JEE Advanced - Page 4 of 4 - Vidhyarthi Darpan

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

JEE Advanced 2008 Paper II Previous Year Paper

JEE Advanced 2008 Paper 2

Q. 1 A particle P starts from the point z₀ = 1 + 2i, where i = √-1 It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves √2 units in the direction of the vector î + ĵ and then it moves through an angle π/2 in anticlockwise direction on a circle with centre at origin, to reach a point z₂. The point z₂ is given by

A. 6 + 7i

B. − 7 + 6i

C. 7 + 6i

D. − 6 + 7i

Q. 2 Let the function g: (−∞, ∞) → (-π/2, π/2) be given by g(n) = 2tan⁻¹ (eⁿ) − π/2 . Then, g is

A. even and is strictly increasing in (0, ∞)

B. odd and is strictly decreasing in (−∞, ∞)

C. odd and is strictly increasing in (−∞, ∞)

D. neither even nor odd, but is strictly increasing in (−∞, ∞)

Q. 3 Consider a branch of the hyperbola x² − 2y² − 2√2x – 4√2y – 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is

A. 1 – √(2/3)

B. √(3/2) – 1

C. 1 + √(2/3)

D. √(3/2) + 1

Q. 4 The area of the region between the curves y = √((1 + sinx)/cosx) and y = √((1 – sinx)/cosx) bounded by the lines x = 0 and x = π/4 is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 5 Consider three points P = (−sin(β − α), − cosβ), Q = (cos(β − α), sinβ) and R = (cos(β − α + θ), sin(β − θ)), where 0 < α, β, θ < π/4. Then

A. P lies on the line segment RQ

B. Q lies on the line segment PR

C. R lies on the line segment QP

D. P, Q, R are non-collinear

Q. 6 An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is

A. 2, 4 or 8

B. 3, 6 or 9

C. 4 or 8

D. 5 or 10

Q. 7 Let two non-collinear unit vectors â and b̂ form an acute angle. A point P moves so that at any time t the position vector O̅P̅ (where O is the origin) is given by âcos t + b̂sin t. When P is farthest from origin O, let M be the length of O̅P̅ and û be the unit vector along O̅P̅. Then,

A. û = (â + b̂)/|â + b̂| and M = (1 + â.b̂̂ )^½

B. û = (â – b̂)/|â – b̂| and M = (1 + â.b̂̂ )^½

C. û = (â + b̂)/|â + b̂| and M = (1 + 2â.b̂̂ )^½

D. û = (â – b̂)/|â – b̂| and M = (1 + 2â.b̂̂ )^½

Q. 8 Let I = ∫(e^x)/(e^(4x) + e^(2x) +1)dx, J = ∫(e^(-x))/(e^(-4x) + e^(-2x) +1)dx. Then, for an arbitrary constant C, the value of J − I equals

A. 1/2 log((e^(4x) – e^(2x) +1)/(e^(4x) + e^(2x) +1)) + C

B. 1/2 log((e^(2x) + e^(x) +1)/(e^(2x) – e^(x) +1)) + C

C. 1/2 log((e^(2x) – e^(x) +1)/(e^(2x) + e^(x) +1)) + C

D. 1/2 log((e^(4x) + e^(2x) +1)/(e^(4x) – e^(2x) +1)) + C

Q. 9 Let g(x) = log(f(x)) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3, …,

g′′ (N + (1/2)) – g′′ (1/2) =

A. -4{1 + 1/9 + 1/25 + ….. + 1/((2N – 1)²)}

B. 4{1 + 1/9 + 1/25 + ….. + 1/((2N – 1)²)}

C. -4{1 + 1/9 + 1/25 + ….. + 1/((2N + 1)²)}

D. 4{1 + 1/9 + 1/25 + ….. + 1/((2N + 1)²)}

Q. 10 Suppose four distinct positive numbers a₁, a₂, a₃, a₄ are in G.P. Let b₁ = a₁, b₂ = b₁ + a₂, b₃ = b₂ + a₃ and b₄ = b₃ + a₄.

STATEMENT−1 : The numbers b₁, b₂, b₃, b₄ are neither in A.P. nor in G.P.

And STATEMENT−2 : The numbers b₁, b₂, b₃, b₄ are in H.P.

A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1

B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.

C. STATEMENT−1 is True, STATEMENT−2 is False

D. STATEMENT−1 is False, STATEMENT−2 is True

Q. 11 Let a, b, c, p, q be real numbers. Suppose α, β are the roots of the equation x² + 2px + q = 0 and α, 1/β are the roots of the equation ax² + 2bx + c = 0, where β² ∉{−1, 0, 1}. STATEMENT−1 : (p² − q) (b² − ac) ≥ 0

And

STATEMENT−2 : b ≠ pa or c ≠ qa

A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1

B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.

C. STATEMENT−1 is True, STATEMENT−2 is False

D. STATEMENT−1 is False, STATEMENT−2 is True

Q. 12 Consider

L1 : 2x + 3y + p − 3 = 0

L2 : 2x + 3y + p + 3 = 0,

where p is a real number, and C : x² + y² + 6x − 10y + 30 = 0.

STATEMENT – 1 : If line L₁ is a chord of circle C, then line L₂ is not always a diameter of circle C.

and

STATEMENT – 2 : If line L₁ is a diameter of circle C, then line L₂ is not a chord of circle C.

A. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is a correct explanation for STATEMENT – 1

B. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is NOT a correct explanation for STATEMENT – 1.

