Engineering Entrance Exam - Page 4 of 5

JEE Advanced 2011 Paper II Previous Year Paper

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

JEE Advanced 2011 Paper I Previous Year Paper

JEE Advanced 2011 Paper 1

Q. 1 Extra pure N₂ can be obtained by heating

A. A

B. B

C. C

D. D

Q. 2 Geometrical shapes of the complexes formed by the reaction of Ni₂+ with Cl- , CN- and H₂0, respectively, are

A. octahedral, tetrahedral and square planar

B. tetrahedral, square planar and octahedral

C. square planar, tetrahedral and octahedral

D. octahedral, square planar and octahedral

Q. 3 Bombardment of aluminum by α-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and 2 respectively are

A. proton, neutron, positron

B. neutron, positron, proton

C. proton, positron, neutron

D. positron, proton, neutron

Q. 4 Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is

A. 1.78 M

B. 2.00 M

C. 2.05 M

D. 2.22 M

Q. 5 AgNO₃ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (A) versus the volume of AgNO₃ is

A. (P)

B. (Q)

C. (R)

D. (S)

Q. 6 Among the following compounds, the most acidic is

A. p-nitrophenol

B. p-hydroxybenzoic acid

C. o-hydroxybenzoic acid

D. p-toluic acid

Q. 7 The major product of the following reaction is

A. A

B. B

C. C

D. D

Q. 8 Extraction of metal from the ore cassiterite involves

A. carbon reduction of an oxide ore

B. self-reduction of a sulphide ore

C. removal of copper impurity

D. removal of iron impurity

Q. 9 The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

A. Adsorption is always exothermic.

B. Physisorption may transform into chemisorption at high temperature.

C. Physisorption increases with increasing temperature but chemisorption decreases

with increasing temperature.

D. Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

Q. 10 According to kinetic theory of gases

A. collisions are always elastic.

B. heavier molecules transfer more momentum to the wall of the container.

C. only a small number of molecules have very high velocity.

D. between collisions, the molecules move in straight lines with constant velocities.

Q. 11 Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)

A. A

B. B

C. C

D. D

Questions: 12 – 14

When a metal rod M is dipped into an aqueous colourless concentrated solution of compound N, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate 0. Addition of aqueous NH₃ dissolves O and gives an intense blue solution

Q. 12 The metal rod M is

A. Fe

B. Cu

C. Ni

D. Co

Q. 13 The compound N is

A. AgNO₃

B. Zn(NO₃)₂

C. Al(NO₃)₂

D. Pb(NO₃)₂

Q. 14 The final solution contains

A. [Pb(NH₃)₄]₂- and [CoCl₄]₂⁻

B. [Al(NH₃)₄]₃+ and [Cu(NH₃)₄]₂⁺

C. [Ag(NH₃)₂]⁺ and [Cu(NH₃)₄]₂⁺

D. [Ag(NH₃)₂]⁺ and [Ni(NH₃)₆]₂⁺

Questions: 15 – 16

An acyclic hydrocarbon P, having molecular formula CsHm, gave acetone as the only organic product through the following sequence of reactions, in which Q is an intermediate organic compound.

Q. 15 Choose the correct option

A. A

B. B

C. C

D. D

Q. 16 Choose the correct option

A. A

B. B

C. C

D. D

Q. 17 The difference in the oxidation numbers of the two types of sulphur atoms in Na₂S₄O₆ is

Q. 18 Reaction of Br₂ with Na₂CO₃ in aqueous solution gives sodium bromide and sodium bromate with evolution of CO₂ gas. The number of sodium bromide molecules involved in the balanced chemical equation is

Q. 19 The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, ms = -1/2, is

Q. 20 The work function (Φ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is

Q. 21 To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0°C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0°C is close to

Q. 22 The total number of alkenes possible by dehydrobromination of 3-bromo-3-

cyclopentylhexane using alcoholic KOH is

Q. 23 A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysis products. The number of glycine units present in the decapeptide is

Q. 24 A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is

A. 8.50 kHz

B. 8.25 kHz

C. 7.75 kHz

D. 7.50 kHz

Q. 25 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T1, the work done in the process is

A. 9/8 RT1

B. 3/2 RT1

C. 15/8 RT1

D. 9/2 RT1

Q. 26 Consider an electric field E̅ = Eo x̂, where Eo is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A. 2Eo a²

B. √2Eo a²

C. Eo a²

D. Eo a²/√2

Q. 27 The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A. 1215 Å

B. 1640 Å

C. 2430 Å

D. 4687 Å

Q. 28 A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

A. 9

B. 18

C. 27

D. 36

Q. 29 A meter bridge is set-up as shown, to determine an unknown resistance ‘X’ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of ‘X’ is

A. 10.2 ohm

B. 10.6 ohm

C. 10.8 ohm

D. 11.1 ohm

Q. 30 A 2 μF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch 8 is turned to position 2 is

A. 0 %

B. 20 %

C. 75 %

D. 80 %

Q. 31 A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge ‘+Q’. Now they are connected by a thin metal wire. Then

A. A

B. B

C. C

D. D

Q. 32 An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A. They will never come out of the magnetic field region.

B. They will come out travelling along parallel paths.

C. They will come out at the same time.

D. They will come out at different times.

Q. 33 A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat ‘Q’ flows only from left to right through the blocks. Then in steady state

A. heat flow through A and E slabs are same.

B. heat flow through slab E is maximum.

C. temperature difference across slab E is smallest.

D. heat flow through C = heat flow through B + heat flow through D.

Q. 34 A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disk of mass ‘M’ and radius ‘R’ (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

A. Restoring torque in case A = Restoring torque in case B

B. Restoring torque in case A < Restoring torque in case B

C. Angular frequency for case A > Angular frequency for case B.

D. Angular frequency for case A < Angular frequency for case B.

Questions: 35 – 37

Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis. The phase space diagram is x(t) vs. p(t) curve in this plane. The arrow on the curve indicates the time flow. For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure. We use the sign convention in which position or momentum upwards (or to right) is positive and downwards (or to left) is negative.

Q. 35 Choose the correct option

A. A

B. B

C. C

D. D

Q. 36 Choose the correct option

A. A

B. B

C. C

D. D

Q. 37 Choose the correct option

A. A

B. B

C. C

D. D

Questions: 38 – 39

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ‘N’ be the number density of free electrons, each of mass ‘m’. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. if the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ‘ωp’, which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As ω approaches ωp, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Q. 38 Taking the electronic charge as ‘e’ and the permittivity as ‘εo’, use dimensional analysis to determine the correct expression for ωp.

A. √(Ne/mεo)

B. √(mεo/Ne)

C. √(Ne²/mεo)

D. √(mεo/Ne²)

Q. 39 Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N ≈ 4 x 10²⁷ m-³. Take ε0 ≈ 10⁻¹¹ and m ≈ 10⁻³⁰, where these quantities are in proper SI units.

