JEE Advanced 2009 Paper 1
Q. 1 Given that the abundances of isotopes ⁵⁴Fe, ⁵⁶Fe and ⁵⁷Fe are 5%, 90%, 5% respectively, the atomic mass of Fe is
A. 55.85
B. 55.95
C. 55.75
D. 56.05
Q. 2 The term that corrects for the attractive forces present in a real gas in the van der Waals equation is
A. nb
B. an²/V²
C. -an²/V²
D. -nb
Q. 3 Among the electrolytes Na₂SO₄, CACl₂, Al₂(SO₄)₃, and NH₄Cl, the most effective coagulating agent for Sb₂S₃ sol is
A. Na₂SO₄
B. CACl₂
C. Al₂(SO₄)₃
D. NH₄Cl
Q. 4 The Henry’s law constant for the solubility of N₂ gas in water at 298 K’ is 1.0 x 10⁵ atm. The mole fraction of N₂ in air is 0.8. The number of moles of N₂ from air dissolved in 10 moles of water at 298 K and 5 atm pressure is
A. 4.0 x 10⁻⁴
B. 4.0 x 10⁻⁵
C. 5.0 x 10⁻⁴
D. 4.0 x 10⁻⁶
Q. 5 The reaction of P₄ with X leads selectively to P₄O₆. The X is
A. Dry O₂
B. A mixture of O₂ and N₂
C. Moist O₂
D. O₂ in the presence of aqueous NaOH
Q. 6 The correct acidity order of the following is
A. (III) > (IV) > (II) > (I)
B. (IV) > (III) > (I) > (II)
C. (III) > (II) > (I) > (IV)
D. (II) > (III) > (IV) > (I)
Q. 7 Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is
A. Nylon
B. Polyvinyl chloride
C. Cellulose
D. Natural Rubber
Q. 8 The IUPAC name of the following compound is
A. 4-Bromo-3-cyanophenol
B. 2-Bromo-5-hydroxybenzonitrile
C. 2-Cyano-4-hydroxybromobenzene
D. 6-Bromo-3-hydroxybenzonitrile
Q. 9 The correct. statements regarding defects in solids is(are)
A. Frenkel defect. is usually favoured by a very small difference in the sizes of cation and anion
B. Frenkel defect is a dislocation defect.
C. Trapping of an electron in the lattice leads to the formation of F-center
D. Schottky defects have no effect on the physical properties of solids
Q. 10 The compound(s) that exhibit(s) geometrical isomerism is(are)
A. A
B. B
C. C
D. D
Q. 11 The compound(s) formed upon combustion of sodium metal in excess air is(are)
A. Na₂O₂
B. Na₂O
C. NaO₂
D. NaOH
Q. 12 The correct statement(s) about the compound H₃C(HO)HC-CH=CH-CH(OH)CH₃ (X) is(are)
A. The total number of stereoisomers possible for X is 6
B. The total number of diastereoisomers possible for X is 3
C. If the stereochemistry about the double bond in X is trans, the number of
enantiomers possible for X is 4
D. If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is 2
Questions: 13 – 15
p-Amino-N, N-dimethylaniline is added to a strongly acidic solution of X.The resulting solution is treated with a few drops of an aqueous solution of Y to yield blue coloration due to the formation of methylene blue, Treatment of the aqueous solution of Y with the reagent potassium hexacyanoferrate(II) leads to the formation of an intense blue precipitate. The precipitate dissolves on excess addition of the reagent. Similarly, treatment of the solution of Y with the solution of Potassium hexacyanoferrate(III) leads to a brown coloration due to the formation of Z.
Q. 13 The compound X is
A. NaNO₃
B. NaCl
C. Na₂SO₄
D. Na₂S
Q. 14 The compound Y is
A. MgCl₂
B. FeCl₂
C. FeCl₃
D. ZnCl₂
Q. 15 The compound Z is
A. Mg₂[Fe(CN)₆]
B. Fe[Fe(CN)₆]
C. Fe₄[Fe(CN₆]₃
D. K₂Zn₃[Fe(CN)₆]₂
Questions: 16 – 18
A carbonyl compound P, which gives positive iodoform test. undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R. which undergoes intramolecular aldol reaction to give predominantly S.
