FIITJEE PET XII (EXTENDED-2)

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1 FIITJEE PET XII (EXTENDED-) MAINS DATE: Time: 3 hours Maximum Marks: 360 INSTRUCTIONS: Instructions to the Caniates. This Test Booklet consists of 90 questions. Use Blue/Black ball Point Pen only for writing particulars an bubbling of OMR.. For each correct answer 4 Marks will aware an for each wrong answer Mark will be eucte. 3. Attempt all questions. 4. In case you have not arkene any bubble you will be aware 0 mark for that question. 5. Use of calculator/logarithmic table is not permitte. Don t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowe to continue the exam. NAME: ENROLLMENT NO.:

2 PET-XII (EXTENDED-)-08-MPC-. If A = (,, 3), B = (, 4, ) an AOB =, where O is the origin, then is (A) 6 (B) 6 (C) 0 (D). If the points A(,, ), B(, 6, ) an C(,, 4) are collinear, then is (A) 0 (B) (C) (D) 3. The equation of the straight line passing through the origin an perpenicular to the lines x y z x y z an has the equation 3 3 (A) x = y = z (B) x y z (C) x y z (D) none of these If A = (p, q, r) an B = (p, q, r) are two points on the line x = y = z such that OA = a, OB = b, then pp + qq + rr is equal to (A) a + b (B) ab (C) a b (D) none of these 5. x y z x y z If the lines an are parallel to each other, then the value of the pair (, ) is (A), 3 (B), 3 (C), 3 (D) cannot be foun r r 6. The equation of the locus of the point,, 4 3, where r R, is given by (A) x y z (B) x y z (C) 4x 3y = 7 (D) z = If the line x y z lies in the plane 3x y + 5z = 0, then is 7 (A) (B) (C) 5 (D) no possible value 5 7

3 PET-XII (EXTENDED-)-08-MPC-3 8. The equations of the line of intersection of the planes x + y + z = an 3x y + z = 5 in symmetric form are 7 7 x y y z z (A) 4 4 x (B) x 3y 3z 7 (C) (D) none of these 4 9. The equations of the perpenicular from the point (, 4, ) to the plane 7x y + 3z = are (A) x 5 y z 4 (B) x y 4 z (C) x y 4 z (D) none of these 4 0. The istance of the point (, 0, 3) from the plane 5x y = 0 is (A) 0 (B) 46 (C) (D) none of these. If a line makes angles of 60 an 45 with the positive irections of the x-axis an y-axis respectively, then the acute angle between the line an the z-axis is (A) 60 (B) 45 (C) 75 (D) 5. Let A = (, 3, ), B = (,, ). A point C on the y-axis such that AB BC has the coorinates (A),0, 4 4 (B) 0,,0 9 (C) 0,,0 4 (D) 0,, The angle between the lines joining the points (,, 0), 3, 3,3 an (0,, 0),, 3, cos 8. If is an integer, then its value is (A) (B) 0 (C) (D) 4. The points A(,, ), B(, 5, ), C(4, 4, 3) an D(3,, ) are (A) collinear (B) vertices of a rectangle (C) vertices of a square (D) vertices of a rhombus is 5. Let P r (x, y, z ); r =,, 3; be three points where x, x, x 3 ; y, y, y 3 an z, z, z 3 are each in G.P with the same common ratio. Then P, P, P 3 are (A) coplanar points (B) collinear points (C) vertices of an equilateral triangle (D) none of these

4 PET-XII (EXTENDED-)-08-MPC-4 6. Given that f(x) = x /x, x > 0 has the maximum value at x = e, then (A) e > e (B) e < e (C) e = e (D) e e 7. The smallest value of the polynomial x 3 8x + 96x in the interval [0, 9] is (A) 6 (B) 0 (C) 35 (D) The function f(x) = x + 4 x has (A) a local maxima at x = an local minima at x = (B) local minima at x = an local maxima at x = (C) absolute maxima at x = an absolute minima at x = (D) absolute minima at x = an absolute maxima at x = 9. If a ifferentiable function f(x) has a relative minima at x = 0, then the function y = f, y = f(x) + ax + b has a relative minimum at x = 0 for (A) all a an all b (B) all b if a = 0 (C) all b > 0 (D) all a > 0 0. Let f(x) have secon erivative at c such that f(c) = 0 an f(c) > 0, then c is a point of (A) local maxima (B) local minima (C) point of inflexion (D) none of these. Let f(x) have secon erivative at c such that f(c) = 0 an f(c) < 0, then c is a point of (A) local minima (B) local maxima (C) point of inflexion (D) none of these. Let f have erivative of all orers at x = c such f(c) = f(c) = 0 an f(c) < 0, then for the function f, the point c is a point of (A) local minima (B) local maxima (C) point of inflexion (D) none of these 3. At x = 5, f(x) = sin 3x + 3 cos 3x is 6 (A) maximum (B) minimum (C) zero (D) none of these 4. Minimum value of f(x) = sin x in x is (A) 0 (B) (C) (D) none of these 5. For the curve y = xe x, the point (A) x = is a minimum (C) x = 0 is a minimum (B) x = is a maximum (D) x = 0 is a maximum

