JEE Advanced 2011 Paper 2
Q. 1 Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
A. II, III in haematite and III in magnetite
B. II, III in haematite and II in magnetite
C. II in haematite and II, III in magnetite
D. III in haematite and II, III in magnetite
Q. 2 Among the following complexes (K-P), K₃[Fe(CN)₆] (K), [Co(NH₃)₆]Cl₃ (L), Na₃[Co(oxalate)₃] (M), [Ni(H₂O)₆]Cl₂ (N), K₂[Pt(CN)₄] (O) and [Zn(H₂O)₆](NO₃)₂ (P) the diamagnetic complexes are
A. K, L, M, N
B. K, M, O, P
C. L, M, O, P
D. L, M, N, O
Q. 3 Passing H₂S gas into a mixture of Mn²⁺, Ni²⁺, Cu²⁺ and Hg²⁺ ions in an acidified aqueous solution precipitates
A. CuS and HgS
B. MnS and CuS
C. MnS and NiS
D. NiS and HgS
Q. 4 Consider the following cell reaction:
2Feᵣ + O2ᵤ +4H⁺ᵥₓ → 2Fe²ᵥₓ + 2H₂O(l) E° = 1.67 V
At [Fe²⁺] = 10⁻³ M, P(O₂) = 0.1 atm and pH = 3, the cell potential at 25°C is
A. 1.47 V
B. 1.77 V
C. 1.87 V
D. 1.57 V
Q. 5 The freezing point (in °C) of a solution containing 0.1g of K₃[Fe(CN)₆] (Mol. Wt. 329) in 100g of water (Kᵣ = 1.86 K kg mol⁻¹) is
A. -2.3 x 10⁻²
B. -5.7 x 10⁻²
C. -5.7 x 10⁻²
D. -1.2 x 10⁻²
Q. 6 Amongst the compounds given in figure (A), (B), (C), (D), the one that would form a brilliant colored dye on treatment with NaNO₂ in dil. HCl followed by addition to an alkaline solution of β-naphthol is
.
A. (A)
B. (B)
C. (C)
D. (D)
Q. 7 The major product of the reaction shown in figure is
A. a hemiacetal
B. an acetal
C. an ether
D. an ester
Q. 8 The carbohydrate shown in figure is:
A. a ketohexose
B. an aldohexose
C. an α – furanose
D. an α – pyranose
Q. 9 Reduction of the metal centre in aqueous permanganate ion involves
A. 3 electrons in neutral medium
B. 5 electrons in neutral medium
C. 3 electrons in alkaline medium
D. 5 electrons in acidic medium
Q. 10 The equilibrium 2Cuᶦ⇔ Cuᵒ + Cuᶦᶦ in aqueous medium at 25 °C shifts towards the left in the presence of
A. NO₃⁻
B. Cl⁻
C. SCN⁻
D. CN⁻
Q. 11 For the first order reaction:
2 N₂O₅(g) → 4NO₂(g) + O₂(g)
A. the concentration of the reactant decreases exponentially with time.
B. the half-life of the reaction decreases with increasing temperature.
C. the half-life of the reaction depends on the initial concentration of the reactant.
D. the reactant proceeds to 99.6% completion in eight half-life duration.
Q. 12 The correct functional group X and the reagent / reaction conditions Y in the following scheme given in figure (1) are
A. X = COOCH₃, Y = H₂ / Ni /heat
B. X = CONH₂, Y = H₂ / Ni / heat
C. X = CONH₂, Y = Br₂ / NaOH
D. X = CN, Y = H₂ / Ni / heat
Q. 13 Among the following, the number of compounds that can react with PCl₅ to give POCl₃ is O₂, CO₂, SO₂, H₂O, H₂SO₄, P₄O₁₀.
Q. 14 The volume (in mL) of 0.1 M AgNO₃ required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of [Cr(H₂O)₅Cl]Cl₂, as silver chloride is close to
Q. 15 In 1 L saturated solution of AgCl [Ksp (AgCl) = 1.6 x 10⁻¹⁰], 0.1 mol of CuCl [Ksp (CuCl) = 1.0 x 10⁻⁶] is added. The resultant concentration of Ag⁺ in the solution is 1.6 x 10⁻ⁿ. The value of “n” is:
Q. 16 The number of hexagonal faces that are present in a truncated octahedron is
Q. 17 The maximum number of isomers (including stereoisomers) that are possible on
monochlorination of the compound shown in figure (1), is
Q. 18 The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the carbocation given in figure (1) is
Q. 19 Match the transformations in Column I with appropriate options in Column II given in figure (1):
| Column I | Column II | ||
| (A) | CO2(s) CO2(g) | (p) | Phase transition |
| (B) | CaCO3(s) CaO(s) +CO2(g) | (r) | H is positive |
| (C) | 2 H. H2 (g) | (s) | S is positive |
| (D) | P(white, solid) P(red, soild) | (t) | S is negative |
A. A – p,s ; B – p,q ; C – q ; D – p,t
B. A – p,r,s ; B – r,s ; C – t ; D – p,q,t
C. A – p,r ; B – r ; C – p ; D – p,q
D. A – r,s ; B – p,q ; C – t ; D – q,t
Q. 20 Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II given in figure (1):
A. A – r,s,t ; B – p,s ; C – r,s ; D -q,r
B. A – s,t ; B – p,s ; C – p,t ; D – q,r
C. A – p,t ; B – r,s ; C – p,s ; D – q,r
D. A – r,s ; B – p,q ; C – r,s ; D – p,r
Q. 21 A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted which is given in (1). The correct sketch among (A), (B), (C), (D) is
A. (A)
B. (B)
C. (C)
D. (D)
Q. 22 A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is:
A. 1/2mV²
B. mV²
C. 3/2mV²
D. 2mV²
Q. 23 A long insulated copper wire is closely wound as a spiral of ‘N’ turns. (Given in figure (1)). The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the X-Y plane and a steady current ‘I’ flows through the wire. The Z – component of the magnetic field at the center of the spiral is
A. μ0N I /2(b – a) ln (b/a)
B. μ0N I /2(b – a) ln (b+a/b-a)
C. μ0N I /2b ln (b/a)
D. μ0N I /2b ln (b+a/b-a)
Q. 24 A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t) A sinωt and x2(t) = A sin(ωt + 2π/3). Adding a third sinusoidal displacement x3(t) = B sin(ωt + ø) brings the mass to a complete rest. The values of B and ø are
A. √2A, 3π/4
B. A, 4π/3
C. √3A, 5π/6
D. A, π/3
Q. 25 Which of the field patterns (A), (B), (C), (D) is valid for electric field as well as for magnetic field?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 26 A ball of mass 0.2kg rests on a vertical post of height 5m(Given in figure (1)). A bullet of mass 0.1 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is
A. 250 m/s
B. 250√2 m/s
C. 400 m/s
D. 500 m/s
Q. 27 The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
A. 0.9%
B. 2.4%
C. 3.1%
D. 4.2%
Q. 28 A wooden block shown in figure (1) performs SHM on a frictionless surface with frequency, v₀. The block carries a charge +Q on its surface. If now a uniform electric field is switched on as shown in figure (1), then the SHM of the block will be
A. of the same frequency and with shifted mean position.
B. of the same frequency and with the same mean position.
C. of changed frequency and with shifted mean position.
D. of changed frequency and with the same mean position.
Q. 29 Two solid spheres A and B of equal volumes shown in figure but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density of density dF. They get arranged into an equilibrium state as shown in the figure (1) with a tension in the string. The arrangement is possible only if
A. dA < dF
B. dB > dF
C. dA > dF
D. dA + dB = 2 dF
Q. 30 A series R-C circuit is connected to AC voltage source. Consider two cases; (A) and C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?
A. (A)
B. (B)
C. (C)
D. (D)
Q. 31 Which of the following statement(s) is/are correct?
A. If the electric field due to a point charge varies as r⁻²⁵ instead of r⁻², then the Gauss
law will still be valid.
B. The Gauss law can be used to calculate the field distribution around an electric dipole.
C. If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
D. The work done by the external force in moving a unit positive charge from a point A at potential VA to point B at potential VB is (VB – VA).
Q. 32 A thin ring of mass 2 kg and radius 0.5 m shown in figure (1) is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
A. the ring has pure rotation about its stationary CM.
B. the ring comes to a complete stop.
C. friction between the ring and the ground is to the left.
D. there is no friction between the ring and the ground
Q. 33 A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by 1.15m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s², is
Q. 34 A block of mass 0.18 kg shown in figure is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is rest and the spring is unstretched. An impulse is given to the block as shown in figure (1). The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is
Q. 35 Two batteries of different emfs and different internal resistances are connected as shown in figure (1). The voltage across AB in volts is
Q. 36 Water (with refractive index = 4/3) in a tank shown in figure is 18cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is
Q. 37 A series R-C combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If the impedance of the R-C circuit is R√1.25, the time constant (in millisecond) of the circuit is
Q. 38 A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A x 10ⁿ (where 1 < A < 10). The value of ‘n’ is
Q. 39 One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram given in figure (1). Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I. (Given in figure (2)).
A. A – p, r ,t ; B – p,r ; C – q,s ; D – r,t
B. A – p,q,r ; B – p,t ; C – q,t ; D – q,t
C. A – p ; B – r,t ; C – p,t ; D – p,q
D. A – q,r ; B – p,s ; C – p,s ; D – p,t
Q. 40 Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ₁. Match each system with statements given in Column II describing the nature and wavelength of the standing waves. (Given in figure (1)).