C. STATEMENT – 1 is True, STATEMENT – 2 is False

D. STATEMENT – 1 is False, STATEMENT – 2 is True

Q. 13 Let a solution y = y(x) of the differential equation x√(x² – 1) dy – y√(y² – 1) dx = 0 satisfy y(2) = 2/√3

STATEMENT−1 : y(x) = sec(sec⁻¹x – π/6)

And

STATEMENT−2 : y(x) is given by 1/y = 2√3/x – √(1 – (1/x²))

A. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is a correct explanation for STATEMENT−1

B. STATEMENT−1 is True, STATEMENT−2 is True; STATEMENT−2 is NOT a correct explanation for STATEMENT−1.

C. STATEMENT−1 is True, STATEMENT−2 is False

D. STATEMENT−1 is False, STATEMENT−2 is True

Q. 14 Which of the following is true?

A. (2 + a)² f′′(1) + (2 − a)² f′′(−1) = 0

B. (2 – a)² f′′(1) – (2 + a)² f′′(−1) = 0

C. f′(1) f′(−1) = (2 − a)²

D. f′(1) f′(−1) = -(2 + a)²

Q. 15 Which of the following is true?

A. f(x) is decreasing on (−1, 1) and has a local minimum at x = 1

B. f(x) is increasing on (−1, 1) and has a local maximum at x = 1

C. f(x) is increasing on (−1, 1) but has neither a local maximum nor a local minimum at x = 1

D. f(x) is decreasing on (−1, 1) but has neither a local maximum nor a local minimum at x = 1

Q. 16 which of the following is true?

A. g′(x) is positive on (−∞, 0) and negative on (0, ∞)

B. g′(x) is negative on (−∞, 0) and positive on (0, ∞)

C. g′(x) changes sign on both (−∞, 0) and (0, ∞)

D. g′(x) does not change sign on (−∞, ∞)

Questions: 17 – 19

Consider the line

L1 : (x+1)/3 = (y+2)/1 = (z+1)/2

L2 : (x-2)/1 = (y+2)/2 = (z-3)/3

Q. 17 The unit vector perpendicular to both L1 and L2 is

A. (-î + 7ĵ + 7k̂)/√99

B. (-î – 7ĵ + 5k̂)/5√3

C. (-î + 7ĵ + 5k̂)/5√3

D. (7î – 7ĵ – k̂)/√99

Q. 18 The shortest distance between L₁ and L₂ is

A. 0

B. 17/√3

C. 41/5√3

D. 17/5√3

Q. 19 The distance of the point (1, 1, 1) from the plane passing through the point (−1, −2, −1) and whose normal is perpendicular to both the lines L₁ and L₂ is

A. 2/√75

B. 7/√75

C. 13/√75

D. 23/√75

Q. 20 Consider the lines given by

L1 : x + 3y − 5 = 0

L2 : 3x − ky − 1 = 0

L3 : 5x + 2y − 12 = 0

Match the Statements / Expressions in Column I with the Statements / Expressions in

Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4

matrix given in the ORS.

A. A – s; B – p,q; C – r; D – p, q, s

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

C. A – s; B – p,q, r; D – p, q, s

D. A – s; B – p; C – r; D – p, q

Q. 21 Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.

A. A – s; B – p,q; C – r; D – p, q, s

B. A – s; B – p; C – r; D – p, q

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

D. A – s; B – p,q, r; D – p, q, s

Q. 22 Consider all possible permutations of the letters of the word ENDEANOEL.

Match the Statements / Expressions in Column I with the Statements / Expressions in

Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4

matrix given in the ORS.

A. A – s; B – p,q, r; D – p, q, s

B. A – s; B – p; C – r; D – p, q

C. A – s; B – p,q; C – r; D – p, q, s

D. A – p; B – s; C – q; D -q

Q. 23 Consider a system of three charges q/3, q/3 and -2q/3 placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60°

A. The electric field at point O is q/(8πε0(R²)) directed along the negative x-axis

B. The potential energy of the system is zero

C. The magnitude of the force between the charges at C and B is (q²)/(54πε0(R²))

D. The potential at point O is q/(12πε0R)

Q. 24 A radioactive sample S₁ having an activity 5μCi has twice the number of nuclei as another sample S₂ which has an activity of 10 μCi. The half lives of S₁ and S₂ can be

A. 20 years and 5 years, respectively

B. 20 years and 10 years, respectively

C. 10 years each

D. 5 years each

Q. 25 A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap –shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

A. √(3)π/50 ĵ m/s

B. -√(3)π/50 ĵ m/s

C. √(3)π/50 î m/s

D. -√(3)π/50 î m/s

Q. 26 A block (B) is attached to two unstretched springs S₁ and S₂ with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M₁ and M₂ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is

A. 4

B. 2

C. 1/2

D. 1/4

Q. 27 A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisfie

A. θ = π/4

B. π/4 < θ < π/2

C. π/2 < θ < 3π/4

D. 3π/4 < θ < π

Q. 28 A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

A. air from end 1 flows towards end 2. No change in the volume of the soap bubbles

B. air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

C. no changes occurs

D. air from end 2 flows towards end 1. volume of the soap bubble at end 1 increases

Q. 29 A vibrating string of certain length l under a tension T resonates with a mode

corresponding to the first overtone (third harmonic) of an air column of length 75 cm

inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is

A. 344

B. 336

C. 117.3

D. 109.3

Q. 30 A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 31 A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are n0, n0/2, n0/6 and n0/8, respectively. The angle of incidence θ for which the beam just misses entering Region IV is

A. sin^(-1)(3/4)

B. sin^(-1)(1/8)

C. sin^(-1)(1/4)

D. sin^(-1)(1/3)

Q. 32

STATEMENT-1

For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

and

STATEMENT-2

If the observer and the object are moving at velocities V̅1 and V̅2 respectively with

reference to a laboratory frame, the velocity of the object with respect to the observer is V̅2 – V̅1.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT -1 is True, STATEMENT-2 is False

D. STATEMENT -1 is False, STATEMENT-2 is True

Q. 33

STATEMENT-1

It is easier to pull a heavy object than to push it on a level ground.

and

STATEMENT-2

The magnitude of frictional force depends on the nature of the two surfaces in contact.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT -1 is True, STATEMENT-2 is False

D. STATEMENT -1 is False, STATEMENT-2 is True

Q. 34 STATEMENT-1

For practical purposes, the earth is used as a reference at zero potential in electrical

circuits.

and

STATEMENT-2

The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q/(4πε0R)

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT -1 is True, STATEMENT-2 is False

D. STATEMENT -1 is False, STATEMENT-2 is True

Q. 35

STATEMENT-1

The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

and

STATEMENT-2

Soft iron has a high magnetic permeability and cannot be easily magnetized or

demagnetized.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT -1 is True, STATEMENT-2 is False

D. STATEMENT -1 is False, STATEMENT-2 is True

Questions: 36 – 38

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R.

The charge density ρ (r) [charge per unit volume] is dependent only on the radial

distance r from the centre of the nucleus as shown in figure The electric field is

only along rhe radial direction.