A. 800 nm

B. 600 nm

C. 300 nm

D. 200 nm

Q. 40 A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s². The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is

Q. 41 A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is

Q. 42 Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a ’. The surface tension of the soap film is γ. The system of charges and planar film are in equilibrium, (value of a given in the figure, where ‘k’ is a constant. Then N is

Q. 43 Steel wire of length ‘L’ at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10⁻⁵/ °C, Young’s modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m’ in kg is nearly

Q. 44 The activity of a freshly prepared radioactive sample is 10¹⁰ disintegrations per second, whose mean life is 10⁹ s. The mass of an atom of this radioisotope is 10⁻²⁵ kg. The mass (in mg) of the radioactive sample is

Q. 45 A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = Io cos (300 t) where Io is constant. It the magnetic moment of the loop is N μo Io sin (300 t) , then ‘N’ is

Q. 46 Four solid spheres each of diameter √5 cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N x 10⁻⁴ kg-m² , then N is

Q. 47 Let (x₀, y₀) be the solution of the following equations. Then x₀ is

A. 1/6

B. 1/3

C. 1/2

D. 6

Q. 48 Choose the correct option.

A. A

B. B

C. C

D. D

Q. 49 Let a̅ = î + ĵ + k̂ , b̅ = î – ĵ + k̂ and c̅ = î – ĵ – k̂ be three vectors. A vector v̅ in the plane of a̅ and b̅ , whose projection on c̅ is 1/√3, is given by,

A. î – 3ĵ + 3k̂

B. -3î – 3ĵ – 3k̂

C. 3î – ĵ + 3k̂

D. î + 3ĵ – 3k̂

Q. 50 Let P = {θ: sinθ – cosθ = √2 cosθ} and Q= {θ: sinθ + cosθ = √2 cosθ} be two sets. Then

A. P ⊂ Q and Q – P ≠ ∅

B. Q ⊄ P

C. P ⊄ Q

D. P = Q

Q. 51 Let the straight line x = b divide the area enclosed by y = (1 – x)², y=0 , and x = 0 into two parts R₁ (0 ≤ x ≤ b) and R₂ (b ≤ x ≤ 1) such that R₁ – R₂= 1/4. Then b equals

A. 3/4

B. 1/2

C. 1/3

D. 1/4

Q. 52 Let α and β be the roots of x² – 6x – 2 = 0 with α > β. If an = αⁿ – βⁿ, for n ≥ 1 , then the value of expression in the image is

A. 1

B. 2

C. 3

D. 4

Q. 53 A straight line L through the point (3, -2) is inclined at an angle 60° to the line √3x + y = 1. If L also intersects the x-axis, then the equation of L is

A. y + √3x + 2 – 3√3 = 0

B. y – √3x + 2 + 3√3 = 0

C. √3y – x + 3 + 2√3 = 0

D. √3y + x – 3 + 2√3 = 0

Q. 54 The vector(s) which is/are coplanar with vectors î + ĵ + 2k̂ and î + 2ĵ + k̂ , and perpendicular to the vector î + ĵ + k̂ is/are

A. ĵ – k̂

B. -î + ĵ

C. î – ĵ

D. -ĵ + k̂

Q. 55 Let M and N be two 3×3 non-singular skew-symmetric matrices such that MN = NM. if Pᵗ denotes the transpose of P, then the value of the expression given in the image is?

A. M²

B. -N²

C. -M²

D. MN

Q. 56 Let the eccentricity of the hyperbola x²/a² – y²/b² = 1 be reciprocal to that of the ellipse x² + 4y² = 4.If the hyperbola passes through a focus of the ellipse, then

A. the equation of the hyperbola is x²/3 – y²/2 = 1

B. a focus of the hyperbola is (2, 0)

C. the eccentricity of the hyperbola is √5/3

D. the equation of the hyperbola is x² – 3y² = 3

Q. 57 Let f : ℝ → ℝ be a function such that f(x+y) = f(x) + f(y), Ɐx, y∈R If f (x) is differentiable at x = 0, then

A. (x) is differentiable only in a finite interval containing zero

B. f (x) is continuous Ɐx ∈ ℝ

C. f’(x) is constant Ɐx ∈ ℝ

D. f (x) is differentiable except at finitely many points

Questions: 58 – 60

Let a, b and c be three real numbers satisfying

Q. 58 If the point P(a, b, c), with reference to (E), lies on the plane 2x+ y+ z =1, then the value of 7a +b+c is

A. 0

B. 12

C. 7

D. 6

Q. 59 Choose the correct option:

A. -2

B. 2

C. 3

D. -3

Q. 60 Choose the correct option:

A. 6

B. 7

C. 6/7

D. ∞

Questions: 61 – 62

Let U₁ and U₂ be two urns such that U₁ contains 3 white and 2 red balls, and U₂ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U₁ and put into U₂. However, if tail appears then 2 balls are drawn at random from U₁ and put into U₂. Now 1 ball is drawn at random from U₂.

Q. 61 The probability of the drawn ball from U₂ being white is

A. 13/30

B. 23/30

C. 19/30

D. 11/30

Q. 62 Given that the drawn ball from U₂ is white, the probability that head appeared on the coin is

A. 17/23

B. 11/23

C. 15/23

D. 12/23

Q. 63 Consider the parabola y² = 8x. Let Δ₁ be the area of the triangle formed by the end points of its Latus rectum and the point P(1/2, 2) on the parabola, and Δ₂ be the area of the triangle formed by drawing tangents at P and at the end points of the Latus rectum. Then Δ₁/Δ₂ is

Q. 64 Answer the following question:

Q. 65 The positive integer value of n > 3 satisfying the equation is

Q. 66 Let f : [1,∞) -> [2,∞) be a differentiable function such that f(1) = 2. If the expression in figure is true for all x ≥ , then the value of f(2) is

Q. 67 If z is any complex number satisfying |z – 3 – 2i| ≤ 2, then the minimum value of |2z – 6 + 5i|

Q. 68 Answer the following question:

Q. 69 Answer the following:

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	D	B	A	C	D	C	A	ACD	ABD	ABCD
Question	11	12	13	14	15	16	17	18	19	20
Answer	BC	B	A	C	D	B	5	5	9	4
Question	21	22	23	24	25	26	27	28	29	30
Answer	7	5	6	A	A	C	A	D	B	D
Question	31	32	33	34	35	36	37	38	39	40
Answer	ABCD	BCD	ACD	AD	D	C	B	C	B	4
Question	41	42	43	44	45	46	47	48	49	50
Answer	5	3	3	1	6	9	C	A	C	D
Question	51	52	53	54	55	56	57	58	59	60
Answer	B	C	B	AD	ABCD	BD	BCD	D	A	B
Question	61	62	63	64	65	66	67	68	69
Answer	B	D	2	3 OR 9	7	6	5	8	1

JEE Advanced 2010 Paper II Previous Year Paper

JEE Advanced 2010 Paper 2

Q. 1 The complex showing a spin-only magnetic moment of 2.82 B.M is

A. A

B. B

C. C

D. D

Q. 2 The species having pyramidal shape is

A. A

B. B

C. C

D. D

Q. 3 Choose the correct option

A. A

B. B

C. C

D. D

Q. 4 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 5 The packing efficiency of the two-dimensional square unit cell shown below is

