JEE Advanced 2007 Paper 1
Q. 1 A resistance of 2 Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω , is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is
A. 3 Ω
B. 4 Ω
C. 5 Ω
D. 6 Ω
Q. 2 In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,
A. x < f
B. f < x < 2f
C. x = 2f
D. x > 2f
Q. 3 Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept F on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with m m a small but constant force F. As a result, the particles P move towards each other on the surface. The magnitude of acceleration, when the separation between them 0 becomes 2x , is
A. A
B. B
C. C
D. D
Q. 4 A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.
A. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
B. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
C. No potential difference appears between the two cylinders when a uniform line
charge is kept along the axis of the cylinders
D. No potential difference appears between the two cylinders when same charge density is given to both the cylinders
Q. 5 Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,
A. negative and distributed uniformly over the surface of the sphere
B. negative and appears only at the point on thesphere closest to the point charge
C. negative and distributed non-uniformly over the entire surface of the sphere
D. zero
Q. 6 A circuit is connected as shown in the figure with the switch S open. When the switch is X closed, the total amount of charge that flows from Y to X is
A. 0
B. 54 μC
C. 27 μC
D. 81 μC
Q. 7 A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be
A. only a reflected ray and no refracted ray
B. only a refracted ray and no reflected ray
C. a reflected ray and a refracted ray and the angle between them would be less than
180° – 2θ
D. a reflected ray and a refracted ray and the angle between them would be greater than 180° – 2θ
Q. 8 In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is
A. A
B. B
C. C
D. D
Q. 9 The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is
A. 802 nm
B. 823 nm
C. 1882 nm
D. 1648 nm
Q. 10
STATEMENT-1
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Because
STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 11
STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.
because
STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is False
Q. 12
STATEMENT-1
The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
because
STATEMENT-2
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 13
STATEMENT-1
If the accelerating potential in an X-ray tube is increased, the wavelengths of the
characteristic X-rays do not change. because
STATEMENT-2
When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement 2 is True
Q. 14 The ratio x₁/x₂ is a
A. 2
B. 1/2
C. √2
D. 1/√2
Q. 15 When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is
A. 2Iω/3t
B. 9Iω/2t
C. 9Iω/4t
D. 3Iω/2t
Q. 16 The loss of kinetic energy during the above process is
A. Iω²/2
B. Iω²/3
C. Iω²/4
D. Iω²/6
Q. 17 The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be
A. P₀
B. P₀/2
C. P₀/2 + Mg/(πR²)
D. P₀/2 – Mg/(πR²)
Q. 18 While the piston is at a distance 2L from the top, the hole at the tap is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is
A. A
B. B
C. C
D. D
Q. 19 The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies
A. A
B. B
C. C
D. D
Q. 20 Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.
A. A – p, q ; B – r, s ; C – r, s ; D – r, s
B. A – r, s ; B – p, q ; C – r, s ; D – r, s
C. A – r, s ; B – r, s ; C – p, q ; D – r, s
D. A – r, s ; B – r, s ; C – r, s ; D – p, q
Q. 21 Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column 1 with the statements in Column 11 and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.
A. A – q ; B – r, s ; C – s ; D – p, q, r
B. A – s ; B – r, s ; C – q ; D – p, q, r
C. A – q ; B – p, q,r ; C – s ; D – r, s
D. A – s ; B – p, q, r ; C – r ; D – r, s
Q. 22 Some laws/processes are given in Column 1. Match these with the physical phenomena given in Column 11 and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.