Q. 36 The electric field at r = R is

A. independent of a

B. directly proportional to a

C. directly proportional to a²

D. inversely proportional to a

Q. 37 For a = 0, the value of d (maximum value of ρ as shown in the figure) is

A. (3Ze)/(4πR³)

B. (3Ze)/(πR³)

C. (4Ze)/(3πR³)

D. (Ze)/(3πR³)

Q. 38 The electric field within the nucleus is generally observed to be linearly dependent on r. This implies.

A. a = 0

B. a = R/2

C. a = R

D. a = 2R/3

Questions: 39 – 41

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity V̅₀ = V₀ î . The coefficient of friction is μ.

Q. 39 The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

A. −kx

B. −2kx

C. −2kx /3

D. −4kx /3

Q. 40 The centre of mass of the disk undergoes simple harmonic motion with angular frequency ω equal to

A. √(k/M)

B. √(2k/M)

C. √(2k/3M)

D. √(4k/3M)

Q. 41 The maximum value of V0 for which the disk will roll without slipping is

A. μg√(M/k)

B. μg√(M/2k)

C. μg√(3M/k)

D. μg√(5M/2k)

Q. 42 Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graph given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

A. A – s; B – p,q, r; D – p, q, s

B. A – s; B – p,q; C – r; D – p, q, s

C. A – s; B – p; C – r; D – p, q

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

Q. 43 An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

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

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

C. A – s; B – p; C – r; D – p, q

D. A – s; B – p,q, r; D – p, q, s

Q. 44 Column I Contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

A. A – s; B – p,q; C – r; D – p, q, s

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

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

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

Q. 45 The correct stability order for the following species is

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

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

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

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

Q. 46 Cellulose upon acetylation with excess acetic anhydride/H2SO4 (catalytic) gives cellulose triacetate whose structure is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 47 In the following reaction sequence, the correct structures of E, F and G are

A. (A)

B. (B)

C. (C)

D. (D)

Q. 48 Among the following the coloured compound is

A. CuCl

B. K₃[Cu(CN)₄]

C. CuF₂

D. [Cu(CH₃CN)₄]BF₄

Q. 49 Both [Ni(CO)₄] and [Ni(CN)₄]⁻² are diamagnetic. The hybridization of nickel in these complexes, respectively, are

A. sp₃, sp₃

B. sp₃, dsp₂

C. dsp₂, sp₃

D. dsp₂, dsp₂

Q. 50 The IUPAC name of [Ni(NH₃)₄][NiCl₄] is

A. Tetrachloronickel (II) – tetraamminenickel (II)

B. Tetraamminenickel (II) – tetrachloronickel (II)

C. Tetraamminenickel (II) – tetrachloronickelate (II)

D. Tetrachloronickel (II) – tetraamminenickelate (0)

Q. 51 Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H₂ gas at the cathode is (1 Faraday = 96500 C mol⁻¹)

A. 9.65 × 10⁴ sec

B. 19.3 × 10⁴ sec

C. 28.95 × 10⁴ sec

D. 38.6 × 10⁴ sec

Q. 52 Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is

A. (A)

B. (B)

C. (C)

D. (D)

Q. 53 Solubility product constant (Ksp) of salts of types MX, MX2 and M3X at temperature ‘T’ are 4.0 × 10⁻⁸, 3.2 × 10⁻¹⁴ and 2.7 × 10⁻¹⁵, respectively. Solubilities (mole dm⁻³)) of the salts at temperature ‘T’ are in the order

A. MX > MX₂ > M₃X

B. M₃X > MX₂ > MX

C. MX₂ > M₃X > MX

D. MX > M₃X > MX₂

Q. 54

STATEMENT-1: Aniline on reaction with NaNO₂/HCl at 0°C followed by coupling with β- naphthol gives a dark blue coloured precipitate.

and

STATEMENT-2: The colour of the compound formed in the reaction of aniline with

NaNO₂/HCl at 0°C followed by coupling with β-naphthol is due to the extended conjugation.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 55 STATEMENT-1: [Fe(H₂O)₅NO]SO₄ is paramagnetic.

and

STATEMENT-2: The Fe in [Fe(H₂O)₅NO]SO₄ has three unpaired electrons.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 56

STATEMENT-1: The geometrical isomers of the complex [M(NH₃)₄Cl₂] are optically inactive. and

STATEMENT-2: Both geometrical isomers of the complex [M(NH₃)₄Cl₂] possess axis of symmetry

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 57 STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.

and

STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct

explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Questions: 58 – 60

A tertiary alcohol H upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J and K. Compound J upon reaction with KOH gives benzyl alcohol and a compound L, whereas K on reaction with KOH gives only M,

Q. 58 Compound H is formed by the reaction of (see figure 2)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 59 The structure of compound I is (see figure 3)

A. (A)

B. (B)

C. (C)

D. (D)

Q. 60 The structures of compounds J, K and L, respectively, are (see figure 4)

A. (A)

B. (B)

C. (C)

D. (D)

Questions: 61 – 63

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A spacefilling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assumer radius of every sphere to be ‘r’.

Q. 61 The number of atoms on this HCP unit cell is

A. 4

B. 6

C. 12

D. 17

Q. 62 The volume of this HCP unit cell is

A. 24√2 r³

B. 16√2 r³

C. 12√2 r³

D. (64/3√3) r³

Q. 63 The empty space in this HCP unit cell is

A. 74%

B. 47.6%

C. 32%

D. 26%

Q. 64 Match the compounds in Column I with their characteristic test(s)/ reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix gives in the ORS.

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

B. A – s; B – p,q, r; D – p, q, s

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

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

Q. 65 Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

A. A – s; B – p,q, r; D – p, q, s

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

C. A – p; B – q; C – p, r; D – p, s

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

Q. 66 Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.

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

B. A – s; B – p,q; C – r; D – p, q, s

C. A – s; B – p,q, r; D – p, q, s

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

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

JEE Advanced 2008 Paper I Previous Year Paper

JEE Advanced 2008 Paper 1

Q. 1 Consider the two curves

C₁ : y² = 4x

C₂ : x² + y² – 6x + 1 = 0

Then,

A. C₁ and C₂ touch each other only at one point

B. C₁ and C₂ touch each other exactly at two points

C. C₁ and C₂ intersect (but do not touch) at exactly two points

D. C₁ and C₂ neither intersect nor touch each other

Q. 2 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 3 The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors â, b̂, ĉ such that

â . b̂ = b̂ . ĉ = ĉ . â =1/2

Then, the volume of the parallelepiped is

A. 1/√2

B. 1/2√2

C. √3/2

D. 1/√3

Q. 4 Let a and b be non-zero real numbers. Then, the equation

(ax² + by² + c)(x² – 5xy + 6y²) = 0

represents

A. four straight lines, when c = 0 and a, b are of the same sign

B. two straight lines and a circle, when a = b , and c is of sign opposite to that of a (C)

C. two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a

D. a circle and an ellipse, when a and b are of the same sign and c is of Sign opposite to that of a

Q. 5 Choose the correct option:

A. n = 1, m =1

B. n = 1, m = -1

C. n = 2, m = 2

D. n > 2, m = n

Q. 6 The total number of local maxima and local minima of the function is

A. 0

B. 1

C. 2

D. 3

Q. 7 A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then

A. A

B. B

C. C

D. D

Q. 8 Let P(x₁, y₁) and Q(x₂, y₂), y₁ <0, y₂ 0,, be the endpoints of the latus rectum of the ellipse x²+ 4y² = 4. The equations of parabolas with latus rectum PQ are

A. x² + 2√3y = 3 + √3

B. x² – 2√3y = 3 + √3

C. x²+ 2√3y = 3 – √3

D. x² – 2√3y = 3 – √3

Q. 9 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 10 Let f (x) be a non-constant twice differentiable function defined on (-∞, ∞) such that f(x)= f(1 – x) and f’(1/4) = 0. Then,

A. A

B. B

C. C

D. D

Q. 11 Choose the correct option:

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for

STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 12 Consider three planes

P₁: x – y + z = 1

P₂: x + y – z = -1

P₃: x – 3y + 3z = 2

Let L₁, L₂, L₃ be the lines of intersection of the planes P₂ and P₃, P₃ and P₁, and P₁ and P₂, respectively.

STATEMENT 1: At least two of the lines L₁, L₂ and L₃ are non-parallel.

and

STATEMENT-2: The three planes do not have a common point.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT~2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-l is False, STATEMENT-2 is True

Q. 13 Choose the correct option:

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-l is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is true

Q. 14 Consider the system of equations

ax + by = 0, cx + dy = 0, where a, b, c, d, ∈ {0, 1}.

STATEMENT-1: The probability that the system of equations has a unique solution is ⅜ and STATEMENT-2: The probability that the system of equations has a solution is 1

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Questions: 15 – 17

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ , QR , RP are D, E, F , respectively. The line PQ is given by the equation √3x + y – 6 = 0 and the point D is (3√3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ.

Q. 15 The equation of circle C is

A. (x -2√3)² + (y – 1)² = 1

B. (x -2√3)² + (y + 1/2)² = 1

C. (x -√3)² + (y + 1)² = 1

D. (x -√3)² + (y – 1)² = 1

Q. 16 Points E and F are given by

A. (√3/2, 3/2), (√3, 0)

B. (√3/2, 1/2), (√3, 0)

C. (√3/2, 3/2), (√3/2, 1/2)

D. (3/2, √3/2), (√3/2, 1/2)

Q. 17 Equations of the sides QR , RP are

A. y = (2/√3)x + 1, y = (-2/√3)x – 1

B. y = (1/√3)x, y = 0

C. y = (√3/2)x + 1, y = (-√3/2)x – 1

D. y = √3x, y = 0

Questions: 18 – 20

Consider the functions defined implicitly by the equation y³ -3y +x = 0 on various

intervals in the real line. If x ∈ (-∞, -2)∪(2, ∞) , the equation implicitly defines a unique real value differentiable function y = f(x). If x ∈ (-2, 2), the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0.

Q. 18 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 19 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 20 Choose the correct option:

A. A

B. B

C. C

D. D

Questions: 21 – 23

Let A, B, C be three sets of complex numbers as defined below

A = {z: Im z ≥1}

B={z : |z – 2 – i | = 3}

C={z : Re((1 – i )z ) = √2}.

Q. 21 The number of elements in the set A ∩ B ∩ C is

A. 0

B. 1

C. 2

D. ∞

Q. 22 Let z be any point in A ∩ B ∩ C. Then, |z + 1 – i|² + |z – 5 – i|² lies between

A. 25 and 29

B. 30 and 34

C. 35 and 39

D. 40 and 44

Q. 23 Let z be any point in A ∩ B ∩ C and let w be any point satisfying |w – 2 – i| < 3 Then |z| – |w| + 3 lies between

A. -6 and 3

B. -3 and 6

C. -6 and 6

D. -3 and 9

Q. 24 Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

If Eᵢ, Eᵢᵢ, and Eᵢᵢᵢ are the percentage errors in g, i.e., (Δg/g x 100) for students I, II and III, respectively,

A. Eᵢ = 0

B. Eᵢ is minimum

C. Eᵢ = Eᵢᵢ

D. Eᵢᵢ is maximum

Q. 25 Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

A. P1 > P2 > P3

B. P1 > P3 > P2

C. P2 > P1 > P3

D. P3 > P2 > P1

Q. 26 Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

A. Wavelength of characteristic X-rays decreases when the atomic number of the target increases

B. Cut-off wavelength of the continuous X-rays depends on the atomic number of the target

C. Intensity of the characteristic X-rays depends on the electrical power given to the X Ray tube

D. Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube

Q. 27 Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60°). In the position of minimum deviation. the angle of refraction will be

A. 30° for both the colours

B. greater for the violet colour

C. greater for the red colour

D. equal but not 30° for both the colours

Q. 28 An ideal gas is expanding such that PT² = constant. The coefficient of volume expansion of the gas is

A. 1/T

B. 2/T

C. 3/T

D. 4/T

Q. 29 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 30 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 31 Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

A. Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy

B. Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy

C. Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments

D. Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments

Q. 32 A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is l. Choose the correct choice(s).

A. The particle enters Region III only if its velocity V > qlB/m

B. The particle enters Region III only if its velocity V < qlB/m

C. Path length of the particle in Region II is maximum when velocity V = qlB/m

D. Time spent in Region II is same for any velocity V as long as the particle returns to Region I

Q. 33 In a Young’s double slit experiment, the separation between the two slits is d and the wavelength of the light is λ. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

A. If d = λ , the screen will contain only one maximum A

B. If λ < d < 2λ, at least one more maximum (besides the central maximum) will be

observed on the screen

C. If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase

D. If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase

Q. 34

STATEMENT-1

In a Meter Bridge experiment, null point for an unknown resistance is measured. Now. the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.

and

STATEMENT-2

Resistance of a metal increases with increase in temperature.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 35

STATEMENT-l

An astronaut in an orbiting space station above the Earth experiences weightlessness. and

STATEMENT-2

An object moving around the Earth under the influence of Earth’s gravitational force is in a state of ‘free-fall’.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-l is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 36

STATEMENT-1

Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT-2

By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for

STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-l is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 37

STATEMENT-1

The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT-2

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

A. STATEMENT-l is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Questions: 38 – 40

A small spherical monatomic ideal gas bubble (γ = 5/3) is trapped inside a liquid of density ρl (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is To, the height of the liquid is H and the atmospheric pressure is Po (Neglect surface tension).

Q. 38 As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

A. Only the force of gravity

B. The force due to gravity and the force due to the pressure of the liquid

C. The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid

D. The force due to gravity and the force due to viscosity of the liquid

Q. 39 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 40 Choose the correct option:

A. A

B. B

C. C

D. D

Questions: 41 – 43

In a mixture of H – He⁺ gas (He⁺ is singly ionized He atom), H atoms and He⁺ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He⁺ ions (by collisions). Assume that the Bohr model of an atom is exactly valid.

Q. 41 The quantum number n of the state finally populated in He+ ions is

A. 2

B. 3

C. 4

D. 5

Q. 42 The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is

A. 6.5 x 10⁻⁷ m

B. 5.6 x 10⁻⁷ m

C. 4.8 x 10⁻⁷ m

D. 4.0 x 10⁻⁷ m

Q. 43 The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion

A. 1/4

B. 1/2

C. 1

D. 2

Questions: 44 – 46

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic ( g = 10 m/s²)

Q. 44 The speed of the block at point B immediately after it strikes the second incline is

A. √60 m/s

B. √45 m/s

C. √30 m/s

D. √15 m/s

Q. 45 The speed of the block at point C, immediately before it leaves the second incline is

A. √120 m/s

B. √105 m/s

C. √90 m/s

D. √75 m/s

Q. 46 If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

A. √30 m/s

B. √15 m/s

C. 0 m/s

D. -√15 m/s

Q. 47 Hyperconjugation involves overlap of the following orbitals

A. σ – σ

B. σ – p

C. p – p

D. π – π

Q. 48 The major product of the following reaction is

A. A

B. B

C. C

D. D

Q. 49 An aqueous solution of Na₂S₂0₃ on reaction with Cl₂ gives

A. Na₂S₄O₆

B. NaHSO₄

C. NaCl

D. NaOH

Q. 50 Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of

A. nitrogen

B. oxygen

C. carbon dioxide

D. argon

Q. 51 Under the same reaction conditions, an initial concentration of 1.386 mol dm-³ of a substance becomes half in 40 seconds and 20 seconds through a first order and zero order kinetics, respectively. Ratio (k₁/k₀) of the rate constants for the first order (k₁) and zero order (k₀) of the reactions is

A. 0.5 mol⁻¹ dm-³

B. 1.0 mol dm-³

C. 1.5 mol dm-³

D. 2.0 mol⁻¹ dm-³

Q. 52 2.5 mL of (2/5)M weak monoacidic base (Kb = 1 x 10⁻¹² at 25 °C) is titrated with (2/15) M HCl in water at 25° C. The concentration of H⁺ at equivalence point is (Kw = 1 x 10⁻¹⁴ at 25 °C)

A. 3.7 x 10⁻¹³ M

B. 3.2 x 10⁻⁷ M

C. 3.2 x 10⁻² M

D. 2.7 x 10⁻² M

Q. 53 The correct statement(s) about the compound given below is (are)

A. The compound is optically active

B. The compound possesses centre of symmetry

C. The compound possesses plane of symmetry

D. The compound possesses axis of symmetry

Q. 54 The correct statement(s) concerning the structures E, F and G is (are)

A. E, F and G are resonance structures

B. E, F and E, G are tautomers

C. F and G are geometrical isomers

D. F and G are diastereomers

Q. 55 A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are)

A. NH₄NO₃

B. NH₄NO₂

C. NH₄Cl

D. (NH₄)₂SO₄

Q. 56 A gas described by van der Waals equation

A. behaves similar to an ideal gas in the limit of large molar volumes

B. behaves similar to an ideal gas in the limit of large pressures

C. is characterised by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature

D. has the pressure that is lower than the pressure exerted by the same gas behaving

ideally

Q. 57

STATEMENT-1: Bromobenzene upon reaction with Br₂/Fe gives 1,4-dibromobenzene as the major product.

and

STATEMENT-2:: In bromobenzene, the inductive effect of the bromo group is more

dominant than the mesomeric effect in directing the incoming electrophile.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-I

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-l

C. STATEMENT-l is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 58

STATEMENT-1: Pb⁴⁺ compounds are stronger oxidizing agents than Sn⁴⁺ compounds. and

STATEMENT-2: The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to inert pair effect.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 59 STATEMENT-1: The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45° slope as the atomic number is increased.

and

STATEMENT-2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Q. 60 STATEMENT-1: For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.

and

STATEMENT-2: At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C. STATEMENT-1 is True, STATEMENT-2 is False

D. STATEMENT-1 is False, STATEMENT-2 is True

Questions: 61 – 63

In the following reaction sequence, products I, J and L are formed. K represents a

Reagent.

Q. 61 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 62 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 63 Choose the correct option:

A. A

B. B

C. C

D. D

Questions: 64 – 66

There are some deposits of nitrates and phosphates in earth’s crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory condition but microbes do it easily. Ammonia forms a large number of complexes with transition metal ions. Hybridization easily explains the ease of sigma donation capability of NH3 and PH3 . Phosphine is a flammable gas and is prepared from white phosphorous.

