TEST - 3 (Paper - II)

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3 Test - 3 (Paper-II) PART - I : PHYSICS SECTION - 1 Only One Option Correct Type All India Aakash Test Series for JEE (Advanced)-014 Time : 3 Hrs. MM : 186 TEST - 3 (Paper - II) This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A small ring of radius r rolls without slipping inside a fixed hollow cylinder of radius R with small oscillations about stable equilibrium as shown in the figure. The frequency of oscillation is R r 1 g (A) π ( R r) 1 g (B) π ( R r) 1 3 g (C) π ( R r) 1 g (D) π ( R r). The radii of the core and that of the planet are R and 3R and the densities of core of planet and that of outer shell are ρ and ρ. If the gravitational acceleration is same at surface and at a depth R from the surface, then ratio ρ ρ is 3R (A) 1 : 5 (B) 13 : 4 (C) 15 : 1 (D) 17 : 3 1/19

4 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) GM 3. A planet of mass M and radius R rotates with an angular velocity ω = 3 R. A tunnel lies in the equatorial plane and passes through the centre of the planet. The acceleration of an object w.r.t. tunnel at a distance x from the centre is GMx (A) 3 R GMx (C) 3 R GMx (B) 3 R (D) Zero 4. A rectangular tank of height h filled with water is placed near the bottom of a plane inclined at an angle 45 with horizontal. At height 10 m from bottom a hole is made such that stream coming out from hole strikes the inclined plane normally. Then h is nearly h 10 m 45 (A) 19. m (C) 15. m (B) 17.3 m (D) 13.3 m 5. A thin uniform ring of cross-sectional area a and radius R is rotated about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If density of wire and Young's modulus of elasticity are ρ and Y respectively, then the ratio of its K.E. and elastic P.E. is Y (A) ρr ω Y (B) 3ρR ω Y (C) ρr ω Y (D) ρr ω /19

5 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced) Air is blown across the top of the tube as shown in the figure such that water rises to a height h. If the speed of air is 5 m/s, then h is equal to [Take density of air is 1.8 kg/m 3 and neglect surface tension] h (A) 1.3 cm (C) 5.6 cm (B).04 cm (D) 7.0 cm SECTION - One or More Options Correct Type This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE are correct. 7. Two springs of spring constants k 1 and k are connected in series such that one end is fixed and the other is connected to a block of mass M as shown in figure. The block is pulled to right from its equilibrium position by a distance x 0 and released, select the correct alternative(s) k 1 A k M (A) Displacement of A is (B) Displacement of A is (C) Displacement of A is x0 kx 1 0 k + k 1 kx 0 k + k 1 (D) Time period of resulting oscillatory motion of the block is Mk ( + k) kk π 1 1 3/19

6 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 8. A steel wire of diameter 0.8 mm and length m is stretched between rigid support separated by horizontal distance of m. Now, a load is hung at the centre to produce a stress of N/m. Then [Y = 10 1 N/m ] (A) The displacement of point of suspension is nearly 14. cm (B) The elongation in the wire is cm (C) The elastic potential energy in the wire under this load is 16 πj (D) The elastic potential energy in the wire under this load is 80. J 9. A solid sphere of mass 3 kg and specific gravity 0.8 is held stationary relative to a tank filled with water as shown in the figure. The tank accelerates vertically upward with a = 4 m/s. [Take g = 10 m/s ] a (A) The tension in the thread increases due to acceleration of tank (B) The tension in the thread decreases due to acceleration of tank (C) If the thread snaps, the acceleration of the sphere w.r.t tank is.5 m/s (D) If the thread snaps the acceleration of the sphere w.r.t. tank is 3.5 m/s 10. A block A of mass 1 kg is suspended by an inextensible thread passing over a solid, uniform cylinder B of radius 5 cm and mass 5 kg hinged to rotate without friction. The other end of the thread is attached with a spring as shown in the figure. During the motion of the block, thread does not slip over the cylinder. k = 00 N/m B A (A) When the block is in equilibrium, the elongation in the spring is 5 cm (B) When the block is in equilibrium, the elongation in the spring is 10 cm (C) If block is pulled down slowly and released, then the time period of oscillation is (D) If block is pulled down slowly and released, then the time period of oscillation is 5 3 π s 7 10 π s 4/19