Q. 16 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 17 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 18 Choose the correct option:
A. A
B. B
C. C
D. D
Question 19
This paragraph contains two questions. Each question contains statement given in two columns, which have to be matched. The statement in column I are labelled A, B, C, D while the statements in Column II are labelled p, q, r, s, t. Any given statement in column Column I can have correct matching with one or more statements in column II.
Q. 19 Match each of the diatomic molecules in column I with its properties in Column II
A. A – r, s ; B – p, q, s ; C – p, t ; D – r
B. A – p, q, r, t ; B – q, r, s, t ; C – p, q, r ; D – p, q, r, s
C. A – p, q ; B – p ; C – r, s ; D – p , t
D. A – p, q ; B – q, s ; C – p, t ; D – p, q
Q. 20 Match each of the compounds in column I with its characteristic reaction(s) in Column II
A. A – p, q, s, t ; B – s, t ; C – p; D – r
B. A – s, t ; B – q, r, t; C – p, q, s ; D – r, t
C. A – p, q, r, s ; B – q, s ; C – r, s, t ; D – p, q
D. A – s, t ; B – p, q, s ; C – q, r, t ; D – r, t
Q. 21 Let P(3, 2, 6) be a point in space and Q be a point on the line
r̅ = (î – ĵ + 2k̂) + μ(-3î + ĵ + 5k̂)
Then the value of μ for which the vector P̅Q̅ is parallel to the p;ane x – 4y +3z = 1 is
A. 1/4
B. -1/4
C. 1/8
D. -1/8
Q. 22 Tangents drawn from the point P(1,8) to the circle
x² + y² – 6x – 4y -11 = 0 touch the circle at the points A and B. The equation of the circumcircle of triangle PAB is
A. x² + y² + 4x – 6y + 19 = 0
B. x² + y² – 4x – 10y + 19 = 0
C. x² + y² – 2x + 6y -19 = 0
D. x² + y² – 6x – 4y +19 = 0
Q. 23 Let f be a non-negative function defined on the interval [0, 1]. f(0) = 0, then,
A. A
B. B
C. C
D. D
Q. 24 Let z = x + iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation zz̅³ + z̅z³ = 350 is
A. 48
B. 32
C. 40
D. 80
Q. 25 The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x² + 9y² = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is
A. 31/10
B. 29/10
C. 21/10
D. 27/10
Q. 26 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 27 Choose the correct option:
A. A
B. B
C. C
D. D
Q. 28 The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1. 2 and 3 only, is
A. 55
B. 66
C. 77
D. 88
Q. 29 Area of the region bounded by the curve y =eˣ and lines x = 0 and y = e is
A. A
B. B
C. C
D. D
Q. 30 Choose the correct option:
A. a = 2
B. a = 1
C. L = 1/64
D. L = 1/32
Q. 31 In a triangle ABC with fixed base. BC. the vertex A moves such that
cos B + cos C = 4 sin² (A/2)
If a, b, and c denote the. lengths of the sides of the triangle opposite in the angles A, B and C respectively, then
A. b + c = 4a
B. b + c = 2a
C. locus of point A is an ellipse
D. locus of point A is a pair of straight lines
Q. 32 Choose the correct option:
A. A
B. B
C. C
D. D
Questions: 33 – 35
Let A be the set, of all 3 x 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.
Q. 33 The number of matrices in A is
A. 12
B. 6
C. 9
D. 3
Q. 34 Refer the image for the question and choose the correct option
A. less than 4
B. at least 4 but less than 7
C. at least 7 but less than 10
D. at least 10
Q. 35 Refer the image for the question and choose the correct option
A. 0
B. more than 2
C. 2
D. 1
Questions: 36 – 38
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.