Q. 64 Among the following, the correct statement is

A. Phosphates have no biological significance in humans

B. Between nitrates and phosphates, phosphates are less abundant in earth’s crust

C. Between nitrates and phosphates, nitrates are less abundant in earth’s crust

D. Oxidation of nitrates is possible in soil

Q. 65 Among the following, the correct statement is

A. Between NH₃ and PH₃ , NH₃ is a better electron donor because the lone pair of

electrons occupies spherical ‘s’ orbital and is less directional

B. Between NH₃ and PH₃ , PH₃ is a better electron donor because the lone pair of

electrons occupies sp³ orbital and is more directional

C. Between NH₃ and PH₃ , NH₃ is a better electron donor because the lone pair of

electrons occupies sp³ orbital and is more directional

D. Between NH₃ and PH₃ , PH₃ is a better electron donor because the lone pair of

electrons occupies spherical ‘s’ orbital and is less directional

Q. 66 White phosphorus on reaction with NaOH gives PH₃ as one of the products. This is a

A. dimerization reaction

B. disproportionation reaction

C. condensation reaction

D. precipitation reaction

Questions: 67 – 69

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles. A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9. In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Q. 67 The freezing point of the solution M is

A. 268.7 K

B. 268.5 K

C. 234.2 K

D. 150.9 K

Q. 68 The vapour pressure of the solution M is

A. 39.3 mm Hg

B. 36.0 mm Hg

C. 29.5 mm Hg

D. 28.8 mm Hg

Q. 69 Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is

A. 380.4 K

B. 376.2 K

C. 375.5 K

D. 354.7 K

Answer Sheet
Question	1	2	3	4	5	6	7	8	9	10
Answer	B	C	A	B	C	C	B	C	A	A
Question	11	12	13	14	15	16	17	18	19	20
Answer	A	D	A	B	D	A	D	B	A	D
Question	21	22	23	24	25	26	27	28	29	30
Answer	B	C	D	B	C	B	A	C	C	AD
Question	31	32	33	34	35	36	37	38	39	40
Answer	BD	ACD	AB	D	A	D	A	D	B	B
Question	41	42	43	44	45	46	47	48	49	50
Answer	C	C	A	B	B	C	B	A	B	B
Question	51	52	53	54	55	56	57	58	59	60
Answer	A	D	AD	BCD	AB	ACD	C	C	A	D
Question	61	62	63	64	65	66	67	68	69	70
Answer	D	A	C	C	C	B	D	B	B

JEE Advanced 2007 Paper II Previous Year Paper

JEE Advanced 2007 Paper 2

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

A. Ni(CO)₄

B. [NiCl₄]₂⁻

C. Ni(PPh₃)₄

D. [Ni(CN)₄]₂⁻

Q. 2 The species having pyramidal shape is _

A. SO₃

B. BrF₃

C. Si(O₃)₂⁻

D. OSF₂

Q. 3 In the reaction the structure of the Product T is

A. A

B. B

C. C

D. D

Q. 4 The compounds P, Q, and S were separately subjected to nitration using HNO₃/H₂SO₄ mixture. The major product formed in each case respectively is

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

H₃PO₄ H₂SO₄ H₃PO₃ H₂CO₃ H₂S₂O⁷

H₃BO₃ H₃PO₂ HᵧCRO₄ H₂SO₃

Q. 8 Total number of geometrical isomers for the complex [RhCI(CO)(PPh₃)(NH₃)] 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⁻¹) 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*10ⁿ. The value of n 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 Wd. then the integer closest to the ratio wd/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 The compounds P and Q respectively in fig 1 are

A. A

B. B

C. C

D. D

Q. 13 The compound R in fig 2 is

A. A

B. B

C. C

D. D

Q. 14 The compound S in fig 3 is

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 S₁. 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 following:

A. A: r,s ; B – t ; C – p,q ; D – r

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

C. A – p,q ; B – r ; C – p,r ; D – r

D. A – r,s ; B – q ; C – p,q ; D – s

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

Column I Column II

A)(CH₃)₃SiC p) Hydrogen halide formation

B) XeF₄ q)Redox reaction

C) Cl₂ r)Reacts with glass

D) VCI₅ s)Polarization

t)O2 formation

A. A – r,s ; B – r ; C – p,q ; D – s

B. A – r,s ; B – p ; C – q,t ; D – s

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

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

Q. 20 For r = 0, 1, …. 10, let Ar, Br and Cr denote. respectively, the coefficient of xʳ in the expansions of (1+X)¹⁰, (1+X)²⁰ and (1+X)³⁰. Then Σ(r=1to10)Ar(B10Br – C10Cr)is equal to

A. B₁₀-C₁₀

B. A₁₀(B²₁₀-C₁₀A₁₀)

C. 0

D. C₁₀-B₁₀

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 – 2z = α. where α> 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=2î+10ĵ+11k̂ and AD=-î+2ĵ+2k̂ .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 α 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 then the

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 > O. 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 ∠ABC is obtuse and if r denotes the radius of the incircle of the triangle, then r² is equal to

Q. 28 let f be a function defined on R (the set of all real numbers) such that f(x) = 2010(x- 2009)(x- 2010)²(x – 2011)³ (x – 2012)⁴, for all x ∈R If g is a function defined on R with values in the interval (0. α) such f(x) =ln (g (x)). for all x ∈R then the number of points on R at which g has a local maximum is

Q. 29 What is the correct value :

Q. 30 Let k be a positive real number and let A, B be two matrices as shown in fig. If det (adj A) + det(adj B) =10⁶. then [k] is equal to [Note : adj M denotes file adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k]

Questions: 31 – 33

Consider the polynomial f(x)=1+ 2x + 3x²+4x³ Let S be the sum of all distinct real

roots of f(x) 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. (21/64,11/16)

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 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 the values in Column-II.

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

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

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

D. A – p ; CB- p ; C – q,s ; D – p,s

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

A. A – p ; B – r ; C – p,s ; D – q

B. A – t ; B – r ; C – q,s ; D – q

C. A – p ; B – p ; C – q,s ; D – r

D. A – t ; B – p,r ; C – q,s ; D – r

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

A. 0.02mm

B. 0.05mm

C. 0.1mm

D. 0.2mm

Q. 40 A hollow pipe of length 0.8m is closed at one end. At its open end a 0.5m 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 50N and the speed of sound is 320 ms⁻¹, 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 10cm.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

A. 4.50J

B. 7.50J

C. 5.06J

D. 14.06J

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/7×10⁵ 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/m² and the density of oil = 900 kg/m³, the magnitude of q is

A. 1.6×10⁻¹⁹ C

B. 3.2×10⁻¹⁹ C

C. 4.8×10⁻¹⁹ C

D. 8.0×10⁻¹⁹ 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. 1/ε∘(σ²R²)

B. 1/ε∘(σ²R)

C. 1/ε∘(σ²/R)

D. 1/ε∘(σ²/R²)

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 αTᵢ , the value of α is

Q. 46 At time t=0, a battery of 10V 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 20m 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

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 dropper 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 = 5×10⁻⁴ m, ρ =10³ kg/m³, g =10 m/s² .T= 0.11 N/m. the radius of the drop when it detaches from the dropper is approximately

A. 1.4×10⁻³ m

B. 3.3×10⁻³ m

C. 2.0×10⁻³ m

D. 4.1×10⁻³ m

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

A. 1.4×10^-6J

B. 2.7×10^-6J

C. 5.4×10^-6J

D. 8.1×10^-6J

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(h²/8Π²I)

B. 1/n(h²/8Π²I)

C. n(h²/8Π²I)

D. n²(h²/8Π²I)

Q. 54 It is found that the excitation frequency from the ground to the first excited state of rotation for the CO molecule is close to 4/Πx10¹¹ Hz. Then the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2Πx10⁻³⁴J s)

A. 2.76×10⁻⁴⁶ kg m²

B. 1.87×10⁻⁴⁶ kg m²

C. 4.67×10⁻⁴⁶ kg m²

D. 1.17×10⁻⁴⁶ kg m²

Q. 55 In a CO molecule, the distance between C(mass=12 a.m.u) and O(mass=16 a.m.u.), where 1 a.m.u. =5/3×10^-27kg, is close to

A. 2.4×10^-10 m

B. 1.9×10^-10 m

C. 1.3×10^-10 m

D. 4.4×10^-11 m

Q. 56 Match the following:

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

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

C. A – r ; B – q,t ; C – p,t ; D – q

D. A – p,t ; B – q,s ; C – p ; D – s

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 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,s ; B – q,r ; C – p ; D – q,s

C. A – r ; B – s,t ; C – p ; D – q,r

D. A – s,t ; B – q,r ; C – q ; D – t

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	D	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	B	D	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	B	A

JEE Advanced 2007 Paper I Previous Year Paper

JEE Advanced 2007 Paper 1

Q. 1 A resistance of 2 Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω , is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

A. 3 Ω

B. 4 Ω

C. 5 Ω

D. 6 Ω

Q. 2 In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,

A. x < f

B. f < x < 2f

C. x = 2f

D. x > 2f

Q. 3 Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept F on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with m m a small but constant force F. As a result, the particles P move towards each other on the surface. The magnitude of acceleration, when the separation between them 0 becomes 2x , is

A. A

B. B

C. C

D. D

Q. 4 A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

A. A potential difference appears between the two cylinders when a charge density is given to the inner cylinder

B. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder

C. No potential difference appears between the two cylinders when a uniform line

charge is kept along the axis of the cylinders

D. No potential difference appears between the two cylinders when same charge density is given to both the cylinders

Q. 5 Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

A. negative and distributed uniformly over the surface of the sphere

B. negative and appears only at the point on thesphere closest to the point charge

C. negative and distributed non-uniformly over the entire surface of the sphere

D. zero

Q. 6 A circuit is connected as shown in the figure with the switch S open. When the switch is X closed, the total amount of charge that flows from Y to X is

A. 0

B. 54 μC

C. 27 μC

D. 81 μC

Q. 7 A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

A. only a reflected ray and no refracted ray

B. only a refracted ray and no reflected ray

C. a reflected ray and a refracted ray and the angle between them would be less than

180° – 2θ

D. a reflected ray and a refracted ray and the angle between them would be greater than 180° – 2θ

Q. 8 In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

A. A

B. B

C. C

D. D

Q. 9 The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

A. 802 nm

B. 823 nm

C. 1882 nm

D. 1648 nm

Q. 10

STATEMENT-1

A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Because

STATEMENT-2

The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 11

STATEMENT-1

In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

because

STATEMENT-2

In an elastic collision, the linear momentum of the system is conserved.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is False

Q. 12

STATEMENT-1

The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.

because

STATEMENT-2

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 13

STATEMENT-1

If the accelerating potential in an X-ray tube is increased, the wavelengths of the

characteristic X-rays do not change. because

STATEMENT-2

When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement 2 is True

Q. 14 The ratio x₁/x₂ is a

A. 2

B. 1/2

C. √2

D. 1/√2

Q. 15 When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

A. 2Iω/3t

B. 9Iω/2t

C. 9Iω/4t

D. 3Iω/2t

Q. 16 The loss of kinetic energy during the above process is

A. Iω²/2

B. Iω²/3

C. Iω²/4

D. Iω²/6

Q. 17 The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

A. P₀

B. P₀/2

C. P₀/2 + Mg/(πR²)

D. P₀/2 – Mg/(πR²)

Q. 18 While the piston is at a distance 2L from the top, the hole at the tap is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

A. A

B. B

C. C

D. D

Q. 19 The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies

A. A

B. B

C. C

D. D

Q. 20 Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 21 Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column 1 with the statements in Column 11 and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 22 Some laws/processes are given in Column 1. Match these with the physical phenomena given in Column 11 and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 23 The species having bond order different from that in CO is

A. NO⁻

B. NO⁺

C. CN⁻

D. N₂

Q. 24 Among the following, the paramagnetic compound is

A. Na₂O₂

B. O₃

C. N₂O

D. KO₂

Q. 25 Extraction of zinc from zinc blende is achieved by

A. electrolytic reduction

B. roasting followed by reduction with carbon

C. roasting followed by reduction with another metal

D. roasting followed by self-reduction

Q. 26 In the following reaction, the structure of the major product ‘ X ’ is

A. A

B. B

C. C

D. D

Q. 27 The reagent(s) for the following conversion, is/are,

A. alcoholic KOH

B. alcoholic KOH followed by NaNH₂

C. aqueous KOH followed by NaNH₂

D. Zn/CH₃OH

Q. 28 The number of structural isomers for C₆H₁₄ is

A. 3

B. 4

C. 5

D. 6

Q. 29 The percentage of p-character in the orbitals forming P-P bonds in P₄ is

A. 25

B. 33

C. 50

D. 75

Q. 30 When 20 g of naphthoic acid (C₁₁H₈O₂) is dissolved in 50 g of benzene (Kᵣ =1.72 K kg/mol), a freezing point depression of 2K is observed. The van‘t Hoff factor (i) is

