Column I with the properties Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

Column I	Column II
(A) Two intersecting circles	(p) have a common tangent
(B) Two mutually external circles	(q) have a common normal
(C) two circles, one strictly inside the other	(r) do not have a common tangent
(D) two branches of a hyperbola	(s) do not have a common normal