IIT - JEE 2013 (Advanced) CODE : O

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1 IIT - JEE 0 (Advanced) CODE : O

2 () Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution

3 IIT JEE 0 Advanced : Question Paper & Solution (Paper I) () PART I : PHYSICS SECTION I : (Only One option correct Type) This section contains 0 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. x. The work done on a particle of mass m by a force, ˆ y ˆ K i+ j / / ( x y ) (x + y ) + (K being a constant of appropriate dimension), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is (A) K π (B) K π (C) K π (D) 0 a a a. (D) k F r F is conservative r ˆ i ˆ F K x + i U (x + y ) y (x + y ) U K [potential energy] (x + y ) U(0, a) U(a, 0) W 0. Two rectangular block, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the block has thermal conductivity k and the other k. The temperature difference between the ends along the x- axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is (A).0 s (B).0 s (C) 4.5 s (D) 6.0 s. (A) Thermal resistance of individual block are R and R. For config ; R R; For config ; R Q Ratio of heat currents R Q R 9 Q Q t Q t t t 9s sec Q 9 R

4 (4) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution. two non-reactive monoatomic ideal gases have their atomic masses in the ratio :. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 :. The ratio of their densities is (A) : 4 (B) : (C) 6 : 9 (D) 8 : 9. (D) PV PV P Mρ P Mρ ρ 4 8/9 ρ 4. A particle of mass m is projected from the ground with an initial speed u 0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u 0. The angle that the composite system makes with the horizontal immediately after the collision is π π π π (A) (B) +α (C) α (D) (A) u H sin α g Speed the particle that was thrown vertically at the highest point be v. u0 sin α v u0 g v u 0 cos α g py tan θ p x 5. A pulse of light of duration 00 ns is absorbed completely by a small object initially at rest. Power of the pulse is 0 mw and the speed of light is 0 8 ms. The final momentum of the object is (A) kg ms (B) kg ms (C) kg ms (D) kg ms 5. (B) P h/d or E PC P In the Young s double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is λ λ λ λ (A) ( n + ) (B) (n + ) (C) (n + ) (D) (n + ) (B) I δ 4I0 cos If I I 0 mu 0 cos α θ mu 0 cos α 4

5 IIT JEE 0 Advanced : Question Paper & Solution (Paper I) (5) cos δ cos δ δ π ± nπ± 4 π Δ x π nπ± Δ x n ± λ λ The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is times the wavelength in free space. The radius of the curved surface of the lens is (A) m (B) m (C) m (D) 6 m 7. (C) v 8 m, μ m v v m v u f f u f v m f f 8 f f 6 f R μ R 6 R ( ) 8. One end of a horizontal thick copper wire of length L and radius R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (A) 0.5 (B) 0.50 (C).00 (D) (C) F R L L R F F F 4A A Δ Δ L L 4Δ Δ Δ Δ Δ Δ 9. A ray of light travelling in the direction ( i j ˆ ) reflection, it travels along the direction ( i j ˆ ) + is incident on a plane mirror. After. The angle of incidence is (A) 0 (B) 45 (C) 60 (D) 75 5

6 (6) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution 9. (A) Angle between IandR is ( i ˆj)( i ˆ IR. + j) cos δ I R ( ) ( ) 4 δ 0 80 i 0 i 60 i 0 0. The diameter of a cylinder is measured using a Vernier caliper with no zero error. It is found that the zero of the Vernier scale lies between 5.0 cm and 5.5 cm of the main scale. The Vernier scale has 50 divisions equivalent to.45 cm. The 4 th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is (A) 5. cm (B) 5.4 cm (C) 5.6 cm (D) 5.48 cm 0. (B) M.S.R. 5. cm V. C cm. 50 L.C cm V.S.R. 4 d (5.) cm cm SECTION II : (One or more options correct Type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.. In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S is pressed first to fully charge the capacitor C and then released. The switch S is then pressed to charge the capacitor C. After some time, S is released and then S is pressed. After some time, (A) the charge on the upper plate of C is CV 0. (B) the charge on the upper plate of C is CV 0. (C) the charge on the upper plate of C is 0. (D) the charge on the upper plate of C is CV 0. I δ R. (B), (D) After S is released : +CV 0 CV 0 C C 6

7 After S is released IIT JEE 0 Advanced : Question Paper & Solution (Paper I) (7) +CV 0 CV 0 +CV 0 CV 0 C C After S is released +CV 0 CV 0 CV 0 +CV 0 C C. A particle of mass M and positive charge Q, moving with a constant velocity u 4i ˆ ms, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x 0 to x L for all values of y. After passing through this region, the particle emerges on the other side after 0 milliseconds with a velocity u ( i ˆ + ˆj) ms. The correct statement(s) is (are) (A) The direction of the magnetic field is z direction. (B) The direction of the magnetic field is +z direction. (C) The magnitude of the magnetic field 50 π M units. Q (D) The magnitude of the magnetic field is 00 π M units. Q. (A), (C) Magnetic field is clearly in z axis. vy tan θ vx mv r qb π θ 6 rsinθ L mv mv sin θ L B sinθ qb ql r vt Time of travel θ t r v θ vt sin θ L θ mv m π 50πm B. θ q v t q q 7

