JEE Advanced 2012 Paper 2
Q. 1 A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k̂ is coming out of the plane of the paper. the magnetic moment of the current loop is
A. a²Ik̂
B. (Π/2+1)a²Ik̂
C. -(Π/2+1)a²Ik̂
D. (2Π+1)a²Ik̂
Q. 2 An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. the magnitude of the magnitude field, |B̅| as a function of the radial distance r from the axis is best represented by
A. A
B. B
C. C
D. D
Q. 3 A thin uniform cylindrical shell, closed at both ends, is partially filled with water. it is floating vertically in water in half-submerged state. if ρc is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
A. more than half-filled if ρc is less than 0.5
B. more than half-filled if ρc is less than 1.0
C. half-filled if ρc is more than 0.5
D. less than half-filled if ρc is less than 0.5
Q. 4 In the given circuit, a change of +80 μC is given to the upper plate of the 4 μF capacitor. Then in the steady state, the charge on the upper plate of the 3 μF capacitor is
A. +32 μC
B. +40 μC
C. +48 μC
D. +80 μC
Q. 5 Two moles of ideal helium gas are in a rubber balloon at 30°C. The balloon is fully expandable and can be assumed to require no energy in its expansion. the temperature of the gas in the balloon is slowly changed to 35°C. The amount heat required in raising the temperature is nearly (take R=8.31 J/mol.K)
A. 62 J
B. 104 J
C. 124 J
D. 208 J
Q. 6 Consider a disc rotating in the horizontal plane with a constant angular speed co about its, centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebblesPand are simultaneously projected at an angle towards. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back onthe disc before the disc has completed y rotation, (ii) their range is less than half the disc radius, and (iii) w remains constant throughout. Then
A. P lands in the shaded region and in the unshaded region.
B. P lands in the unshaded region and Q in the shaded region
C. Both P and Q land in the unshaded region.
D. Both P and Q land in the shaded region
Q. 7 A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38 C in which the speed of sound is 336 mls. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is
A. 14.0 cm
B. 15.2 cm
C. 16.4 cm
D. 17.6 cm
Q. 8 Two identical discs of the same radius R are rotating about their axes in opposite
directions with the same constant angular speed w. The discs are in the same horizontal plane. At the time!= 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points Pand Q is vᵣ. In one time period (T ) of rotatin of the discs, v, as a function of time is best represented by
A. A
B. B
C. C
D. D
Questions: 9 – 10
Most materials have the refractive index, n > 1. So, when a light ray from the air enters a naturally occurring material, then by Snell’s law, sinθ₁/sinθ₂=n₂/n₁. It is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation, n=(c/v)=±√εᵣμᵣ, where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εᵣ, and μᵣ, are the relative permittivity and permeability of the medium respectively. In normal materials, both Sr and it, are positive, implying positive n for the medium. When both εᵣ and μᵣ are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.
Q. 9 For light incident from air on a meta-material, the appropriate ray diagram is
A. A
B. B
C. C
D. D
Q. 10 Choose the correct statement
A. (A) The speed of light in the meta-material is v = c|n|
B. (B) The speed of light in the meta-material is v =c/|n|
C. (B) The speed of light in the meta-material is v =c
D. (D) The wavelength of the light in the meta-material λₘ is given by λₘ=λₐᵢᵣ|n|, where
λₐᵢᵣ is the wavelength of the light in air.
Questions: 11 – 12
The β-decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p) and an electron ( e⁻) are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a twobody decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous spectrum. Considering a three-body decay process, i.e. n —> p + e⁻ +vₑ around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino(vₑ) to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is 0.8×106 eV. The kinetic energy carried by the proton is only the recoil energy.
Q. 11 What is the maximum energy of the anti-neutrino?
A. Zero
B. Much less than 0.8 x 10⁶ eV
C. Nearly 0.8 x 10⁶ eV
D. Much larger than 0.8 x 10⁶ eV
Q. 12 If the anti-neutrino had a mass of 3 eV/c² (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?
A. 0 ≤K≤ 0.8 x 10⁶ eV
B. 3.0 eV ≤ K≤0.8x 10⁶ eV
C. 3.0 eV ≤ K<0.8x 10⁶ eV
D. 0 ≤K< 0.8 x 10⁶ eV
Questions: 13 – 14
The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. When the disc— stick system is rotated about the origin on a horizontal frictionless plane with angular speed ω, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed ω in this case. Now consider two similar systems as shown in the figure: Case (a) the disc with its face vertical and parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane and its horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are rotated with constant angular speed co about the z-axis.