A. 0.5

B. 1

C. 2

D. 3

Q. 31 Choose the correct option:

A. 5

B. 10

C. 95

D. 100

Q. 32 STATEMENT-1 : Boron always forms covalent bond.

because

STATEMENT-2: The small size of B3+ favours formation of covalent bond.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 33 STATEMENT-1: In water, orthoboric acid behaves as a weak monobasic acid.

because

STATEMENT-2: In water, orthoboric acid acts as a proton donor.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 34 STATEMENT-1: p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.

because

STATEMENT-2: o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-l is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 35 STATEMENT-1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).

because

STATEMENT-2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 36 Argon is used in arc welding because of its

A. low reactivity with metal

B. ability to lower the melting point of metal

C. flammability

D. high calorific value

Q. 37 The structure of XeO₃ is

A. linear

B. planar

C. pyramidal

D. T-shaped

Q. 38 XeF₄ and XeF₆ are expected to be

A. oxidizing

B. reducing

C. unreactive

D. strongly basic

Questions: 39 – 41

Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately 6.023 x 10²³) are present in a few grams of any chemical compound varying with their atomic/molecular masses. To handle such large numbers conveniently, the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry, biochemistry, electrochemistry and radiochemistry. The following example illustrates a typical case, involving chemical/electrochemical reaction, which requires a clear understanding of the mole concept.

A 4.0 molar aqueous solution of NaCl is prepared and 500 mL of this solution is

electrolysed. This leads to the evolution of chlorine gas at one of the electrodes

(atomic mass : Na = 23, Hg = 200; l Faraday = 96500 coulombs).

Q. 39 The total number of moles of chlorine gas evolved is

A. 0.5

B. 1.0

C. 2.0

D. 3.0

Q. 40 If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is

A. 200

B. 225

C. 400

D. 446

Q. 41 The total charge (coulombs) required for complete electrolysis is

A. 24125

B. 48250

C. 96500

D. 193000

Q. 42 Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 43 Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 44 Match gases under specified conditions listed in Column I with their properties/laws in

Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 45 Let α, β be the roots of the equation x² – px + r = 0 and α/2, 2β be the roots of the equation x² – qx + r = 0. Then the value of r is

A. (2/9)(p – q)(2q – p)

B. (2/9)(q – p)(2p – q)

C. (2/9)(q – 2p)(2q – p)

D. (2/9)(2p – q)(2q – p)

Q. 46 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 47 One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

A. 1/2

B. 1/3

C. 2/5

D. 1/5

Q. 48 Choose the correct option:

A. on the left of x = c

B. on the right of x = c

C. at no point

D. at all points

Q. 49 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 50 A hyperbola, having the transverse axis of length 2 sinθ, is confocal with the ellipse 3x² + 4y² = 12. Then its equation is

A. x² cosec² θ – y² sec² θ = 1

B. x² sec² θ – y² cosec² θ = 1

C. x² sin² θ – y² cos² θ = 1

D. x² cos² θ – y² sin² θ = 1

Q. 51 The number of distinct real values of λ, for which the vectors -λ²î + ĵ + k̂, î – λ²ĵ + k̂, and î + ĵ – λ²k̂ are coplanar, is

A. zero

B. one

C. two

D. three

Q. 52 A man walks a distance of 3 units from the origin towards the north-east (N 45° E) direction. From there, he walks a distance of 4 units towards the north-west (N 45° W) direction to reach a point P. Then the position of P in the Argand plane is

A. A

B. B

C. C

D. D

Q. 53 The number of solutions of the pair of equations

2 sin²θ – cos2θ = 0

2 cos²θ – 3sinθ = 0

in the interval [0, 2π] is

A. zero

B. one

C. two

D. four

Q. 54 Choose the correct option:

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-l is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 55 Tangents are drawn from the point (17, 7) to the circle x² + y² = 169.

STATEMENT-1 : The tangents are mutually perpendicular.

because

STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x² + y² = 338

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 56 Choose the correct option:

A. Statement-l is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-1 is False, Statement-2 is True

Q. 57 Let F (x) be an indefinite integral of sin²x

STATEMENT-1 :The function F(x) satisfies F(x + π) = F(x) for all real x.

because

STATEMENT-2 : sin²(x + π) = sin²x for all real x.

A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1

B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1

C. Statement-1 is True, Statement-2 is False

D. Statement-l is False, Statement-2 is True

Questions: 58 – 60

Read the paragraph given to the side and answer the questions that follow:

Q. 58 Choose the correct option:

A. A

B. B

C. C

D. D

Q. 59 Tᵣ is always

A. an odd number

B. an even number

C. a prime number

D. a composite number

Q. 60 Which one of the following is a correct statement?

A. Q1, Q2, Q3,… are in AP. with common difference 5

B. Q1, Q2, Q3,… are in AP. with common difference 6

C. Q1, Q2, Q3,… are in AP. with common difference 11

D. Q1 = Q2 : Q3

Questions: 61 – 63

Consider the circle x² + y² = 9 and the parabola y² = 8x . They intersect at P and Q

in the first and the fourth quadrants, respectively. Tangents to the circle at P and

Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the xaxis at S.

Q. 61 The ratio of the areas of the triangles PQS and PQR is

A. 1 : √2

B. 1 : 2

C. 1 : 4

D. 1 : 8

Q. 62 The radius of the circumcircle of the triangle PRS is

A. 5

B. 3√3

C. 3√2

D. 2√3

Q. 63 The radius of the incircle of the triangle PQR is

A. 4

B. 3

C. 8/3

D. 2

Q. 64 Consider the following linear equations

ax + by + cz = O

bx + cy + az = 0

cx + ay + bz = 0

Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

A. A – r ; B – q ; C – p ; D – s

B. A – s ; B – q ; C – p ; D – r

C. A – r ; B – p ; C – q ; D – s

D. A – s ; B – p ; C – q ; D – r

Q. 65 In the following [ x ] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.

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

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

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

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

Q. 66 Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the CBS.

A. A – s ; B – s ; C – p ; D – r

B. A – r ; B – s ; C – p ; D – s

C. A – r ; B – q ; C – p ; D – s

D. A – r ; B – s ; C – q ; D – s

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