Q. 36 The probability that X = 3 equals
A. 25/216
B. 25/36
C. 5/36
D. 125/216
Q. 37 The probability that X ≥ 3 equals
A. 125/216
B. 25/36
C. 5/36
D. 25/216
Q. 38 The conditional probability that X ≥ 6 given X > 3 equals
A. 125/216
B. 25/216
C. 5/36
D. 25/36
Q. 39 Match the statement/expressions in Column I with the open intervals in Column II
A. A – p, q, r, s ; B -r, t ; C – q, s ; D – q, r, t
B. A – p, q, s ; B – p , t ; C – p, q, r, t ; D – s
C. A – p, q, t ; B – q , t ; C – p, q, r, t ; D – p, q
D. A – p, q, r ; B -q, t ; C – q, s, r ; D – q, t
Q. 40 Match the conics in Column I with the statements/expressions in Column II
A. A – p ; B – s, t ; C – r ; D – q, s
B. A – r ; B – s, t ; C – p ; D – q, s
C. A – r ; B – q, t ; C – p ; D – r, s
D. A – q ; B – q, t ; C – r ; D – q, s
Q. 41 Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q₁, Q₂, Q₃, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells Q₁ : Q₂ : Q₃ is
A. 1 : 2 : 3
B. 1 : 3 : 5
C. 1 : 4 : 9
D. 1 : 8 : 18
Q. 42 A block of base 10 cm x 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is √3. The inclination θ at this inclined plane from the horizontal plane is gradually increased from 0°. Then
A. at θ= 30°, the block will start sliding down the plane
B. the block will remain at rest on the plane up to certain θ and then it will topple
C. at θ= 60°, the block will start sliding down the plane and continue to do so at higher angles
D. at θ= 60°, the block will start sliding down the plane and on further increasing θ, it will topple at certain 0
Q. 43 A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake. in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface. the fish sees the speed of ball as [Take g = 10 m/s²]
A. 9 m/s
B. 12 m/s
C. 16 m/s
D. 21.33 m/s
Q. 44 Look at the drawing given in the figure, which has been drawn with ink of uniform line thickness. The mass of ink used to draw each of the two inner circles and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle (-a, a ), right inner circle (a, a ), vertical line (0, 0) and horizontal line. (0, -a). The y-coordinate of the centre of mass of the ink in this drawing is
A. a/10
B. a/8
C. a/12
D. a/3
Q. 45 Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?
A. 4
B. 3
C. 2
D. 1
Q. 46 The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. I₁ and I₂ are the currents in the segments ab and cd . Then,
A. I₁ > I₂
B. I₁ < I₂
C. I₁ is in the direction ba and I₂ is in the direction cd
D. I₁ is in the direction ab and I₂ is in the direction dc
Q. 47 A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a /4. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = ±a/2, y = ±a/2, z = ±a, /2. The electric flux through this cubical surface is
A. -2C/εo
B. 2C/εo
C. 10C/εo
D. 12C/εo
Q. 48 The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is
A. A
B. B
C. C
D. D
Q. 49 If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that
A. linear momentum of the system does not change in time
B. kinetic energy of the system does not change in time
C. angular momentum of the system does not change in time
D. potential energy of the system does not change in time
Q. 50 A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)
A. (42, 56)
B. (48, 48)
C. (66, 33)
D. (78, 39)
Q. 51 For the circuit shown in the figure
A. the current I through the battery is 7.5 mA
B. the potential difference across RL is 18 V
C. ratio of powers dissipated in R₁ and R₂ is 3
D. if R1 and R2 are interchanged, magnitude of the power dissipated in RL, will decrease by a factor of 9
Q. 52 Cᵥ and Cₚ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then
A. Cₚ – Cᵥ is larger for a diatomic ideal gas than for a monatomic ideal gas
B. Cₚ + Cᵥ is larger for a diatomic ideal gas than for a monatomic ideal gas
C. Cₚ/Cᵥ is larger for a diatomic ideal gas than for a monatomic ideal gas
D. Cₚ -Cᵥ, is larger for a diatomic ideal gas than for a monatomic ideal gas
Questions: 53 – 55
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, ¹H₂, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is given in the image. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ¹H₂ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time t₀ before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product nt₀ is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than 5 x10¹⁴ s/cm³. It may be helpful to use the following: Boltzmann constant k = 8.6 x 10⁻⁵ eV/K; e²/4πεo = 1.44 x 10⁻⁹ eVm.