A. 39.27%

B. 68.02%

C. 74.05%

D. 78.54%

Q. 6 Assuming that Hund’s rule is violated. the bond order and magnetic nature of the diatomic molecule B₂ is

A. 1 and diamagnetic

B. 1 and paramagnetic

C. 0 and diamagnetic

D. 0 and paramagnetic

Q. 7 The total number of diprotic acids among the following is

Q. 8 Total number of geometrical isomers for the complex is

Q. 9 Among the following. the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn Tl, Na, Ti

Q. 10 Silver (atomic weight = 108 g/mol) has a density of 10.5 g cm-³. The number of silver atoms on a surface of area 10⁻¹² m² can be expressed in scientific notation as y x 10ˣ. The value of x is

Q. 11 One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is Wₛ and that along the dotted line path is W􀀁. then the integer closest to the ratio W􀀁/Wₛ is

Questions: 12 – 14

Two aliphatic aldehydes P and Q react in the presence of aqueous K₂CO₃ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below

Q. 12 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 13 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 14 Choose the correct option:

A. A

B. B

C. C

D. D

Questions: 15 – 17

The hydrogen-like species Li²⁺ is in a spherically symmetric state S₁ with one radial node. Upon absorbing light the ion undergoes transition to a state S₂. The state S₂ has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

Q. 15 The state S₁ is

A. 1s

B. 2s

C. 2p

D. 3s

Q. 16 Energy of the state S₁ in units of the hydrogen atom ground state energy is

A. 0.75

B. 1.50

C. 2.25

D. 4.50

Q. 17 The orbital angular momentum quantum number of the state S₂ is

A. 0

B. 1

C. 2

D. 3

Q. 18 Match the reactions in Column I with appropriate options in Column II.

A. A – r, s ; B – t ; C – p, q ; D – r

B. A – q, s ; B – t ; C – p, q ; D – r

C. A – p, q ; B – t ; C – q, s ; D – r

D. A – r, s ; B – r ; C – p, q ; D – t

Q. 19 All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

A. A – p, s ; B – p, q, r, t ; C – p, q ; D – p

B. A – p, s ; B – p, q, r, t ; C – p, q ; D – p, r

C. A – p, q ; B – p, q, r, t ; C – p, s ; D – p

D. A – p, r ; B – p, q, r, t ; C – p, q ; D – p, s

Q. 20 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 21 Let S = {1. 2. 3. 4}. The total number of unordered pairs of disjoint subsets of S is equal to

A. 25

B. 34

C. 42

D. 41

Q. 22 Choose the correct option:

A. 1

B. 1/3

C. 1/2

D. 1/e

Q. 23 If the distance of the point P(1, -2, 1) from the plane x + 2y – 22 = a. where a > 0, is 5, then the foot of the perpendicular from P to the plane is

A. (8/3, 4/3, -7/3)

B. (4/3, -4/3, 1/3)

C. (1/3, 2/3, 10/3)

D. (2/3, -1/3, 5/2)

Q. 24 Two adjacent sides of a parallelogram ABCD are given by

AB =2i + 10j + 11k and AD = -i + 2j + 2k

The side AD is rotated by an acute angle a in the plane of the parallelogram so that AD becomes AD’. If AD’ makes a right angle with the side AB. then the cosine of the angle a is given by

A. 8/9

B. √17/9

C. 1/9

D. 4√5/9

Q. 25 A signal which can be green or red with probability 4/5 and 1/5 respectively. is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is

A. 3/5

B. 6/7

C. 20/23

D. 9/20

Q. 26 Two parallel chords of a circle of radius 2 are at a distance √3 +1 apart. If the chords subtend at the center angles of π/k and 2π/k where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]

Q. 27 Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle. then r² is equal to

Q. 28 Answer the following:

Q. 29 Answer the following:

Q. 30 Answer the following:

Questions: 31 – 33

Consider the polynomial

f(x) = 1 + 2x + 3x² + 4x³

Let s be the sum of all distinct real roots of fix) and let t = |s|.

Q. 31 The real number s lies in the interval

A. (-1/4, 0)

B. (-11, -3/4)

C. (-3/4, -1/2)

D. (0, 1/4)

Q. 32 The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval

A. (3/4, 3)

B. (24/64, 11/16)

C. (9, 10)

D. (0, 21/64)

Q. 33 The function f ‘(x) is

A. increasing in (-t, -1/4) and decreasing in (-1/4, t)

B. decreasing in (-t, -1/4) and increasing in (-1/4, t)

C. increasing in (-t, t)

D. decreasing in (-t, t)

Questions: 34 – 36

Tangents are drawn from the point P(3, 4) to the ellipse x²/9 + y²/4 = 1 touching the ellipse at points A and B.

Q. 34 The coordinates of A and B are

A. (3, 0) and (0, 2)

B. (-8/5, 2√161/15) and (-9/5, 8/5)

C. (-8/5, 2√161/15) and (0, 2)

D. (3, 0) and (-9/5, 8/5)

Q. 35 The orthocenter of the triangle PAB is

A. (5, 8/7)

B. (7/5, 25/8)

C. (11/5, 8/5)

D. (8/25, 7/5)

Q. 36 The equation of the locus of the point whose distances from the point P and the line AB are equal is

A. 9x² + y² – 6xy – 54x – 62y + 241 = 0

B. x² + 9y² + 6xy – 54x + 62y – 241 = 0

C. 9x² + 9y² – 6xy – 54x – 62y – 241 = 0

D. x² + y² – 2xy + 27x + 31y – 120 = 0

Q. 37 Match the statements in Column-I with those in Column-II.

[Note: Here z takes values in the complex plane and Im z and Re z denote respectively, the imaginary part and the real part of z.]

A. A – p, r; B – q ; C – p, s, t ; D – q, r, s, t

B. A – p, r, s, t ; B – p ; C – p, s, t ; D – q, r

C. A – q, r; B – p ; C – p, s, t ; D – q, r, s, t

D. A – q, r ; B – p ; C – s, t ; D – r, s, t

Q. 38 Match the statements in Column-I with those in Column-II.

A. A – t ; B – p, r ; C – q, s ; D – r

B. A – t ; B – q, s ; C – p, r ; D – r

C. A – r ; B – p, r ; C – q, s ; D – t

D. A – r ; B – q, s ; C – p, r ; D – t

Q. 39 A Vernier caliper has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers. the least count is

A. 0.02 mm

B. 0.05 mm

C. 0.1 mm

D. 0.2 mm

Q. 40 A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the Wire is 50 N and the speed of sound is 320 m/s. the mass of the string is

A. 5 grams

B. 10 grams

C. 20 grams

D. 40 grams

Q. 41 A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

A. virtual and at a distance of 16 cm from the mirror

B. real and at a distance of 16 cm from the mirror

C. Virtual and at a distance of 20 cm from the mirror

D. real and at a distance of 20 cm from the mirror

Q. 42 A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

A. 4.50 J

B. 7.50 J

C. 5.06 J

D. 14.06 J

Q. 43 A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81π/7 x 10⁵ V/m. When the field is switched off, the drop is observed to fall with terminal velocity 2 x 10⁻³ m/s. Given g = 9.8 m/s²,. viscosity of the air = 1.8 x 10⁻⁵ Ns m-² and the density of oil = 900 kg/m³, the magnitude of q is

A. 1.6 x 10⁻¹⁹ C

B. 3.2 x 10⁻¹⁹ C

C. 4.8 x 10⁻¹⁹ C

D. 8.0 x 10⁻¹⁹ C

Q. 44 A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells held together by pressing them with force F (see figure). F is proportional to

A. A

B. B

C. C

D. D

Q. 45 A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. In the initial temperature of the gas is Tᵢ (in Kelvin) and the final temperature is aTᵢ. the value of a is

Q. 46 At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?

[Take ln 5 = 1.6, ln 3 = 1.1]

Q. 47 Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 25/3 m to 50/7 m in 30 seconds. What is the speed of the object in km per hour ?

Q. 48 A large glass slab (μ = 5/ 3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?

Q. 49 To determine the half life of a radioactive element. a student plots a graph of ln|dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is Years

Questions: 50 – 52

When liquid medicine of density ρ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the chopper is pressed. a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

Q. 50 If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r <

A. 2πrT

B. 2πRT

C. 2πr²T/R

D. 2πR²T/r

Q. 51 If r = 5 x 10^(-4) ρ =10 kg/m³. g=10 m/s², T=0.11N/m, the radius of the drop when it detaches from the dropper is approximately

A. 1.4 x 10-³ m

B. 3.3 x 10-³ m

C. 2.0 x 10-³ m

D. 4.1 x 10-³ m

Q. 52 After the drop detaches. its surface energy is

A. 1.4 x 10⁻⁶ J

B. 2.7 x 10⁻⁶ J

C. 5.4 x 10⁻⁶ J

D. 8.1 x 10⁻⁶ J

Questions: 53 – 55

The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.

Q. 53 A diatomic molecule has moment of inertia I. By Bohr’s quantization condition its rotational energy in the nth level (n = 0 is not allowed) is

A. 1/n² x (h²/(8π²I))

B. 1/n x (h²/(8π²I))

C. n x (h²/(8π²I))

D. n² x (h²/(8π²I))

Q. 54 It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 4/π x 10¹¹ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take h = 2 x 10³⁴ J s)

A. 2.76 x 10⁻⁴⁶ kg m²

B. 1.87 x 10⁻⁴⁶ kg m²

C. 4.67 x 10⁻⁴⁷ kg m²

D. 1.17 x 10⁻⁴⁷ kg m²

Q. 55 In a CO molecule. the distance between C (mass = 12 a.m.u.) and 0 (mass = 16 a.m.u.) where 1 a.m.u = (5/3) x 10⁻²⁷ is close to

A. 2.4 x 10⁻¹⁰ m

B. 1.9 x 10⁻¹⁰ m

C. 1.3 x 10⁻¹⁰ m

D. 4.4 x 10⁻¹¹ m

Q. 56 Two transparent media of refractive indices μ₁ and μ₃ have a solid lens shaped transparent material of refractive index μ₂ between them as shown in figures in Column II. A traversing these media is also shown in the figures. In Column I different relationship between μ₁, μ₂ and μ₃ are given. Match them to the ray diagrams shown in Column

A. A – p, r ; B – q, s, t ; C – p, r, t ; D – q, s

B. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r

C. A – p, r ; B – p, r, t ; C – q, s, t ; D – q, s

D. A – q, s ; B – q, s, t ; C – p, r, t ; D – p, r

Q. 57 You are given many resistances. capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V₁ and V₂. (indicated in circuits) are related as shown in column I. Match the two

A. A – r, s, t ; B – q, r, s, t ; C – p, q; D – q, r, s, t

B. A – r, t ; B – r, s, t ; C – p, q; D – q, r, s, t

C. A – s, t ; B – q, r, s, t ; C – p, q; D – q, r, s

D. A – r, s, t ; B – q, r ; C – p, q; D – q, r

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	D	C	C	D	A	6	3	2	7
Question	11	12	13	14	15	16	17	18	19	20
Answer	2	B	A	D	B	C	B	A	A	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	D	B	A	B	C	3	3	1	0	4
Question	31	32	33	34	35	36	37	38	39	40
Answer	C	A	B	D	C	A	C	A	D	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	B	C	D	A	4	2	3	6	8	C
Question	51	52	53	54	55	56	57
Answer	A	B	D	B	C	A	A

JEE Advanced 2010 Paper I Previous Year Paper

JEE Advanced 2010 Paper 1

Q. 1 The correct structure of ethylenediaminetetraacetic acid (EDTA) among the structures (A), (B), (C), (D) is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 2 The ionization isomer of [Cr(H₂O)₄Cl(NO₂)]Cl is

A. [Cr(H₂O)₄(O₂N)]Cl₂

B. [Cr(H₂O)₄Cl₂](NO₂)

C. [Cr(H₂O)₄Cl(ONO)]Cl

D. [Cr(H2O)4Cl2(NO2)] . H2O

Q. 3 The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

A. BrCH₂CH₂CH₂CH₂CH₃ and CH₃CH₃C ≡ CH

B. BrCH₂CH₂CH₃ and CH₃CH₂CH₂C ≡ CH

C. BrCH₂CH₂CH₂CH₂CH₃ and CH₃C ≡ CH

D. BrCH₂CH₂CH₂CH₃ and CH₃CH₂C ≡ CH

Q. 4 The correct statement about the disaccharide shown in figure (1) is

A. Ring (a) is pyranose with α – glycosidic link

B. Ring (a) is furanose with α – glycosidic link

C. Ring (b) is furanose with α – glycosidic link

D. Ring (b) is pyranose with β- glycosidic link

Q. 5 In the reaction given in figure (1) , the products among (A), (B), (C), (D) are

A. (A)

B. (B)

C. (C)

D. (D)

Q. 6 Plots showing the variation of the rate constant (k) with temperature (T) are given in (A), (B), (C), (D). The plot that follows Arrhenius equation is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 7 The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

A. Br₂ (g)

B. Cl₂ (g)

C. H₂O (g)

D. CH₄ (g)

Q. 8 The bond energy (in kcal mol⁻¹) of a C-C single bond is approximately

A. 1

B. 10

C. 100

D. 1000

Q. 9 The reagent(s) used for softening the temporary hardness of water is(are)

A. Ca₃(PO₄)₂

B. Ca(OH)₂

C. Na₂CO₃

D. NaOCl

Q. 10 In the reaction given in figure (1), the intermediate(s) among (A), (B), (C), (D) is(are)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 11 In the Newman projection for 2, 2-dimethybutane given in figure (1), X and Y can respectively be

A. H and H

B. H and C₂H₅

C. C₂H₅ and H

D. CH₃ and CH₃

Q. 12 Among the following, the intensive property is (properties are)

A. molar conductivity

B. electromotive force

C. resistance

D. heat capacity

Q. 13 Aqueous solutions of HNO₃, KOH, CH₃COOH, and CH₃COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)

A. HNO₃ and CH₃COOH

B. KOH and CH₃COONa

C. HNO₃ and CH₃COONa

D. CH₃COOH and CH₃COONa

Questions: 14 – 16

Copper is the most noble of the first row transition metals and occur in small deposits in several countries. Ores of copper include chalcanthite (CuSO₄ . 5H₂O), atacamite (Cu₂Cl(OH)₃), Cuprite (Cu₂O), copper glance (Cu₂S) and malachite (Cu₂(OH)₂CO₃). However, 80% of the world copper production comes from the ore chalcopyrite (CuFeS₂). The extraction of copper from chalcopyrite involves partial roasting, removal of iron and self-reduction.

Q. 14 Partial roasting of chalcopyrite produces

A. Cu₂S and FeO

B. Cu₂O and FeO

C. CuS and Fe₂O₃

D. Cu₂O and Fe₂O3₃

Q. 15 Iron is removed from chalcopyrite is

A. FeO

B. FeS

C. Fe₂O₃

D. FeSiO₃

Q. 16 In self-reduction, the reducing species is

A. S

B. O²⁻

C. S²⁻

D. SO₂

Questions: 17 – 18

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in higher processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:

M(s) | M⁺(aq; 0.05 molar) || M⁺(aq; 1 molar) | M(s) For the above electrolytic cell the magnitude of the cell potential |E Cell| = 70 mV

Q. 17 For the above cell

A. E cell < 0; ΔG > 0

B. E cell > 0; ΔG < 0

C. E cell < 0; ΔG⁰ > 0

D. E cell > 0; ΔG⁰ < 0

Q. 18 If the 0.05 molar solution of M⁺ is replaced by a 0.0025 molar M⁺ solution, then the magnitude of the cell potential would be

A. 35 mV

B. 70 mV

C. 140 mV

D. 700 mV

Q. 19 The total number of basic groups in the following form of lysine given in figure is

Q. 20 The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C₄H₆ is

Q. 21 In the figure given , the total number of intramolecular aldol condensation products formed from ‘Y’ is

Q. 22 Amongst the following compounds given in figure (1), the total number of compounds soluble in aqueous NaOH is

Q. 23 Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is

KCN, K₂SO₄, (NH₄)2C₂O₄, NaCl, Zn(NO₃)₂, FeCl₃, K₂CO₃, NH₄NO₃, LiCN

Q. 24 Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF₅ is

Q. 25 The value of n in the molecular formula BenAl₂Si₆O₁₈ is

Q. 26 A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL and 25.0 mL. The number of significant figures in the average titre value is

Q. 27 The concentration of R in the reaction R → P was measured as a function of time and the following data is obtained given in figure . The order of the reaction is

Q. 28 The number of neutrons emitted when ²³⁵₉₂U undergoes controlled nuclear fission to ¹⁴²₅₄Xe and ⁹⁰₃₈Sr is

Q. 29 If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression a/c sin2C + c/a sin 2A is

A. 1/2

B. √3/2

C. 1

D. √3

Q. 30 Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is

A. x + 2y – 2z = 0

B. 3x + 2y – 2z = 0

C. x – 2y + z = 0

D. 5x + 2y – 4z = 0

Q. 31 Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that ωʳ₁ + ωʳ₂ + ωʳ₃ = 0 is

A. 1/18

B. 1/9

C. 2/9

D. 1/36

Q. 32 Let P, Q, R and S be the points on the plane with position vectors -2î – ĵ, 4î, 3î + 3ĵ and -3î + 2ĵ respectively. The quadrilateral PQRS must be a

A. parallelogram, which is neither a rhombus nor a rectangle

B. square

C. rectangle, but not a square

D. rhombus, but not a square

Q. 33 The number of 3 x 3 matrices A (given in figure ), whose entries are either 0 and 1 and for which the system A has exactly two distinct solutions, is

A. 0

B. 2⁹ – 1

C. 168

D. 2

Q. 34 Find the value of the equation given in figure (1).

A. 0

B. 1/12

C. 1/24

D. 1/64

Q. 35 Let p and q be real numbers such that p ≠ 0, p³ ≠ q and p³ ≠ -q. If α and β are nonzero complex numbers satisfying α + β = -p and α³ + β³ = q, then a quadratic equation having α/β and β/α as its roots is

A. (p³ + q)x² – (p³ + 2q)x + (p³ + q) = 0

B. (p³ + q)x² – (p³ – 2q)x + (p³ + q) = 0

C. (p³ – q)x² – (5p³ – 2q)x + (p³ – q) = 0

D. (p³ – q)x² – (5p³ + 2q)x + (p³ – q) = 0

Q. 36 Let f, g and h be real – valued functions defined on the interval [0, 1] by f(x) = e^x^2 + e^-x^2, g(x) = xe^x^2 + e^-x^2 and h(x) = x^2e^-x^2 + e^-x^2. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then

A. a = b and c ≠ b

B. a = c and a ≠ b

C. a ≠ b and c ≠ b

D. a = b = c

Q. 37 Let A and B be two distinct points on the parabola y² = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

A. -1/r

B. 1/r

C. 2/r

D. -2/r

Q. 38 Let ABC be a triangle such that ∠ACB = π/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x² + x + 1, b = x² – 1 and c = 2x + 1 is (are)

A. -(2 + √3)

B. 1 + √3

C. 2 + √3

D. 4√3

Q. 39 Let z₁ and z₂ be two distinct complex numbers and let z = (1 – t)z₁ + tz₂ for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then which is the correct option among (A), (B), (C), (D)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 40 Let f be a real-valued function defined on the interval (0, ∞) by f(x) given in figure (1). Then which of the following statement(s) is (are) true?

A. f”(x) exists for all x ∈ (0, ∞)

B. f'(x) exists for all x ∈ (0, ∞) and f’ is continuous on (0, ∞), but not differentiable on (0, ∞)

C. there exists α > 1 such that |f'(x)| < |f(x)| for all x ∈ (0, ∞)

D. there exists β > 1 such that |f(x)| + |f'(x)| ≤ β for all x ∈ (0, ∞)

Q. 41 Find the value(s) of the equation given in figure (1):

A. 22/7 – π

B. 2/105

C. 0

D. 71/15 – 3π/2

Questions: 42 – 44

Let p be an odd prime number and Tp be the following set of 2 x 2 matrices (given in figure (1):

Q. 42 The number of A in Tp such that A is either symmetric or skew – symmetric or both, and det (A) divisible by p is

A. (p – 1)²

B. 2 (p – 1)

C. (p-1)² + 1

D. 2p – 1

Q. 43 The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is

[NOTE: The trace of a matrix is the sum of its diagonal entries.]

A. (p – 1)(p² – p + 1)

B. p³ – (p – 1)²

C. (p – 1)²

D. (p – 1)(p² – 2)

Q. 44 The number of A in Tp such that det (A) is not divisible by p is

A. 2p³

B. p³ – 5p

C. p³ – 3p

D. p³ – p²

Questions: 45 – 46

The circle x² + y² – 8x = 0 and hyperbola x²/⁹ – y²/⁴ = 1 intersect at the points A and B.

Q. 45 Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

A. 2x – √5y – 20 = 0

B. 2x – √5y + 4 = 0

C. 3x – 4y + 8 = 0

D. 4x – 3y + 4 = 0

Q. 46 Equation of the circle with AB as its diameter is

A. x² + y² – 12x + 24 = 0

B. x² + y² + 12x + 24 = 0

C. x² + y² + 24x – 12 = 0

D. x² + y² – 12x – 24 = 0

Q. 47 The number of values of θ in the interval (-π/2, π/2) such that θ ≠ nπ/5 for n = 0, ±1, ±2 and tanθ = cot5θ as well as sin 2θ = cos 4θ is

Q. 48 The maximum value of the expression 1 / (sin²θ + 3sinθcosθ + 5cos²θ) is

Q. 49 If a⃗ and b⃗ are vectors in space given by a⃗ = î – 2ĵ/√5 and b⃗ = 2î + ĵ + 3k̂/√14, then the value of (2a⃗ + b⃗) . [(a⃗ x b⃗) x (a⃗ – 2b⃗)] is

Q. 50 The line 2x + y = 1 is tangent to the hyperbola x²/a² – y²/b² = 1. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

Q. 51 If the distance between the plane Ax – 2y + z = d and the plane containing the lines x-1/2 = y- 2/3 = z-3/4 and x-2/3 = y-3/4 = z-4/5 is √6, then |d| is

Q. 52 For any real number x, let |x| denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x – [x], if [x] is odd, 1 + [x] – x, if [x] is even. Then the value of the equation given in figure (1)

Q. 53 Let ω be the complex number cos 2π/3 + i sin 2π/3. Then the number of distinct complex numbers z satisfying the determinant given in figure (1), is equal to

Q. 54 Let Sk, k = 1, 2, …….., 100, denote the sum of the infinite geometric series whose first term is k-1/k! and the common ratio is 1/k. Then find the value of the equation given in figure (1)

Q. 55 The number of all possible values of θ, where 0 < θ < π, for which the system of equations (y + z) cos 3θ = (xyz) sin 3θ

x sin 3θ = 2 cos 3θ/y + 2 sin 3θ/z

(xyz) sin 3θ = (y + 2z) cos 3θ + y sin 3θ

have a solution (xo, yo, zo) with yo zo ≠ 0, is

Q. 56 Let f be a real – valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to

Q. 57 Consider a thin square sheet of side L and thickness t, made of a material of resistivity ρ. The resistance between two opposite faces, shown by the shaded areas in the figure (1) is

A. directly proportional to L

B. directly proportional to t

C. independent of L

D. independent of t

Q. 58 A real gas behaves like an ideal gas if its

A. pressure and temperature are both high

B. pressure and temperature are both low

C. pressure is high and temperature is low

D. pressure is low and temperature is high

Q. 59 Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100W, 60W and 40W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀, respectively, the relation between these resistances is

A. 1/R₁₀₀ = 1/R₄₀ + 1/R₆₀

B. R₁₀₀ = R₄₀ = R₆₀

C. R₁₀₀ > R₆₀ > R₄₀

D. 1/R₁₀₀ > 1/R₆₀ > 1/R₄₀

Q. 60 To verify Ohm’s law, a student is provided with a test resistor RT, a high resistance R₁, a small resistance R₂, two identical galvanometers G₁ and G₂, and a variable voltage source V. The correct circuit to carry out the experiment among figure (A), (B), (C), (D) is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 61 An AC voltage source of variable angular frequency ω and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased

A. the bulb glows dimmer

B. the bulb glows brighter

C. total impedance of the circuit is unchanged

D. total impedance of the circuit increases

Q. 62 A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of circle. The tension in the wire is

A. IBL

B. IBL/π

C. IBL/2π

D. IBL/4π

Q. 63 A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg(sinθ – μ cosθ) to P₂ = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

A. (A)

B. (B)

C. (C)

D. (D)

Q. 64 A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

A. 2GM/7R (4√2 – 5)

B. -2GM/7R (4√2 – 5)

C. GM/4R

D. 2GM/5R (√2-1)

Q. 65 A few electric field lines for a system of two charges Q₁ and Q₂ fixed at two different points on the x-axis are shown in the figure . These lines suggest

A. |Q₁| > |Q₂|

B. |Q₁| < |Q₂|

C. at a finite distance to the left of Q1 the electric field is zero

D. at a finite distance to the right of Q2 the electric field is zero

Q. 66 A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stopwatch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

A. Error Δt in measuring T, the time period, is 0.05 seconds

B. Error ΔT in measuring T, the time period , is 1 second

C. Percentage error in the determination of g is 5%

D. Percentage error in the determination of g is 2.5%

Q. 67 A point mass of 1 kg collides elastically with a stationary point mass of 5kg. After their collision, the 1 kg mass reverse its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are) correct for the system of theses two masses?

A. Total momentum of the system is 3 kg ms⁻¹

B. Momentum of 5 kg mass after collision is 4 kg ms⁻¹

C. Kinetic energy of the centre of mass is 0.75 J

D. Total kinetic energy of the system is 4J

Q. 68 A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure (1)). If the refractive index of the material of the prism is √3, which of the following is (are) correct?

A. The ray gets totally internally reflected at face CD

B. The ray comes out through face AD

C. The angle between the incident ray and the emergent ray is 90°

D. The angle between the incident ray and the emergent ray is 120°

Q. 69 One mole of an ideal gas in initial stage A undergoes a cyclic process ABCD, as shown in the figure (1). Its pressure at A is P₀. Choose the correct option(s) from the following

A. Internal energies at A and B are the same

B. \Work done by the gas in process AB is P₀V₀ ln 4

C. Pressure at C is P₀/4

D. Temperature at C is T₀/4

Questions: 70 – 72

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx², it performs simple harmonic motion. The corresponding time period is proportional to √m/k, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to Vo for |x| ≥ X₀. (See figure (1)).

Q. 70 If the total energy of the particle is E, it will perform periodic motion only if

A. E < 0

B. E > 0

C. V₀ > E > 0

D. E > V₀

Q. 71 For periodic motion of small amplitude A, the time period T of this particle is proportional to

A. A√m/α

B. 1/A√m/α

C. A√α/m

D. 1/A√α/m

Q. 72 The acceleration of this particle for |x| > X₀ is

A. proportional to V₀

B. proportional to V₀/mX₀

C. proportional to √V₀/mX₀

D. Zero

Questions: 73 – 74

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc(0) if they are placed in a magnetic field, i.e., the critical temperature Tc(B) is a function of the magnetic field strength B. The dependence of Tc(B) on B is shown in the figure (1).

Q. 73 In the graphs (A), (B), (C), (D), the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B₂ (dashed line). If B2 is larger than B₁, which of the following graphs shows the correct variation of R with T in these fields?

A. (A)

B. (B)

C. (C)

D. (D)

Q. 74 A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when

A. B = 5 Tesla, Tc (B) = 80 K

B. B = 5 Tesla, 75 K < Tc (B) < 100 K

C. B = 10 Tesla, 75 K < Tc (B) < 100 K

D. B = 10 Tesla, Tc (B) = 70 K

Q. 75 The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m₂₅ to m₅₀. The ratio m₂₅/m₅₀ is

Q. 76 An α-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are λα and λp respectively. The ratio λα/λp, to the nearest integer, is

Q. 77 When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂. If J₁ = 2.25 J₂ then the value of R in Ω is

Q. 78 Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperature T₁ and T₂, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B?