A. A – p,t ; B – p,s ; C – q,s ; D – q,r
B. A – p,r ; B – s,t ; C – q,r ; D – p,s
C. A – q,r ; B – p,t ; C – p,q ; D – s,t
D. A – p,t ; B – p,q ; C – q,s ; D – q,r
Q. 41 Let P(6, 3) be a point on the hyperbola x² / a³ – y² / b² = 1. If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is
A. √5/2
B. √3/2
C. √2
D. √3
Q. 42 A value of b for which the equations
x² + bx – 1 = 0
x² + x + b = 0
have one root in common is
A. -√2
B. -i√3
C. i√5
D. √2
Q. 43 Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form given in figure where each of a, b, and c is either ω or ω². Then the number of distinct matrices in the set S is
A. 2
B. 6
C. 4
D. 8
Q. 44 The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point
A. (-3/2, 0)
B. (-5/2, 2)
C. (-3/2, 5/2)
D. (-4, 0)
Q. 45 Find the value of θ in the equation given in figure .
A. ±π/4
B. ±π/3
C. ±π/6
D. ±π/2
Q. 46 Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1-x) for all x ∈ [-1, 2]. The value of R₁ is given in the figure (1) and R² be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then
A. R₁ = 2R₂
B. R₁ = 3R₂
C. 2R₁ = R₂
D. 3R₁ = R₂
Q. 47 Let f(x) = x² and g(x) = sinx for all x ∈ R. Then the set of all x satisfying (f ∘ g ∘ g ∘ f)(x) = (g ∘ g ∘ f)(x), where (f ∘ g)(x) = f(g(x)), is
A. ±√nπ, n ∈ {0, 1, 2, ……….}
B. ±√nπ, n ∈ {1, 2, …………}
C. π/2 + 2nπ, n ∈ {…………….., -2, -1, 0, 1, 2, ………}
D. 2nπ, n ∈ {…………….., -2, -1, 0, 1, 2, ………}
Q. 48 Let (x, y) be any point on the parabola y² = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1: 3. Then the locus of P is
A. x² = y
B. y² = 2x
C. y² = x
D. x² = 2y
Q. 49 If the value of f(x), given in the figure (1), then
A. f(x) is continuous at x = -π/2
B. f(x) is not differentiable at x = 0
C. f(x) is differentiable at x = 1
D. f(x) is differentiable at x = -3/2
Q. 50 Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then
A. P(E) = 4/5, P(F) = 3/5
B. P(E) = 1/5, P(F) = 2/5
C. P(E) = 2/5, P(F) = 1/5
D. P(E) = 3/5, P(F) = 4/5
Q. 51 Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is given by
A. y – x + 3 = 0
B. y + 3x – 33 = 0
C. y + x – 15 = 0
D. y – 2x + 12 = 0
Q. 52 Let f : (0, 1) → R be defined by f(x) = b – x / 1 – bx, where b is a constant such that 0 < b < 1. Then
A. f is not invertible on (0, 1)
B. f ≠ f⁻¹ on (0, 1) and f'(b) = 1/f'(0)
C. f = f⁻¹ on (0, 1) and f'(b) = 1 / f'(0)
D. f⁻¹ is differentiable on (0, 1)
Q. 53 Let ω = e^iπ/3, and a, b, c, x, y, z be non-zero complex number such that
a + b + c = x
a + bω + cω² = y
a + bω² + cω = z
Then the value of |x|² + |y|² + |z|² / |a|² + |b|² + |c|² is
Q. 54 The number of distinct real roots of x⁴ – 4x³ + 12x³ + x – 1 = 0 is
Q. 55 Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ∈ R, where f'(x) denotes df(x) / dx and g(x) is a given non-constant differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
Q. 56 Let M be a 3 x 3 matrix satisfying the information given in figure , then the sum of the diagonal entries of M is
Q. 57 Let a = -î – k̂, b = -î + ĵ and c = î + 2ĵ + 3k̂ be three given vectors. If r is a vector such that r x b = c x b and r . a = 0, then the value of r . b is
Q. 58 The straight line 2x – 3y = 1 divides the circular region x² + y² ≤ 6 into two parts. If S = {(2, 3/4), (5/2, 3/4), (1/4, 1/4), (1/8, 1/4)}, then the number of point(s) in S lying inside the smaller part is
Q. 59 Match the statements given in Column I with the values given in Column II. (Given in figure).
A. A – p ; B – p,q ; C – s ; D – q,r
B. A – q ; B – q,s ; C – p ; D – r,t
C. A -q ;B – p,q,r,s,t ; C -s ; D – t
D. A – p ; B – p,s ; C – q ; D – p,t
Q. 60 Match the statement given in column I with the intervals/union of intervals given in Column II (given in figure (1)).
A. A -p ; B – q ; C – r ; D – s
B. A – p,q ; B – r,s ; C – r ; D – s
C. A – s ; B – t ; C – p , D – r
D. A – s ; b – t ; C – r ; D – r
| Answer Sheet |
||||||||||
| Question | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Answer | D | C | A | D | A | C | B | B | ACD | BCD |
| Question | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Answer | ABD | CD | 4 | 6 | 7 | 8 | 8 | 6 | B | A |
| Question | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| Answer | C | B | A | B | C | D | C | A | ABD | BC |
| Question | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| Answer | CD | AC | 5 | 4 | 5 | 2 | 4 | 7 | A | A |
| Question | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Answer | B | B | A | D | D | C | A | C | ABCD | AD |
| Question | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| Answer | ABD | A | 3 | 2 | 0 | 9 | 9 | 2 | C | D |