A. A – p, r ; B – q, s ; C – q ; D – p
B. A – p, r ; B – q, s ; C – p ; D – q
C. A – p, r ; B – q, s ; C – p ; D – p, s
D. A – q, r ; B – q, s ; C – p ; D – q
Q. 23 The species having bond order different from that in CO is
A. NO⁻
B. NO⁺
C. CN⁻
D. N₂
Q. 24 Among the following, the paramagnetic compound is
A. Na₂O₂
B. O₃
C. N₂O
D. KO₂
Q. 25 Extraction of zinc from zinc blende is achieved by
A. electrolytic reduction
B. roasting followed by reduction with carbon
C. roasting followed by reduction with another metal
D. roasting followed by self-reduction
Q. 26 In the following reaction, the structure of the major product ‘ X ’ is
A. A
B. B
C. C
D. D
Q. 27 The reagent(s) for the following conversion, is/are,
A. alcoholic KOH
B. alcoholic KOH followed by NaNH₂
C. aqueous KOH followed by NaNH₂
D. Zn/CH₃OH
Q. 28 The number of structural isomers for C₆H₁₄ is
A. 3
B. 4
C. 5
D. 6
Q. 29 The percentage of p-character in the orbitals forming P-P bonds in P₄ is
A. 25
B. 33
C. 50
D. 75
Q. 30 When 20 g of naphthoic acid (C₁₁H₈O₂) is dissolved in 50 g of benzene (Kᵣ =1.72 K kg/mol), a freezing point depression of 2K is observed. The van‘t Hoff factor (i) is
A. 0.5
B. 1
C. 2
D. 3
Q. 31 Choose the correct option:
A. 5
B. 10
C. 95
D. 100
Q. 32 STATEMENT-1 : Boron always forms covalent bond.
because
STATEMENT-2: The small size of B3+ favours formation of covalent bond.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 33 STATEMENT-1: In water, orthoboric acid behaves as a weak monobasic acid.
because
STATEMENT-2: In water, orthoboric acid acts as a proton donor.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 34 STATEMENT-1: p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.
because
STATEMENT-2: o-Hydroxybenzoic acid has intramolecular hydrogen bonding.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-l is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 35 STATEMENT-1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).
because
STATEMENT-2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 36 Argon is used in arc welding because of its
A. low reactivity with metal
B. ability to lower the melting point of metal
C. flammability
D. high calorific value
Q. 37 The structure of XeO₃ is
A. linear
B. planar
C. pyramidal
D. T-shaped
Q. 38 XeF₄ and XeF₆ are expected to be
A. oxidizing
B. reducing
C. unreactive
D. strongly basic
Questions: 39 – 41
Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 x 10²³) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.
A 4.0 molar aqueous solution of NaCl is prepared and 500 mL of this solution is
electrolysed. This leads to the evolution of chlorine gas at one of the electrodes
(atomic mass : Na = 23, Hg = 200; l Faraday = 96500 coulombs).
Q. 39 The total number of moles of chlorine gas evolved is
A. 0.5
B. 1.0
C. 2.0
D. 3.0
Q. 40 If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is
A. 200
B. 225
C. 400
D. 446
Q. 41 The total charge (coulombs) required for complete electrolysis is
A. 24125
B. 48250
C. 96500
D. 193000
Q. 42 Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
A. A – p, q, s ; B – p, r, s ; C – q, s ; D – q, s
B. A – p, r, s ; B – p, q, s ; C – q, s ; D – q, s
C. A – q, s ; B – r, s ; C – q, s ; D – q, s
D. A – p, q, s ; B – p, r, s ; C – p, s ; D – p, s
Q. 43 Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
A. A – p, r ; B – q, r ; C – p, r ; D – r
B. A – p, s ; B – s ; C – p, r ; D – q, r
C. A – p, r ; B – q, r ; C – p, s ; D – s
D. A – p, s ; B – q, r ; C – p, r ; D – s
Q. 44 Match gases under specified conditions listed in Column I with their properties/laws in
Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
A. A – s ; B – r ; C – p, q ; D – p, s
B. A – p, q ; B – r ; C – p, s ; D – p, s
C. A – p, s ; B – r ; C – p, q ; D – p, s
D. A – p, q ; B – r ; C – p, s ; D – p, r
Q. 45 Let α, β be the roots of the equation x² – px + r = 0 and α/2, 2β be the roots of the equation x² – qx + r = 0. Then the value of r is
A. (2/9)(p – q)(2q – p)
B. (2/9)(q – p)(2p – q)
C. (2/9)(q – 2p)(2q – p)
D. (2/9)(2p – q)(2q – p)
Q. 46 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 47 One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is
A. 1/2
B. 1/3
C. 2/5
D. 1/5
Q. 48 Choose the correct option:
A. on the left of x = c
B. on the right of x = c
C. at no point
D. at all points
Q. 49 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 50 A hyperbola, having the transverse axis of length 2 sinθ, is confocal with the ellipse 3x² + 4y² = 12. Then its equation is
A. x² cosec² θ – y² sec² θ = 1
B. x² sec² θ – y² cosec² θ = 1
C. x² sin² θ – y² cos² θ = 1
D. x² cos² θ – y² sin² θ = 1
Q. 51 The number of distinct real values of λ, for which the vectors -λ²î + ĵ + k̂, î – λ²ĵ + k̂, and î + ĵ – λ²k̂ are coplanar, is
A. zero
B. one
C. two
D. three
Q. 52 A man walks a distance of 3 units from the origin towards the north-east (N 45° E) direction. From there, he walks a distance of 4 units towards the north-west (N 45° W) direction to reach a point P. Then the position of P in the Argand plane is
A. A
B. B
C. C
D. D
Q. 53 The number of solutions of the pair of equations
2 sin²θ – cos2θ = 0
2 cos²θ – 3sinθ = 0
in the interval [0, 2π] is
A. zero
B. one
C. two
D. four
Q. 54 Choose the correct option:
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-l is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 55 Tangents are drawn from the point (17, 7) to the circle x² + y² = 169.