Q. 13 Which of the following s statements about the instantaneous axis (passing through the centre of mass) is correct?
A. It is vertical for both the cases (a) and (b).
B. It is vertical for case (a); and is at 45° to the x-z plane and lies in the plane of the disc for case (b).
C. It is horizontal for case (a); and is at 45° to the x-z plane and is normal to the plane of the disc for case (b).
D. It is vertical for case (a); and is at 45° to thex-z plane and is normal to the plane of the disc for case (b).
Q. 14 Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?
A. It is √2ω for both the cases.
B. It is ω for case (a); and ω/√2 for case (b)
C. It is ω for case (a); and √2ω for case (b)
D. It is ω for both the cases
Q. 15 In the given circuit, the AC source has w = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)
A. The current through the circuit, I is 0.3 A
B. The current through the circuit, I is 0.3√2A
C. The voltage across 100Ω resistor =10√2V
D. The voltage across 50Ω resistor=10V
Q. 16 A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)
A. The emf induced in the loop is zero if the current is constant.
B. The emf induced in the loop is finite if the current is constant.
C. The emf induced in the loop is zero if the current decreases at a steady rate
D. The emf induced in the loop is finite if the current decreases at a steady rate.
Q. 17 Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that K=(1/4Πεo)q/L² which of the following statement(s) is(are) correct ?
A. The electric field at O is 6K along OD.
B. The potential at O is zero
C. The potential at all points on the line PR is same.
D. The potential at all points on the line ST is same.
Q. 18 Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct ?
A. Both cylinders P and Q reach the ground at the same time.
B. Cylinder P has larger linear acceleration than cylinder Q.
C. Both cylinders reach the ground with same translational kinetic energy.
D. Cylinder Q reaches th ground with larger angular speed.
Q. 19 Two spherical planets P and Q have the same uniform density ρ, masses Mₚ and Mᵩ, and surface areas A and 4A, respectively. A spherical planet R also has uniform density ρ and its mass is ( Mₚ+ Mᵩ). The escape velocities from the planets P, Q, and R are Vₚ, Vᵩ, and Vᵣ, respectively. Then
A. Vᵩ > Vᵣ > Vₚ
B. Vᵣ > Vᵩ > Vₚ
C. Vᵣ /Vₚ =3
D. Vₚ / Vᵩ =1/2
Q. 20 The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface,
A. the point O has a linear velocity 3Rωî
B. the point P has a linear velocity 11/4Rωî+√3/4Rωk̂
C. the point P has a linear velocity 13/4Rωî-√3/4Rωk̂
D. the point P has a linear velocity (3-√3/4)Rωî+1/4Rωk̂
Q. 21 NiCl₂{P(C₂H₅)₂(C₆H5₅)}₂ exhibits temperature dependent magnetic behaviour paramagnetic/diamagnetic). The coordination geometries of Ni²⁺ in the paramagnetic and diamagnetic states are respectively
A. tetrahedral and tetrahedral
B. square planar and square planar
C. tetrahedral and square planar
D. square planar and tetrahedral
Q. 22 In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are
A. O₂ and CO respectively
B. O₂ and Zn dust respectively
C. HNO₃ and Zn dust respectively
D. HNO₃ and CO respectively.
Q. 23 The reaction of white phosphorus with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively
A. redox reaction; — 3 and — 5
B. redox reaction; + 3 and + 5
C. disproportionation reaction; — 3 and + 5
D. disproportionation reaction; — 3 and + 3
Q. 24 The shape of XeO₂F₂ molecule is
A. trigonal bipyramidal
B. square planar
C. tetrahedral
D. see-saw
Q. 25 For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100 g of water, the elevation in boiling point at 1 atm pressure is 2°C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take kᵦ = 0.76 K kg mol⁻¹)
A. 724
B. 740
C. 736
D. 718
Q. 26 The compound that undergoes’decarboxylation most readily under mild condition is
A. A
B. B
C. C
D. D
Q. 27 Using the data provided, calculate the multiple bond energy (kJ mol⁻¹) of a C ≡ C bond in C₂H₂. That energy is (take the bond energy of a C-H bond as 350 kJ mol⁻¹)
2C (s) + H₂(g)——–> C₂H₂(g) ΔH= 225 kJ mol⁻¹
2C (s)——–> 2C (g) ΔH= 1410 kJ mol⁻¹
H₂(g)——–>2H(g) ΔH = 330 kJ mol⁻¹
A. 1165
B. 837
C. 865
D. 815
Q. 28 The major product H of the given reaction sequence is
A. A
B. B
C. C
D. D
Questions: 29 – 30
Bleaching powder and bleach solution are produced on a large scale and used in several house¬hold products. The effectiveness of bleach solution is often measured by iodometry.
Q. 29 Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is
A. Cl₂O
B. Cl₂O₇
C. ClO₂
D. Cl₂O₆
Q. 30 25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N Na₂S₂O₃ was used to reach the endpoint. The molarity of the household bleach solution is
A. 0.48M
B. 0.96M
C. 0.25M
D. 0.024M
Questions: 31 – 32
The electrochemical cell shown below is a concentration cell. M ∣ M²⁺ (saturated solution of a sparingly soluble salt, MX₂) ∥ M²⁺ (0.001 mol dm⁻³) ∣ M. The emf of the cell depends on the difference in concentrations of M²⁺ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.
Q. 31 The solubility product (Kₛₚ; mol³ dm⁻⁹) of MX₂; at 298 K based on the information available for the given concentration cell is (take 2.303 x R x 298/F = 0.059V)
A. 1 x 10¹⁵
B. 4 x 10⁻¹⁵
C. 1 x 10
D. 4 x 10⁻¹²
Q. 32 The value of ΔG (kJ mol⁻¹) for the given cell is (take 1F = 96500 C mot⁻¹)
A. -5.7
B. 5.7
C. 11.4
D. -11.4
Questions: 33 – 34
In the following reaction sequence, the compound J is an intermediate. J (C₉H₈O₂) gives effervescence on treatment with NaHCO₃ and a positive Baeyer’s test.
Q. 33 The compound I is
A. A
B. B
C. C
D. D
Q. 34 The compound K in figure 1 is
A. A
B. B
C. C
D. D
Q. 35 The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?
A. T₁ = T₂
B. T₃ > T₁
C. (w)isothermal > (w)adiabatic
D. (ΔU)isothermal > (ΔU)adiabatic
Q. 36 The given graphs / data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice(s) about I, II, III and IV is (are) correct?
A. I is physisorption and II is chemisorption
B. I is physisorption and III is chemisorption
C. IV is chemisorption and II is chemisorption
D. IV is chemisorption and III is chemisorption
Q. 37 For the given aqueous reactions, which of the statement(s) is (are) true ?
A. The first reaction is a reoox reaction.
B. White precipitate is Zn₃[Fe(CN)₆]₂
C. Addition of filtrate to starch solution gives blue cofoui
D. White precipitate is soluble in NaOH solution.
Q. 38 With respect to graphite and diamond, which of the statement(s) given below is (are) correct ?
A. Graphite is harder than diamond.
B. Graphite has higher electrical conductivity than diamond.
C. Graphite has higher thermal conductivity than diamond.
D. Graphite has higher C-C bond order than diamond.
Q. 39 With reference to the scheme given, which of the given statment(s) , bout T, U, V and W is (are) correct ?
A. T is soluble in hot aqueous NaOH
B. U is optically active
C. Molecular formula of W is C₁₀H₁₈O₄
D. V gives effervescence on treatment with aqueous NaHCO₃
Q. 40 Which of the given statement(s) about N, O, P and Q with respect to M is (are) correct ?
A. M and N are non-mirror image stereoisomers
B. M and O are identical
C. M and P are enantiomers
D. M and Q are identical
Q. 41 The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x y + z = 3 and at a distance 2/√3 from the point (3, 1,-1) is
A. 5x— 11y + z = 17
B. √2x+y=3√2-1
C. x+y+z=√3
D. x-√2y=1-√2
Q. 42 Let PQR be a triangle of area Δ with a= 2, b =7/2 and c = 5/2 , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then (2 sin P – sin 2P)/(2 sin P+sin 2P) equals
A. 3/4Δ
B. 45/4Δ
C. (3/4Δ)²
D. (45/4Δ)²
Q. 43 If a̅ and b̅ are vectors such that |a̅ + b̅| =√29 and âx(2î + 3ĵ + 4k̂)=(2î+3ĵ+4k̂) x b̅, then a possible value of (a̅ + b̅).(-7î + 2ĵ + 3k̂) is
A. 0
B. 3
C. 4
D. 8
Q. 44 If P is a 3 x 3 matrix such that Pᵀ =2P + I, where Pᵀ is the transpose of P and I is the 3 x 3 identity matrix, then there exists a column matrix
A. A
B. B
C. C
D. D
Q. 45 Choose the correct option:
A. -5/2 and 1
B. -1/2 and -1
C. -7/2 and 2
D. -9/2 and 3
Q. 46 Four fair dice D₁, D₂, D₃ and D₄, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D₁, D₂ and D₃ is
A. 91/216
B. 108/216
C. 125/216
D. 127/216
Q. 47 The value of the integral is :
A. 0
B. Π²/2-4
C. Π²/2+4
D. Π²/2
Q. 48 Let a₁, a₂, a₃, … be in harmonic progression with a₁= 5 and a₂₀= 25. The least positive integer n for which aₙ < 0 is
A. 22
B. 23
C. 24
D. 25
Questions: 49 – 50
Let aₙ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let bₙ= the number of such n-digit integers ending with digit 1 and cₙ=the number of such n-digit integers ending with digit 0.