5 PET-XII (EXTENDED-)-08-MPC-5 6. f(x) = + [cos x]x, in 0 < x (A) is continuous in 0, (C) has a minimum value 0 (B) has a maximum value (D) is not ifferentiable at x = a b 7. The minimum raius vector of the curve = is of length x y (A) a b (B) a + b (C) a + b (D) none of these 8. A cone of maximum volume is inscribe in a given sphere. Then the ratio of the height of the cone to the iameter of the sphere is (A) 3 (B) 3 4 (C) 3 (D) 4 9. The largest interval for which x x 9 + x 4 x + > 0 is (A) 4 < x 0 (B) 0 < x < (C) 00 < x < 00 (D) < x < 30. Two towns A an B are 60km apart. A school is to be built to serve 50 stuents in town A an 50 stuents in town B. If the total istance to be travele by all 00 stuents is to be as small as possible, then the school shoul be built at (A) town B (B) 45km from town A (C) town A (D) 45km from town B 3. In the circuit shown in figure, the cell is ieal, with e.m.f = 5 V. Each resistance is of 3. The potential ifference across the capacitor is (A) 0 (B) 4 V (C) 3 V (D) V 3. In the shown network, the ratio of charges on capacitors of capacitances 5 F, 3 F in steay state will be (A) : (B) : (C) : (D) None 5F 3 3F 0 V 4

6 PET-XII (EXTENDED-)-08-MPC Capacitor C of capacitance F an capacitor C of capacitance F are separately charge fully by a common battery. The two capacitors are then separately allowe to ischarge through equal resistors at time t 0. (A) the current in each of the two ischarging circuits is zero at t 0 (B) the currents in the two ischarging circuits at t 0 are equal but not zero (C) the currents in the two ischarging circuits at t 0 are unequal (D) capacitor C, loses 50% of its initial charge in the same time C loses 50% of its initial charge 34. Four capacitors with capacitances C = F, C =.5 F, C 3 =.5 F an C 4 = 0.5 F are connecte as shown an are connecte to a 30 volt source. The potential ifference between points a an b is (A) 5 V (B) 9 V (C) 0 V (D) 3 V A C a C C 3 b C 4 30V B 35. The plates of a parallel plate capacitor are charge up to 00 volt. A mm thick plate is inserte between the plates, then to maintain the same potential ifference, the istance between the capacitor plates is increase by.6 mm. The ielectric constant of the plate is (A) 5 (B).5 (C) 4 (D) Seven capacitors each of capacitance F are to be connecte to obtain a capacitance of (0/) F. Which of the following combinations is possible? (A) 5 in parallel, in series (B) 4 in parallel, 3 in series (C) 3 in parallel, 4 in series (D) in parallel, 5 in series 37. Conenser A has a capacity of 5F when it is fille with a meium of ielectric constant 5. Another conenser B has a capacity of F with air between the plates. Both are charge separately by a battery of 00V. After charging, both are connecte in parallel without the battery an the ielectric material being remove. The common potential is now (A) 400V (B) 800V (C) 00V (D) 600V 38. Seven capacitors, a switch S an a source of e.m.f. are connecte as shown in the figure. Initially, S is open an all capacitors are uncharge. After S is close an steay state is attaine, the potential ifference in volt across the plates of the capacitor A is (A) (B) 5 (C) 7 (D) 9 A 50V + 7F 8F 3F F 4F F

7 PET-XII (EXTENDED-)-08-MPC A ielectric is place in between the two parallel plates of a capacitor as shown in figure, the ielectric constant of the ielectric being K. If the initial capacity is C, then the new capacity will be (A) KC (B) (K + )C (C) C(K + )/ (D) (K )C K 40. Two ientical capacitors A an B are charge to the same potential an then mae to ischarge through resistances R A an R B respectively, with R A >R B (A) A will require greater time than B to ischarge completely. (B) More heat will be prouce in A than in B. (C) more heat will be prouce in B than in A. (D) All the above options are incorrect. 4. Two spherical conuctors A an B of raii a an b (b > a) are place concentrically in air. The two are connecte by a copper wire as shown in figure. Then the equivalent capacitance of the system is 4 (A) 0ab (B) 4 0 ( a b) (C) 4 0b (D) 4 0a ( b a) B b A a 4. Six metallic plates each with a surface area of one sie A, are place at a istance from each other. The alternate plates are connecte to points P an Q as shown in figure. The capacitance of the system is (A) A 0 (B) 5 A 0 (C) 6 A 0 P (D) A Q 43. Three uncharge capacitors of capacitance C, C an C 3 are connecte as shown in figure tone another an to points A, B an D at potentials V A, V B an V D. Then the potential at O will be (A) V V V A B D C C C 3 (B) V C V C V C A B D 3 C C C 3 (C) V V V V V V A B B D D A C C C 3 (D) B C A O C VVV A B D C 3 D C C C C C C 3 3

8 PET-XII (EXTENDED-)-08-MPC Eight rops of mercury of equal raii an each possessing the same charge combine to form a big rop. The capacitance of this big rop as compare to that of each smaller rop is (A) times (B) 4 times (C) 8 times (D) 6 times 45. The capacitor shown in the figure has been charge to a potential ifference of V volt so that it carries a charge CV with both the switches S an S remaining open. Switch S is close at t = 0. What is charge on capacitor at t = R C. t t R C RC (A) q CVe (B) q CVe t t R C RC (C) q CVe (D) q CVe E S S C R R 46. Two ientical capacitors an are connecte in series to a battery as shown in the figure. Capacitor contains a ielectric slab of ielectric constant K as shown. Q an Q are the charges store in the capacitors. Now the ielectric slab is remove an the corresponing charges are Q an Q. Then (A) Q Q K K (B) Q Q K (C) Q Q K K (D) Q Q K E 47. Three very large plates are given charges as shown in the figure. If the cross-sectional area of each plate is the same, the final charge istribution on plate C is (A) +5Q on the inner surface, +5Q on the outer surface (B) +6Q on the inner surface, +4Q on the outer surface (C) +7Q on the inner surface, +3Q on the outer surface (D) +8Q on the inner surface, +Q on the outer surface Q 5Q 0Q A B C Inner Surface Outer Surface 48. The expression for the equivalent capacitance of the system shown is (A is the cross-sectional area of one of the plates) (A) 0 A/3 (B) 3 0 A/ (C) 0 A/6 (D) none of these a a a 3 3a

9 PET-XII (EXTENDED-)-08-MPC Fin equivalent capacitance between points A an B. [Assume each conucting plate is having same imensions 0 an neglect the thickness of the plate, A 7 F, where A is area of plates] (A) 7 F (B) F (C) F (D) 5 F B A 50. A f capacitor C is charge to a voltage 00 V an a 4 F capacitor C is charge to a voltage 50V. The capacitors are then connecte in parallel. What is the loss of energy ue to parallel connection? (A).7 J (B) 0.7 J (C).7 x 0 J (D).7 x 0 3 J 5. Two insulating plates are both uniformly charge in such a way that the potential ifference between them is V V = 0 volt (i.e. plate is at a higher potential). The plates are separate by = 0. m an can be treate as infinitely large. An electron is release from rest on the inner surface of plate. What is its spee when it hits plate? (e =.6 x 0 9 C, m e = 9. x 0 3 kg) (A) 3 x 0 9 m/s (B).65 x 0 6 m/s (C) 7.0 x 0 m/s (D).87 x 0 6 m/s 0. m Y X 5. A parallel plate conenser with the plate are A an separation is fille with two ielectric material as shown in the ajoining figure. The ielectric constants are K an K respectively. The capacitance will be / K / K (A) 0A (K K ) (B) A K K KK 0 (C) 0A KK K K (D) AK K KK For the circuit shown in the figure, the charge on 4 F capacitor is (A) 30 C (B) 40 C (C) 4 C (D) 54 C 4 F F 5 F 3 F + 0 V

10 PET-XII (EXTENDED-)-08-MPC The time constant of charging of the circuit shown in figure is: (A) 3 RC (B) RC (C) 3 RC (D) 3 RC 55. In the circuit shown in figure C = C. Capacitor C is charge to a potential of V. The current in the circuit just after the switch S is close is: (A) zero (C) infinite (B) V R V (D) R 56. A 4F capacitor, a resistance of.5 M is in series with V battery. Fin the time after which ifference across the capacitor is equal to potential the potential ifference across the resistor: [Given In() = 0.693] (A 3.86 s (B 6.93 s (C 7 s (D None 57. A capacitor of capacitance C is allowe to ischarge through a resistance R. The net charge flown through resistance uring one time constant is : (I 0 is the maximum current) (A CRI 0 (B CRI 0 (C CRI 0 (D None e e 58. In the given circuit with steay current, the potential rop across the capacitor must be: (A) V (B) V/ (C) V/3 (D) V/3 59. A capacitor is charge using an external battery with a resistance x in series. The ashe line shows the variation of ln(i) with respect to time. If the resistance is change to x, the new graph will be (A) P (B) Q (C) R (D) S

11 PET-XII (EXTENDED-)-08-MPC- 60. A Capacitor is connecte to a V battery through a resistance of 00Ω. It is foun that the potential ifference across the capacitor rises to 4.0 V in s. Fin the capacitance of the capacitor. 00 (A) F log.5 0 (B) F log.5 (C) F log.5 0. (D) F log.5 e e 6. Which of the following is a buffer solution? (A) HNO 3 + NaNO 3 (B) CH 3 COOH + HCOONa (C) HNO + KNO (D) H 3 PO 4 + Na 3 PO 4 6. The ph of solution on mixing equal volume of solution having ph = 3 an ph = 4. [log 5.5 = ] (A) 3.4 (B) 3.5 (C) 3.6 (D) The percent of hyrolysis of 0.0 M KCN solution is (K a of HCN = 9 x 0 0 ) (A) 3.3 (B) 4.0 (C).0 (D) Calculate the ph of 6.66 x 0 3 M solution of Al(OH) 3. Its first issociation is 00% whereas secon issociation is 50% an thir issociation is negligible. (A) (B) (C) (D) A certain buffer contains equal concentration of X an HX an K b for X is 0 0. The poh of buffer solution is (A) 4 (B) 7 (C) 0 (D) The issociation constants of HF an HNO are 6.0 x 0 4 an.0 x 0 4 respectively. The ph of a solution which is a mixture of 0.5 mol L of HF an 0.5 M HNO is (A).00 (B).70 (C).30 (D) Nicotinic aci (K a =.4 x 0 5 ) is represente by the formula HNic. Calculate the percentage issociation in a solution which contains 0. mole of nicotinic aci per.0 litre of solution. (A).67% (B).0% (C) 3.8% (D) 5.% 68. A solution of ammonia use for cleaning the glass winows was foun to be 0% ammonia by mass an having a ensity of g/ml. The ph of the solution is (K b of NH 4 OH =.8 x 0 5 ) Assume 99 0 (A) 0 (B) (C) 8 (D) The K a values of formic aci an acetic aci are respectively. 770 an The ratio of the aci strength of 0.M aci is (A) 0 (B) 3.78 (C) 0.3 (D) 0. e e

12 PET-XII (EXTENDED-)-08-MPC- 70. A weak aci HX has pk a = 5. The percent egree of hyrolysis of 0. M solution of salt NaX is (A) 0.00% (B) 0.0% (C) 0. % (D) 0.5% 7. The ph of a M H SO 4 solution is (A) 5.0 (B).0 (C).3 (D) 3.3 Ka 7. Given, HF + H O H3O Which relation is correct? Kb F F H O HF OH (A) K b = K w (B) Kb (C) Ka Kb Kw (D) K w K a K b K w 73. What is the effect of aing soium acetate crystals to L of a 0.50 M acetic aci solution? (A) The concentration of the soium ions ecreases (B) The concentration of the hyrogen ions ecreases (C) The concentration of the hyrogen ions increases (D) The concentrations of both the soium an hyrogen ions ecrease. 74. The pk a of acetyl salicylic aci (aspirin) is 3.5. The ph of gastric juice in the human stomach is about.5 an that in the small intestine is about 8.0. Aspirin will be (A) un ionize in the small intestine an in the stomach (B) completely ionize in the small intestine an in the stomach (C) ionize in the stomach an almost un ionize in the small intestine (D) ionize in the small intestine an almost un ionize in the stomach. 75. Which of the following combinations forms a buffer solution? (A) Strong aci an its salt with a weak base (B) Weak aci an its salt with a strong base (C) Weak aci an its salt with a weak base (D) Strong aci an its salt with a strong base 76. The buffer which controls the ph of bloo is a mixture of (A) HCl an Cl (B) H CO 3 an HCO 3 (C) H CO 3 an Cl (D) HCl an HCO Which of the following is the correct quaratic form of the Ostwal s ilution law equation? (K = aci issociation constant) (A) C K K 0 (B) C K K 0 (C) C K K 0 (D) C K K 0