Q. 53 In the core of nuclear fusion reactor, the gas becomes plasma because of
A. strong nuclear force acting between the deuterons
B. Coulomb force. acting between the deuterons
C. Coulomb force acting between deuteron-electron pairs
D. the high temperature maintained inside the reactor core
Q. 54 Assume that two deuterium nuclei in the core of fusion reactor at. temperature T are moving towards each other, each with kinetic energy 1.5 kT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 x10⁻¹⁵ m is in the range
A. 1.0 x 10⁹ K < T < 2.0 X 10⁹ K
B. 2.0 x 10⁹ K < T < 3.0 X 10⁹ K
C. 3.0 x 10⁹ K < T < 4.0 X 10⁹ K
D. 4.0 x 10⁹ K < T < 5.0 X 10⁹ K
Q. 55 Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most. promising based on Lawson criterion?
A. deuteron density = 2.0 x 10¹² cm-³ , confinement time = 5.0 x 10-³ s
B. deuteron density = 8.0 x 10¹⁴ cm-³ , confinement time = 9.0 x 10⁻¹ s
C. deuteron density = 4.0 x 10²³ cm-³ , confinement time = 1.0 x 10⁻¹¹ s
D. deuteron density = 1.0 x 10²⁴ cm-³ , confinement time = 4.0 x 10⁻¹² s
Questions: 56 – 58
When a particle is restricted to move along x-axis between x = 0 and x = a, where a is of nanometer dimension, its energy can take only certain specific values. The allowed energies of the particle moving in such a restricted region, correspond to the formation of standing waves with nodes at its ends x = 0 and x = a. The wavelength of this standing wave. is related to the linear momentum p of the particle according to the de Broglie relation. The energy of the particle of mass m is related to its linear momentum as E = p²/2m. Thus. the energy of the particle can be denoted by a quantum number ‘n ‘ taking values 1, 2. 3, (n =1, called the ground state) corresponding to the number of loops in the standing wave. Use the model described above to answer the following three questions for a particle moving in the line x =0 to x = a. Take h = 6.6 x 10⁻³⁴ J s and e = 1.6 x 10²⁹ C
Q. 56 The allowed energy for the particle for a particular value of n is proportional to
A. a-²
B. a⁻³/²
C. a⁻¹
D. a²
Q. 57 If the mass of the particle is m = 1.0 x 10⁻³⁰ kg and a = 6.6 nm, the energy of the particle in its ground state is closest to
A. 0.8 meV
B. 8 meV
C. 80 meV
D. 800 meV
Q. 58 The speed of the particle, that can take discrete values, is proportional to
A. n⁻³/²
B. n⁻¹
C. n¹/²
D. n
Q. 59 Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column ll. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let. B he the magnetic field at M and μ be the magnetic moment of the system in this condition. Assume each rotating charge to he equivalent. to a steady current.
A. A – p, r, s ; B – r, s ; C – p, q, t ; D – r, s
B. A – p, r ; B – r, s ; C – q, t ; D – r, s
C. A – q, r ; B – r, s ; C – r, t ; D – p, s
D. A – r, s ; B – r, s ; C – p, q, t ; D – p, r, s
Q. 60 Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these. statements to the appropriate system(s) from Column II.
A. A – q, t ; B – q, s, t ; C – p, r, t ; D – p
B. A – r, t ; B – r, s, t ; C – r, t ; D – s
C. A – p, t ; B – r, s, t ; C – r, t ; D – p, r
D. A – p, t ; B – q, s, t ; C – p, r, t ; D – q
| Answer Sheet |
||||||||||
| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | B | B | C | A | B | A | D | B | BC | CD |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | AB | AD | D | C | B | B | A | B | B | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | A | B | C | A | D | C | D | C | BCD | AC |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | BC | AB | A | B | B | A | B | D | B | A |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | B | B | C | A | C | D | A | D | A | CD |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | AD | BD | D | A | B | A | B | D | A | D |