7 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced) A large tank having a small hole on its wall is kept on a smooth horizontal surface. The tank is held with the help of a wire attached to wall as shown in the figure. H h v (A) The speed of efflux v increases parabolically with increase in h (B) x first increase and then decreases with increase in h (C) The tension in the wire increases linearly with h (D) The maximum value of x is H SECTION - 3 Paragraph Type This section contains paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 1 to 13 A spring of force constant 80 N/m is fixed with top of left limb of a U tube and piston of mass 30 g is attached with lower end of the spring as shown in the figure. The cross-sectional area of the tube is 1 cm. Water is poured into right limb till elongation of the spring reduces to 3 mm. x h 1. The difference h between levels of water in right limb and lower face of the piston is (A) 15 mm (B) 30 mm (C) 45 mm (D) 60 mm 5/19

8 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 13. If mass of the water column is 100 g then time period of oscillation is [Neglect atmospheric pressure] (A) π (B) π (C) π (D) π Paragraph for Question Nos. 14 to 15 According to Canton's law, if V 0 be the volume of a liquid when subject to no pressure upon its surface and ρ 0 be the density; V the volume when the pressure is P and the density ρ, then Here c is the coefficient of compression 14. The value of c depends on the nature of liquid and (A) The unit of measurement of pressure (B) The unit of measurement of volume V 0 V = V 0 cp (C) The unit of measurement of pressure as well as volume (D) Independent of system of units 15. Assume that water obey Canton's law. Taking P 0 as atmospheric pressure at sea level, the pressure P of water at a depth y below the surface is given as (A) P = P 0 + ρ 0 g y (B) ρ0gy P = P0 + c (C) cp0 0 0 c P P = P +ρ gz cp0 (D) P = P0 +ρ0gz 6/19

9 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 SECTION - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 16. The curved surface of a vessel has shape of a truncated cone. The radii of top and bottom are r 1 = cm and r = 10 cm. The height is 15 cm. The vessel is full of water and placed on a smooth horizontal plane. The numerical values of physical quantities in Column I are given in Column II. Match Column I and Column II r 1 h = 15 cm r Column I Column II (P) Force on liquid due to walls of the vessel (N) (1) 47.1 (Q) Force on bottom of the vessel (N) () 0.36 (R) If a small hole is made on wall near bottom, (3) 5 then range of water jet is (in cm) (S) If area of cross-section of hole is cm then (4) 7.6 the horizontal force required to keep vessel in equilibrium (N) Codes : P Q R S (A) (B) (C) (D) /19

10 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 17. A block of mass m is connected to a spring and oscillating as shown. When the block is at one of its extreme position, a wax piece of same mass m falls and sticks to the block. Match the columns. m (P) (Q) Column I New maximum acceleration Old maximum acceleration New maximum velocity Old maximum velocity (1) 1 () Column II (R) New time period Old time period (3) 1 (S) Codes : New amplitude Old amplitude P Q R S (A) (B) (C) (D) (4) 1 SECTION - 5 Integer Value Correct Type This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following : X Y Z /19

11 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced) A liquid of density ρ is poured into a U-tube in which the radius of right hand limb is twice the radius of left hand one. The level of the liquid is at distance l from the upper end of the tube. If the left limb is filled to the top with liquid of density ρ. If the rise in the right limb is l n then find n. 19. A ball made up of a metal of density 6ρ with a cavity weighs m in air and m in a liquid of density ρ. If volume of 3 cavity is m xρ then find the value of x. 0. A thin uniform rod of length a has mass λ per unit length. If the magnitude of gravitational potential at a distance a from the centre along the axis of rod is Gλlnx then find the value of x. PART - II : CHEMISTRY SECTION - 1 Only One Option Correct Type This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. The molar conductivities at infinite dilution (π m ) for Na SO 4, K SO 4, KCl, HCl and HCOONa at 300 K are 60, 308, 150, 46 and 105 S/cm /mol respectively. Hence π m for HCOOH acid at same temperature (in S/cm /mol) is (A) 49 (B) 531 (C) 405 (D) 381. Langmuir adsorption isotherm is given by KP θ = where P is the pressure of adsorbate gas. The Langmuir 1 + KP adsorption isotherm for a diatomic gas A undergoing dissociative adorption is (A) KP 1 + KP (B) KP 1 + KP (C) (KP) (KP) 1 (D) (KP) 1 + (KP) 9/19

12 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 3. N + n x + H, x is moving with 6.03 m/s then λ associated with that particle is (A) m (B) m (C) m (D) m 4. Cu + ion react with Fe + ions according to the following reaction Cu + Fe Cu + Fe (Cu + /Cu = 0.34 V, Fe +3 /Fe + = V) At equilibrium concentration of Cu + ion is not changed by addition of (A) Cu + (B) Fe + (C) Fe +3 (D) Cu 5. In cubic close packing, distance between two closest layer is (edge length is 'a') (A) a (B) a (C) a (D) 0.50 a 6. For a given cell reaction, which of the following is not a state function property? MnO MnO Mn ΔH1 ΔH + 4 ΔG1 ΔG o ΔE1 o ΔE (1) ΔH () ΔG (3) ΔE (4) ne where n = number of e involved (A) (1) & () (C) (4) only (B) (3) only (D) (3) & (4) only SECTION - One or More Options Correct Type This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE are correct. 7. During electrolysis of NaCl aq. solution, the product which are expected to be formed in solution is (A) Cl (B) NaCl (C) H (D) NaClO 3 10/19

13 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced) Reduction potential of the hydrogen electrode change on addition in container is/are Ag Rod 1 M AgNO 3 (A) HCl (B) AgNO 3 (C) NaBr (D) HNO 3 9. A and B form non-ideal solution showing negative deviation. It form azeotropic mixture at 60 : 40 by mole then correct statement(s) is/are (P A > P B ) (A) From a solution of x A = 0., pure A can be obtained as distillate. (B) On heating solution of x A = 0.8, pure A can be obtained. (C) On heating any composition of solution we get azeotrope as residue. (D) On heating a solution of x A = 0.5, we can obtain pure A and pure B. 30. Which of the solid is covalent? (A) Graphite (B) Diamond (C) Ice (D) NaCl 31. Choose the correct statement regarding critical micellisation concentration (A) For soap, CMC is 10 3 to 10 4 M (B) At low temperature, solubility of those solute which can form micelles at CMC is low (C) During micelle formation colligative property is reversed (D) After CMC, equivalent conductance abruptly decrease SECTION - 3 Paragraph Type This section contains paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D). For the opposite reaction A + B C + D K1 K 1 Paragraph for Question Nos. 3 to 33 Forward reaction has value E a = 100 kj/mol and K 1 = M 1 s 1. The equilibrium concentration of A, B, C and D are 1.0 M,.0 M, 5.0 M and 4.0 M respectively at 700 K. 11/19

14 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 3. Rate of backward reaction at equilibrium is (approximately) (A) 40 m/s (C) 69 m/s (B) 690 m/s (D) 400 m/s 33. Rate constant (K 1 ) for the forward reaction at 1000 K is (approximately) (A) M 1 min 1 (B) M 1 s 1 (C) M 1 s 1 (D) M 1 s 1 Paragraph for Question Nos. 34 to 35 Molar conductance of 0.1 M CH 3 COOH is Ω 1 cm /mol and π m of CH 3 COONa, NaCl and HCl is respectively 91, 16 and cm /mol. 34. Osmotic pressure of that solution at 300 K is (A).58 atm (C) 4 atm (B).65 atm (D).9 atm 35. Electrode potential of that hydrogen electrode dipped in that solution is (A) 0.59 V (C) Zero (B) V (D) 0.3 V SECTION - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 36. Match the following Column I Column II (P) de = 0 dt (1) ΔS (Q) de > 0 dt () ΔG = ΔH (R) (S) de < 0 dt de nf dt (3) ΔG > ΔH (4) ΔG < ΔH 1/19

15 Test - 3 (Paper-II) Codes : P Q R S (A) (B) (C) (D) Match the following Column I All India Aakash Test Series for JEE (Advanced)-014 Column II (P) (Q) (R) Th Pu U Pb Bi Pb (1) 5β () 7α (3) 6α (S) U U Codes : P Q R S (A) (B) (C) (D) (4) 6β SECTION - 5 Integer Value Correct Type This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following : X Y Z /19

16 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 38. For face centered atom, how many nearest touching neighbours are present in a single isolated fcc unit cell? 39. Method of preparation of colloidal solution is given below. How many solutions are negative? (1) AuCl 3 + 3HCHO + 3H O reduction () Sol of starch (3) 3 FeCl 3 Fe(OH) Colloidal sol (4) AgNO 3 + KI (excess) Colloidal sol (5) Basic dye stuffs (6) NaOH Fe(OH) 3 Colloidal sol (7) Acid dyes colloidal sol 40. How many pair among the following show positive deviation? (1) Acetone and benzene () HCl and water (3) Ethyl alcohol and water (4) CCl 4 and CHCl 3 (5) Ethyl chloride and ethyl bromide (6) Water and HClO 4 PART - III : MATHEMATICS SECTION - 1 Only One Option Correct Type This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 41. The value of sin47º + sin61º sin11º sin5º is equal to (A) cos54º (B) sin54º (C) cos83º (D) sin83º 4. If 1 sin x 1 sin x, then sin x lies in + 3 (A) (C) 1 1,, 1 1, 1 (B),1 (D) [ 1, 1] 14/19

17 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced) The sum of all the solutions of the equation 7cosx cos4x = 6 in the interval [0, 100π] is (A) 4950 π (C) 5000 π 44. If in a triangle (scalene) ABC, (A) A.P. (C) H.P. (B) 5050 π (D) 4900 π A cosb+ cosc = 4sin, then b, a, c are in (B) G.P. (D) A.G.P. 45. If the distances of the vertices of a triangle from the points of contact of the incircle with the sides be α, β, γ, and 46. If inradius of the triangle is 3, then the value of αβγ α+β + γ is (A) (B) 3 3 (C) 3 (D) 9 1 x + 4 sin sin <π 3 1+ x, then (A) 1 < x 0 (B) 0 x 1 (C) 1 < x < 1 (D) x R SECTION - One or More Options Correct Type This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE OR MORE are correct. 47. If α and β are acute angles such that α + β and α β satisfy the equation tan θ 4tanθ + 1 = 0, then (A) π α= (B) 4 π α= 6 (C) π β = 4 (D) π β = If in a triangle ABC, a = 5, b = 4, c = and D, E are the points on BC such that BD = DE = EC, CAE = θ, then (A) AE = (B) AE = 3 9 (C) 3 tanθ= (D) 8 59 cosθ= /19

18 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) 49. If I is the incentre of the triangle ABC; R 1, R and R 3 are the radii of the circumcircle of the triangles IBC, ICA and IAB respectively, then a A (A) R1 = sec b B (B) R = sec c C (C) R3 = sec (D) R 1 R R 3 = R r (where R and r are the circum-radius and in-radius of ΔABC respectively) 1 1 x 50. If α, β are two values of x satisfying the equation ( ) x tan tan 3 = 0 5 5, α > β, then (A) α+β= 5π 1 (B) 35π α β = 1 (C) 5π αβ = (D) 3α + 4β = If a, b, c are the sides of the ΔABC and a, b, c are the roots of x 3 lx + mx n = 0, then (A) cos A cosb cosc l + + = a b c n (B) acosa + bcosb + ccosc = 4 m l n (C) asina + bsinb + csinc = l n Δ, (where Δ is area of ΔABC) (D) sina sinb sinc = 3 8Δ n 16/19

19 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 SECTION - 3 Paragraph Type This section contains paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D). Paragraph for Question Nos. 5 to 53 ABC is a triangle in which a = 1, b = 6 and cos ( ) perpendicular to AD. Now, answer the followings : 5. Radius of the circumcircle of the triangle ABC is (A) A B =. AD is the median through A, BAD = θ, CL is 5 (B) 5 3 (C) 3 5 (D) L is the (A) Centroid of ΔABC (C) Orthocentre of ΔACD f(x) = sin{cot 1 (x+1)} cos(tan 1 x) a = cos(tan 1 (sin(cot 1 x))) b = sin(sin 1 x + cos 1 x) Now, Answer the followings : 54. The value of x, for which f(x) = 0 is 55. If (A) (B) Circumcentre of ΔACD (D) Incentre of ΔABC Paragraph for Question Nos. 54 to 55 1 (B) (C) 1 (D) 4 (A) (C) 6 a =, then the value of b equals (B) (D) /19

20 All India Aakash Test Series for JEE (Advanced)-014 Test - 3 (Paper-II) SECTION - 4 Matching Column Type This section contains multiple choice questions. Each question has matching Columns. The codes for the Columns have choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 56. A root of the equation on LHS satisfies RHS Column I Column II (P) 4sin x + sin x = 3 (1) tanx = 4 3 (Q) 3(1 + sinx) = 1 + cosx () tanx = 1 π = π (R) sin cos x 1 cos( sinx) (3) tanx = 1 (S) 7cos x + sinxcosx 3 = 0 (4) sinx = 1 Codes : P Q R S (A) (B) (C) (D) Match the number of real solutions from given equation in LHS to RHS Column I Column II (P) 6sin 1 (x 4x + 5) = π (1) 1 π 1 π 1 tan + cos x tan cos x 4 + = 4 (Q) 1 1 () (R) (S) tan x + tan tan x x = x x tan tan tan x 1 + = 4x x (3) 3 (4) 0 18/19

21 Test - 3 (Paper-II) All India Aakash Test Series for JEE (Advanced)-014 Codes : P Q R S (A) (B) (C) (D) SECTION - 5 Integer Value Correct Type This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example, if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will look like the following : X Y Z If sin A = x and sina sina sin3a sin4a = ax + bx 3 + cx 4 + dx 5, then the value of a + b + c + d is 59. In a triangle ABC, sides a, b, c are such that α+β a = and b c β = = α b c where α, β are two positive real numbers. If b+ c sinb sin C k = + 1, then k is a sinc sinb 60. The sides of a triangle are a 1, a, a + 1; where a is a natural number and a > 1. Its largest angle is twice the smallest. Then the value of a is. 19/19

24 Test - (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-014 TEST - (Paper - II) ANSWERS PHYSICS 1. (B). (D) 3. (D) 4. (C) 5. (D) 6. (C) 7. (A, B, C, D) 8. (A, B, C) 9. (A, C) 10. (A, B) 11. (A, B, C, D) 1. (C) 13. (D) 14. (B) 15. (A) 16. (C) 17. (B) 18. (5) 19. (4) 0. (3) CHEMISTRY 1. (B). (A) 3. (D) 4. (A) 5. (B) 6. (A) 7. (A, B, D) 8. (A, B, C) 9. (A, C) 30. (A, C, D) 31. (A, B, C) 3. (B) 33. (A) 34. (B) 35. (C) 36. (C) 37. (A) 38. (4) 39. (5) 40. (4) MATHEMATICS 41. (C) 4. (D) 43. (B) 44. (A) 45. (C) 46. (D) 47. (B, C) 48. (B, C) 49. (A) 50. (A, D) 51. (A, D) 5. (A) 53. (D) 54. (C) 55. (D) 56. (C) 57. (A) 58. (6) 59. (5) 60. (8) 1/1

IIT JEE PAPER The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part has 4 sections.

IIT JEE PAPER The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part has 4 sections. IIT JEE - 2009 PAPER 2 A. Question paper format: 1. The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part has 4 sections. 2. Section I contains 4 multiple choice questions.