13 PET-XII (EXTENDED-)-08-MPC Ionic issociation of acetic aci is represente as : CH COOH H O CH COO H O Accoring to Lowry an Bronste, the reaction possesses : (A) an aci an three bases (B) two acis an two bases (C) an aci an a base (D) three acis an a base 79. (egree of hyrolysis) of ammonium benzoate can be calculate by the formula k (A) w k (B) w k (C) w k (D) h kac ka kb kb c c 80. Of the four values of ph given below, which is closest to the ph of M carbonic aci? 7 Ka 4 0, Ka 0 (A) 4.4 (B) 5.0 (C) 5.4 (D) Calculate the ph of solution obtaine by mixing equal volume of 0.05 M HOCl & 0. M CH 3 COOH 4 solution given that Ka HOCl 0 5, K a CH3COOH 0 (A).5 (B).69 (C) 3.5 (D) ml of 0. M NaOH is ae to 00 ml of a 0. M CH 3 COOH solution. The ph of the resulting solution will be (K a for CH 3 COOH =.8 x 0 5 ) (A) 4.74 (B) 5.74 (C) 3.74 (D) When water is heate to 65C, the neutral ph changes to 6.7. The ionic prouct of water at this temperature is (A) x 0 4 (B) 4 x 0 4 (C) 5 x 0 3 (D).8 x Equal volumes of two solutions of ph 5 an 3 are mixe an ilute 0 times. The ph of the resultant solution is (A) 4 (B) 0.4 (C) 4.3 (D) 3.3

14 PET-XII (EXTENDED-)-08-MPC ml of one normal HCl is mixe with 00 ml of NaOH solution containing 3g of NaOH per litre. The ph value of the resultant solution is (A) (B) (C) (D) ph of a solution =. Calculate the no. of hyrogen ions present per ml of the solution. (A) 6.0 x 0 9 (B) 6.0 x 0 (C) 6.0 x 0 0 (D) 6.0 x A solution containing H + ions is ilute 000 times. Then the ph of the solution (A) increase by 3 (B) increases 3 times (C) ecreases 3 times (D) ecreases to At 90 C, pure water has [H + ] = 0 6 moles/lit. What is the value of K w at this temperature? (A) 0 6 (B) 0 (C) 0 4 (D) Choose correct statements (I) NH 3 is a lewis base (II) HCl (aq) is an Arhenius aci (A) only (I) (B) only (II) (C) both (I) & (II) (D) none mole of NaOH was ae to 0 litre of water at 5 0 C. The ph will change by (A) 4 (B) 3 (C) (D) 7

15 PET-XII (EXTENDED-)-08-MPC-5 FIITJEE PET XII (EXTENDED-) MAINS_ANSWERS DATE: MATHEMATICS PHYSICS CHEMISTRY. D. A 3. A 4. B 5. C 6. B 7. B 8. B 9. A 0. A. A. C 3. BONUS 4. B 5. B 6. A 7. B 8. B 9. B 0. B. B. C 3. D 4. C 5. A 6. A 7. B 8. A 9. D 30. C 3. BONUS 3. A 33. B 34. D 35. A 36. A 37. B 38. BONUS 39. C 40. D 4. C 4. B 43. B 44. A 45. A 46. C 47. C 48. D 49. B 50. D 5. B 5. C 53. C 54. B 55. D 56. B 57. B 58. C 59. B 60. BONUS 6. C 6. C 63. A 64. B 65. C 66. B 67. A 68. B 69. B 70. B 7. B 7. C 73. B 74. D 75. B 76. B 77. A 78. B 79. B 80. A 8. B 8. A 83. B 84. C 85. A 86. A 87. A 88. B 89. C 90. A

1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity

AP Physics Multiple Choice Practice Electrostatics 1. The electron volt is a measure of (A) charge (B) energy (C) impulse (D) momentum (E) velocity. A soli conucting sphere is given a positive charge Q.