Q. 79 When two progressive waves y₁ = 4sin(2x – 6t) and y₂ = 3sin(2x – 6t – π/2) are superimposed, the amplitude of the resultant wave is

Q. 80 A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 x 10⁻⁷ m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young’s modulus of the material of the wire is n x 10⁹ Nm⁻², the value of n is

Q. 81 A binary star consists of two stars A (mass 2.2Ms) and B (mass 11Ms), where Ms is the mass of the sun. They are separated by the distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

Q. 82 Gravitational acceleration on the surface of a planet is √6/11 g, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is ⅔ times that of the earth. If the escape speed on the surface of the earth is taken to be 11kms⁻¹, the escape speed on the surface of the planet in kms⁻¹ will be

Q. 83 A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = 3.36 x 10⁵ J kg⁻¹) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

Q. 84 A stationary source is emitting sound at a fixed frequency fo, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of fo. What is the difference in the speeds of the cars (in km per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is ms⁻¹

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	C	B	D	A	D	A	B	C	B	AC
Question	11	12	13	14	15	16	17	18	19	20
Answer	BD	AB	CD	A	D	C	B	C	2	5
Question	21	22	23	24	25	26	27	28	29	30
Answer	1	4	3	0 OR 8	3	3	0	4	D	C
Question	31	32	33	34	35	36	37	38	39	40
Answer	C	A	A	B	B	D	CD	B	ACD	BC
Question	41	42	43	44	45	46	47	48	49	50
Answer	A	D	C	D	B	A	3	2	5	2
Question	51	52	53	54	55	56	57	58	59	60
Answer	6	4	1	3	3	9	C	D	D	C
Question	61	62	63	64	65	66	67	68	69	70
Answer	B	C	A	A	AD	AC	AC	ABC	ABCD	C
Question	71	72	73	74	75	76	77	78	79	80
Answer	B	D	A	B	6	3	4	9	5	4
Question	81	82	83	84
Answer	6	3	8	7

JEE Advanced 2009 Paper II Previous Year Paper

JEE Advanced 2009 Paper 2

Q. 1 For a first order reaction A→P, the temperature (T) dependent rate constant(k) was found to follow the equation logk = – (2000) 1/T + 6.0. The pre-exponential factor A and the activation energy Ea,respectively, are –

A. 1.0 × 10^6 s^(–1) and 9.2 kJ mol^(–1)

B. 6.0 s^(–1) and 16.6 kJ mol^(–1)

C. 1.0 × 10^6 s^(–1) and 16.6 kJ mol^(–1)

D. 1.0 × 10^6 s^(–1) and 38.3 kJ mol^(–1)

Q. 2 The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)6 is –

A. 0

B. 2.84

C. 4.90

D. 5.92

Q. 3 In the following carbocation, H/CH3 that is most likely to migrate to the positively charged carbon is –

A. CH3 at C-4

B. H at C-4

C. CH3 at C-2

D. H at C-2

Q. 4 The correct stability order of the following resonance structures is –

A. (I) > (II) > (IV) > (III)

B. (I) > (III) > (II) > (IV)

C. (II) > (I) > (III) > (IV)

D. (III) > (I) > (IV) > (II)

Q. 5 For the reduction of NO3- ion in an aqueous solution, E° is + 0.96V. Values of E° for some metal ions are given in the figure –

The pair(s) of metals that is (are) oxidized by NO3- in aqueous solution is (are)

A. V and Hg

B. Hg and Fe

C. Fe and Au

D. Fe and V

Q. 6 Among the following, the state function(s) is (are)-

A. Internal energy

B. Irreversible expansion work

C. Reversible expansion work

D. Molar enthalpy

Q. 7 In the reaction,

2X + B₂H₆ → [BH₂(X)₂]⁺ [BH₄]⁻ the amine(s) X is (are)-

A. NH3

B. CH3NH2

C. (CH3)2NH

D. (CH3)3N

Q. 8 The nitrogen oxide(s) that contain(s) N-N bond(s) is (are) –

A. N2O

B. N2O3

C. N2O4

D. N2O5

Q. 9 The correct statement(s) about the following sugars X and Y is (are) –

A. X is a reducing sugar and Y is a non-reducing sugar

B. X is a non-raducing sugar and Y is a reducing sugar

C. The glucosidic linkages in X and Y are α and β, respectively

D. The glucosidic linkages in X and Y are β and α, respectively

Q. 10 Match the statements/expressions given in Column I with the values given in Column II

Column I	Column II
(A)	Cu + dil HNO3	(p)	NO
(B)	Cu + cone HNO3	(q)	NO2
(C)	Zn + dil HNO3	(r)	N2O
(D)	Zn + cone HNO3	(s)	Cu(NO3)2
(t)	Zn(NO3)2

A. A – p, q ; B – p, q, r ; D – r

B. A – p, q, t; B – q; C – s; D – s

C. A – p, s; B – q; C – t; D – r, s, t

D. A – p, s; B – q, s; C – r, t; D – q, t

Q. 11 Match the statements/expressions given in Column I with the values given in Column II

A. A – p, q, r ; A – s, t ; C – p, t ; D – r, s

B. A – p, s; B – q; C – t; D – r, s, t

C. A – p, q, t; B – p, s, t; C – r, s; D – p

D. A – p, q, t; B – q; C – s; D – s

Questions: 12 – 19

This section contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :

Q. 12 In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that the heat capacity of the calorimeter is 2.5 kJ K^(–1), the numerical value for the enthalpy of combustion of the gas in kJ mol^(–1) is

Q. 13 At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is –

Q. 14 The dissociation constant of a substituted benzoic acid at 25ºC is 1.0 × 10^(–4). The pH of a 0.01M solution of its sodium salt is –

Q. 15 The total number of α and β particles emitted in the nuclear reaction given in figure 2 is-

Q. 16 The oxidation number of Mn in the product of alkaline oxidative fusion of MnO2 is –

Q. 17 The number of water molecule(s) directly bonded to the metal centre in CuSO4. 5H2O is –

Q. 18 The coordination number of Al in the crystalline state of AlCl3 is –

Q. 19 The total number of cyclic structural as well as stereo isomers possible for a compound with the molecular formula C5H10 is

Q. 20 If the sum of first n terms of an A.P. is cn², then the sum of squares of these n terms is :

A. (A)

B. (B)

C. (C)

D. (D)

Q. 21 A line with positive direction cosines passes through the point P(2, –1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals :

A. 1

B. √2

C. √3

D. 2

Q. 22 The normal at a point P on the ellipse x² + 4y² = 16 meets the x- axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points :

A. (±(3√5)/2 , ±2/7)

B. (±(3√5)/2 , ±√19/4)

C. (±2√3 , ±1/7)

D. (±2√3 , ±(4√3)/7)

Q. 23 The locus of the orthocentre of the triangle formed by the lines

(1 + p)x – py + p(1 + p) = 0

(1 + q)x – qy + q (1 + q) = 0,

and y = 0, where p ≠ q, is :

A. a hyperbola

B. a parabola

C. an ellipse

D. a straight line

Q. 24 Choose the correct option:

A. (A)

B. (B)

C. (C)

D. (D)

Q. 25 An ellipse intersects the hyperbola 2x² – 2y² = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then :

A. Equation of ellipse is x² + 2y² = 2

B. The foci of ellipse are (± 1, 0)

C. Equation of ellipse is x² + 2y² = 4

D. The foci of ellipse are (±√2, 0)

Q. 26 For the function f(x) = x cos(1/x), x ≥ 1,

A. for at least one x in the interval [1, ∞), f(x + 2) – f(x) < 2

B. lim x→∞ f ‘(x) = 1

C. for all x in the interval [1, ∞), f(x + 2) – f(x) > 2

D. f ‘(x) is strictly decreasing in the interval [1, ∞)

Q. 27 The tangent PT and the normal PN to the parabola y² = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose :

A. vertex is (2a/3, 0)

B. directrix is x = 0

C. latus rectum is (2a/3)

D. focus is (a, 0)

Q. 28 For 0 < θ < π/2 the solution (s) of given figure is (are) :

A. π/4

B. π/6

C. π/12

D. 5π/12

Q. 29 Match the statements/expressions given in Column I with the values given in Column II

A. A – p, q, r ; A – s, t ; C – p, t ; D – r, s

B. A – q, s ; B – p, r, s, t ; C – t ; D – r

C. A – p, q ; B – p, q, r ; D – r

D. A – q, s ; B – p, r, s, t ; C – s , t ; D – r, t

Q. 30 Match the statements/expressions given in Column I with the values given in Column II

A. A – p, q ; B – p, q, r ; D – r

B. A – q, s ; B – p, r, s, t ; C – s , t ; D – r, t

C. A – p, q, r ; B – s, t ; C – p, t ; D – r, s

D. A – p; B – q, s; C – q, r, s, t; D – r

Questions: 31 – 38

Q. 31 The maximum value of the function f(x) = 2x^3 – 15x^2 + 36x – 48 on the set A = {x|x^2 + 20 ≤ 9x} is :

Q. 32 Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations :

3x – y – z – 0

– 3x + z = 0

– 3x + 2y + z = 0.

Then the number of such points for which x^2 + y^2 + z^2 ≤ 100 is :

Q. 33 Let ABC and ABC’ be two non-congruent triangles with sides AB = 4, AC = AC’ = 2√2 and angle B = 30º. The absolute value of the difference between the areas of these triangles is :

Q. 34 Let p(x) be a polynomial of degree 4 having extremum at x = 1,2 and lim x→0(1+(p(x)/x²)) = 2. Then the value of p(2) is :

Q. 35 Let f: R → R be a continuous function which satisfies the given function in figure 2. Then the value of f(ln 5) is :

Q. 36 The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is :

Q. 37 The smallest value of k, for which both the roots of the equation x^2 –8kx + 16 (k^2 – k + 1) = 0 are real, distinct and have values at least 4, is :

Q. 38 If the function f(x) = x³ + e^(x/2) and g(x) = f⁻¹(x), then the value of g'(1) is :

Q. 39 The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is –

A. k₁A/k₂

B. k₂A/k₁

C. k₁A/(k₁ + k₂)

D. k₂A/(k₁ + k₂)

Q. 40 A piece of wire is bent in the shape of a parabola y = kx^2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is –

A. a/gk

B. a/2gk

C. 2a/gk

D. a/4gk

Q. 41 Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions φp = 2.0 eV, φq = 2.5 eV and φr = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is :

[Take hc = 1240 eV nm]

A. (A)

B. (B)

C. (C)

D. (D)

Q. 42 A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle θ in one direction and released. The frequency of oscillation is –

A. 1/2π √(2k/M)

B. 1/2π √(k/M)

C. 1/2π √(6k/M)

D. 1/2π √(24k/M)

Q. 43 Two metallic rings A and B, identical in shape and size but having different resistivities ρA and ρB, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights hA and hB, respectively, with hA > hB. The possible relation(s) between their resistivities and their masses mA and mB is (are) –

A. ρA > ρB and mA = mB

B. ρA < ρB and mA = mB

C. ρA > ρB and mA > mB

D. ρA < ρB and mA < mB

Q. 44 A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then –

A. the intensity of the sound heard at the first resonance was more than that at the second resonance

B. the prongs of the tuning fork were kept in a horizontal plane above the resonance tube

C. the amplitude of vibration of the ends of the prongs is typically around 1 cm

D. the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air

Q. 45 The figure shows the P–V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then –

A. the process during the path A → B is isothermal

B. heat flows out of the gas during the path B → C → D

C. work done during the path A → B → C is zero

D. positive work is done by the gas in the cycle ABCDA

Q. 46 Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an elliptical orbital. Find out the correct statement(s).

A. The angular momentum of the charge – q is constant

B. The linear momentum of the charge –q is constant

C. The angular velocity of the charge –q is constant

D. The linear speed of the charge –q is constant

Q. 47 A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then –

A. V̅C – V̅A = 2(V̅B – V̅C)

B. V̅C – V̅B = V̅B – V̅A

C. |V̅C – V̅A| = 2 |V̅B – V̅C|

D. |V̅C – V̅A| = 4 |V̅B|

Q. 48 Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the

appropriate process(es) from Column II.

A. A – p, q, t; B – q; C – s; D – s

B. A – p, q, r ; A – s, t ; C – p, t ; D – r, s

C. A – q, s ; B – p, r, s, t ; C – s , t ; D – r, t

D. A – p, q ; B – p, q, r ; D – r

Q. 49 Column I shows four situations of standard Young’s double slit arrangement with the screen placed far away from the slits S1 and S2. In each of these cases S1P0 = S2P0, S1P1 – S2P1 = λ/4 and S1P2 – S2P2 = λ/3, where λ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index μ and thickness t is pasted on slit S2. The thicknesses of the sheets are different in different cases. The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by δ(P) and the intensity by I(P). Match each situation given in Column I with the statement(s) in Column II valid for that situation.

A. A – p, s; B – q; C – t; D – r, s, t

B. A – p, q, t; B – q; C – s; D – s

C. A – p, s; B – q, t; C – t; D – r

D. A – p, q ; B – p, q, r ; D – r

Questions: 50 – 57

Q. 50 A metal rod AB of length 10x has its one end A in ice at 0°C and the other end B in water at 100°C. If a point P on the rod is maintained at 400°, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of λx from the ice end A, find the value of λ.

[Neglect any heat loss to the surrounding.]

Q. 51 A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice.

[Take atmospheric pressure = 1.0 × 10^5 N/m^2, density of water = 1000 kg/m^3 and g = 10 m/s^2. Neglect any effect of surface tension.]

Q. 52 Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m^2 . The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio nB/nA where nA and nB are the number of moles of air in bubbles A and B, respectively. [Neglect the effect of gravity.]

Q. 53 Three objects A, B and C are kept in a straight line on a frictionless horizontal surface as shown in figure 2. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

Q. 54 A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k(μ0I/48πx), find the value of k.

Q. 55 A light inextensible string that goes over a smooth fixed pulley as shown in the figure 3 connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s^2 , find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

Q. 56 A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = κr^a , where κ and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times that at r = R, find the value of a.

Q. 57 A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	D	A	D	B	ABD	AD	ABC	ABC	BC	D
Question	11	12	13	14	15	16	17	18	19	20
Answer	C	9	4	8	8	6	4	6	7	C
Question	21	22	23	24	25	26	27	28	29	30
Answer	C	C	D	ABC	AB	BCD	AD	CD	B	D
Question	31	32	33	34	35	36	37	38	39	40
Answer	7	7	4	0	0	8	2	2	D	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	A	C	BD	AD	BD	A	BC	A	A	9
Question	51	52	53	54	55	56	57
Answer	6	6	4	7	8	2	5

JEE Advanced 2009 Paper I Previous Year Paper

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