8 (8) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution. A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) (0.0 m) sin [(6.8 m )x]. cos[(68 s )t]. Assuming π.4, the correct statement(s) is (are) (A) The number of nodes is 5. (B) The length of the string is 0.5 m. (C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.0 m. (D) The fundamental frequency is 00 Hz.. (B), (C) y 0.0 sin [(6.8 m ) x] cos [(68 s ) t] 0.0 sin (0π x) cos (00 πt) π k 0 π λ m 0cm K 0 ω ω 00 π ν 00s π ω v 0 m/s k in 5 th harmonic. 5v 5 ν λ 5cm (B) 6 nodes A is wrong. Mid-point is antinode. sin (0 πx) y 0.0 cos (00 π t) y max 0.0 m (C) ν v hz. (D) is wrong A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density ρ. The complete arrangement is placed in a liquid of density ρ and is allowed to reach equilibrium. The correct statement(s) is (are) 4πR ρg (A) the net elongation of the spring is k 8πR ρ g (B) the net elongation of the spring is. k (C) the light sphere is partially submerged. (D) the light sphere is completely submerged. 4. (A), (D) B ρ vg mg ρ vg Kx + B mg Kx ρ vg Kx B m mg 8

9 IIT JEE 0 Advanced : Question Paper & Solution (Paper I) (9) x 4 Rg ρ π ρvg K K B mg + Kx ρ vg + ρ vg B ρ vg ρ Δvg ρ vg v Δv Sphere is completely submerged 4πR ρg K 5. Two non-conducting solid spheres of radii R and R, having uniform volume charge densities ρ and ρ respectively, touch each other. The net electric field at a distance R from the centre of the smaller sphere, along the line joining the centres of the spheres, is ρ zero. The ratio ρ (A) 4 5. (B), (D) Q ρ V Q 8ρ V can be (B) A R P R B ρ V 8 ρ V (C) 5 5 B Kx mg (D) 4 ρ Case I : If P is between A and B then + V e ρ ρ Case II : If P is left of A then ve ρ Case II Case I +ve ve R R P R Q Q Q Q (R) 4 πε0(r) 4 πε0(5r) 4 πε0(r) 4 πε0(r) Q 4 Q Q Q ρ V 4 Q 8 ρ V 5 Q ρ ρ V ρ 5 8ρ V ρ ρ 4 ρ 5 ρ 9

10 (0) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution SECTION III : (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 6. A bob of mass m, suspended by a string of length l, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio is 6. [5] m g m 5g 5 5 5g m m 7. A particle of mass 0. kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms ) of the particle is zero, the speed (in ms ) after 5 s is 7. [5] d P mv dt d dt ν P m ν t dν P ν dt m ; P ν dv dt m 0 0 ν P t m ν P 0.5 t 5 5 m 0. ν 5 m/s ν 5 8. The work functions of Silver and Sodium are 4.6 and. ev, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is 8. [] V s h φ ν e e Slope h for both silver and Na e Ratio of slope 0

11 IIT JEE 0 Advanced : Question Paper & Solution (Paper I) () 9. A freshly prepared sample of a radioisotope of half-life 86 s has activity 0 disintegrations per second. Given that n 0.69, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is 9. [4] t N Ne λ 0 N e λt N0 N λt e N0 ΔN λt ( e ) N0 λ t << λt e λ t ΔN λt N0 n t t / Δ N 00 4 ΔN % 4 % N 0 0. A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 0 rad s about its own axis, which is vertical. Two uniform circular rings, each of mass 6.5 kg and radius 0. m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s ) of the system is 0. [8] R 0.4 M 50 km ω 0 m R 6.5 kg r 0. mr ω ( mrr ) mr + ω ω ω ( ) ω ω 8 R