Q. 49 The value of b₆ is
A. 7
B. 8
C. 9
D. 11
Q. 50 Which of the following is correct?
A. a₁₇ =a₁₆ + a₁₅
B. c₁₇ = c₁₆ + c₁₅
C. b₁₇ = b₁₆ + c₁₆
D. a₁₇ =c₁₇ +b₁₆
Q. 51 Choose the correct option based on the figure .
Which of the following is true?
A. g is increasing on (1, ∞)
B. g is decreasing on (1, ∞)
C. g is increasing on (1, 2) and decreasing on (2,∞)
D. g is decreasing on (1, 2) and increasing on (2, ∞)
Q. 52 Choose the correct option based on the figure .
Consider the statements :
P : There exists some X E IR such that f(x)+2x= 2(1 +x²)
Q : There exists some x E IR such that 2f(x)+ 1= 2x(1 + x)
Then
A. both P and Q are true
B. P is true and Q is false
C. P is false and Q is true
D. both P and Q are false
Questions: 53 – 54
A tangent PT is drawn to the circle x² + y² = 4 at the point P (√3,1). A straight line L, perpendicular to PT is a tangent to the circle (x-3)² + y² = 1.
Q. 53 A possible equation of L is
A. x-√3y=1
B. x+√3y=1
C. x-√3y=-1
D. x+√3y=5
Q. 54 A common tangent of the two circles is
A. x=4
B. y=2
C. x+√3y=4
D. x+2√2y=6
Q. 55 For every integer n, let aₙ and bₙ be real numbers. Let function f: IR —> IR be given by f(x) = aₙ+sinπx, for x∈[2n,2n+1] = bₙ+cosπx, for x∈[2n-1,2n], for all integers of n. If f is continuous, then which of the following hold(s) for all n?
A. aₙ₋₁ – bₙ₋₁ =0
B. aₙ -bₙ =1
C. aₙ – bₙ₊₁=1
D. aₙ₋₁ – bₙ=-1
Q. 56 choose the correct one:
A. f has a local maximum at x = 2
B. f is decreasing on (2, 3)
C. there exists some c∈(0,α) such that f″(c)=0
D. f has a local minimum at x=3
Q. 57 If the straight lines x-1/2=y+1/k=z/2 and x+1/5=y+1/2=z/k are coplanar, then the plane(s) containing these two lines is(are)
A. y+2z=-1
B. y+z=-1
C. y-z=-1
D. y-2z=-1
Q. 58 X and Y be two events such that P(X∣Y)=1/2, P(Y∣X)=1/3 and P(X∩Y)=1/6.Which of the following is (are) correct?
A. P(X∪Y)=2/3
B. X and Y are independent
C. X and Y are not independent
D. P(xᶜ∩Y)=1/3
Q. 59 Choose the correct option:
A. -2
B. -1
C. 1
D. 2
Q. 60 Choose the correct option:
A. 1-√(3/2)
B. 1+√(3/2)
C. 1-√(2/3)
D. 1+√(2/3)
| Answer Sheet |
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| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | B | D | A | C | D | CD | B | A | C | B |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | C | D | A | D | AC | AC | ABC | D | BD | AB |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | C | B | ABCD | D | A | B | D | A | A | C |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | B | D | A | C | ACD | AC | ACD | BD | ACD | ABC |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | A | C | C | D | B | A | B | D | B | A |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | B | C | A | D | BD | ABCD | BC | AB | AD | ABCD |