STATEMENT-1 : The tangents are mutually perpendicular.
because
STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x² + y² = 338
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 56 Choose the correct option:
A. Statement-l is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True
Q. 57 Let F (x) be an indefinite integral of sin²x
STATEMENT-1 :The function F(x) satisfies F(x + π) = F(x) for all real x.
because
STATEMENT-2 : sin²(x + π) = sin²x for all real x.
A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for
Statement-1
B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for
Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-l is False, Statement-2 is True
Questions: 58 – 60
Read the paragraph given to the side and answer the questions that follow:
Q. 58 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 59 Tᵣ is always
A. an odd number
B. an even number
C. a prime number
D. a composite number
Q. 60 Which one of the following is a correct statement?
A. Q1, Q2, Q3,… are in AP. with common difference 5
B. Q1, Q2, Q3,… are in AP. with common difference 6
C. Q1, Q2, Q3,… are in AP. with common difference 11
D. Q1 = Q2 : Q3
Questions: 61 – 63
Consider the circle x² + y² = 9 and the parabola y² = 8x . They intersect at P and Q
in the first and the fourth quadrants, respectively. Tangents to the circle at P and
Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the xaxis at S.
Q. 61 The ratio of the areas of the triangles PQS and PQR is
A. 1 : √2
B. 1 : 2
C. 1 : 4
D. 1 : 8
Q. 62 The radius of the circumcircle of the triangle PRS is
A. 5
B. 3√3
C. 3√2
D. 2√3
Q. 63 The radius of the incircle of the triangle PQR is
A. 4
B. 3
C. 8/3
D. 2
Q. 64 Consider the following linear equations
ax + by + cz = O
bx + cy + az = 0
cx + ay + bz = 0
Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.
A. A – r ; B – q ; C – p ; D – s
B. A – s ; B – q ; C – p ; D – r
C. A – r ; B – p ; C – q ; D – s
D. A – s ; B – p ; C – q ; D – r
Q. 65 In the following [ x ] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.
A. A – p, q, r ; B – p, s : C – r, s ; D – p, q
B. A – p, q, r ; B – p, r : C – r, s ; D – p, q
C. A – p, q ; B – p, s : C – q, s ; D – p, q, r
D. A – p, q ; B – p, s : C – r, s ; D – p, q, r
Q. 66 Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the CBS.
A. A – s ; B – s ; C – p ; D – r
B. A – r ; B – s ; C – p ; D – s
C. A – r ; B – q ; C – p ; D – s
D. A – r ; B – s ; C – q ; D – s
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | A | B | B | A | D | C | C | A | B | C |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | B | C | B | C | A | B | A | D | C | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | A | B | A | D | B | B | B | C | D | A |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | B | A | C | D | B | A | C | A | B | D |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | D | A | D | C | D | A | C | A | A | A |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | C | D | C | D | A | C | D | B | D | B |
| Question | 61 | 62 | 63 | 64 | 65 | 66 | ||||
| Answer | C | B | D | A | A | A |