12 () Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution PART II : CHEMISTRY SECTION I : (Only One option correct Type) This section contains 0 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.. Consider the following complex ions, P, Q and R. P [FeF 6 ], Q [V(H O) 6 ] + and R [Fe(H O) 6 ] + The correct order of the complex ions, according to their spin only magnetic moment values (in B.M.) is (A) R < Q < P (B) Q < R < P (C) R < P < Q (D) Q < P < R. (B) P FeF Fe Ar d 5 [ ] 6 i.e. [ ] Magnetic moment n( n+ ) 5 BM BM ( ) V + [ ] Q V H O + 6 Ar d Magnetic moment 5 BM ( ) i.e. Fe + 6 [ ] Magnetic moment 4( 4+ ) R Fe H O + P > R > Q 4 BM 6 Ar d. The arrangement of X ions around A + ion in solid AX is given in the figure (not drawn to scale). If the radius of X is 50 pm, the radius of A + is (A) 04 pm (B) 5 pm (C) 8 pm (D) 57 pm. (A) + + ra ra 0.44 rx rx r A pm 04 pm. Sulfide ores are common for the metals (A) Ag, Cu and Pb (B) Ag, Cu and Sn (C) Ag, Mg and Pb (D) Al, Cu and Pb. (A) Factual 4. The standard enthalpies of formation of CO (g), H O ( ) and glucose (s) at 5 C are 400 kj/mol, 00 kj/mol and 00 kj/mol, respectively. The standard enthalpy of combustion per gram of glucose at 5 C is (A) kj (B) 900 kj (C) 6. kj (D) + 6. kj 4. (C) CH 6 O6 + O 6CO + 6HO CO 400 kj/ mol

13 IIT JEE 0 Advanced : Question Paper & Solution (Paper I) () H O 00 kj / mol Glucose 00 kj / mol ΔH ΔH P ΔH R 6ΔHf(CO) + 6Hf(HO) Δ Hf( C6H Ο6) (6 400) + 6( 00) ( 00) kj / mol 900 ΔH 6. kj / gm Upon treatment with ammoniacal H S, the metal ion that precipitates as a sulfide is (A) Fe(III) (B) Al(III) (C) Mg(II) (D) Zn(II) 5. (D) White ppt of zinc sulfide by adding ammoniacal H S to Zn(II). ZnS + HCl ZnCl + HS ZnCl + NaOH Zn(OH) + NaCl Zn(OH) + NaOH NaZnO + H O Na ZnO H S ZnS NaOH + + white ppt. 6. Methylene blue, from its aqueous solution is adsorbed on activated charcoal at 5 C. for this process, the correct statement is (A) The adsorption requires activation at 5 C. (B) The adsorption is accompanied by a decrease in enthalpy. (C) The adsorption increases with increase of temperature. (D) The adsorption is irreversible. 6. (B) Factual 7. KI in acetone, undergoes S N reaction with each of P, Q, R and S. The rates of the reaction vary as (A) P > Q > R > S (B) S > P > R > Q (C) P > R > Q > S (D) R > P > S > Q 7. (B) S N reactions are through back attack of attacking Nu and not on the basis of stability of carbocation. 8. In the reaction, P+ Q R + S the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is (A) (B) (C) 0 (D)

14 (4) Vidyalankar : IIT JEE 0 Advanced : Question Paper & Solution 8. (D) For P, t 75% t 50% I st order wrt P For Q, [Q] [Q 0 ] kt. i.e. zero order. i.e. overall order of a reaction 9. Concentrated nitric acid, upon long standing, turns yellow brown due to the formation of (A) NO (B) NO (C) N O (D) N O 4 9. (B) Sunlight 4HNO 4NO + H O + O 0. The compound that does NOT liberate CO, on treatment with aqueous sodium bicarbonate solution, is (A) Benzoic acid (B) Benzenesulphonic acid (C) Salicylic acid (D) Carbolic acid (Phenol) 0. (D) Compound with COOH gr or SO H group can liberate CO with NaHCO solution. SECTION II : (One or more options correct Type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.. The initial rate of hydrolysis of methyl acetate (M) by a weak acid (HA, M) is /00 th of that of a strong acid (HX, M), at 5 C. the K a of HA is (A) 0 4 (B) 0 5 (C) 0 6 (D) 0. (A) Ka Cα (0.0) 0 4. The hyperconjugative stabilities of tert butyl cation and butene, respectively, are due to (A) σ p (empty) and σ π * electron delocalisations. (B) σ σ * and σ π electron delocalisations. (C) σ p (filled) and σ π electron delocalisations. (D) p(filled) σ * and σ π * electron delocalisations.. (A) H + CH C CH σ p(empty) delocalisation CH CH CH CH (σ π * electron) delocalization.. The pair(s) of coordination complexes / ions exhibiting the same kind of isomerism is (are) (A) [Cr(NH ) 5 Cl]Cl and [Cr(NH ) 4 Cl ]Cl (B) [Co(NH ) 4 Cl ] + and [Pt(NH ) (H O)Cl] + (C) [CoBr Cl ] and [PtBr Cl ] (D) [Pt(NH ) (NO )]Cl and [Pt(NH ) Cl]Br. (B), (D) Factual. 4

JEE ADVANCE PREVIOUS YEAR PAPER Paper-I. Name of the Student:.. Father s Name:. Signature:. Branch Name: Contact No:.

JEE Advance 016 Time:3Hr JEE ADVANCE PREVIOUS YEAR PAPER-013 Paper-I Topics Covered: Maximum Marks: 40 Physics Chemistry Mathematics : Full Syllabus : Full Syllabus : Full Syllabus Important Instruction: