FIITJEE PET XIII (EXTENDED)

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1 FIITJEE PET XIII (EXTENDED) MAINS DATE: Time: 3 hours Maximum Marks: 360 INSTRUCTIONS: Instructions to the Candidates 1. This Test Booklet consists of 90 questions. Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted. 3. Attempt all questions. 4. In case you have not darkened any bubble you will be awarded 0 mark for that question. 5. Use of calculator/logarithmic table is not permitted. Don t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam. NAME: ENROLLMENT NO.: FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

2 PET-XIII (EXTENDED)-018-MPC- 1. Let a,b,c be three unit vectors and ab ac 0. If the angle between b and c is, then 3 a b c is equal to a b c b c a c a b. If a b c = 1, then is equal to c a b a b c b c a If a,b,c are three noncoplanar vectors represented by concurrent edges of a parallelepiped of volume 4, then a b bc b cc a c aa b is equal to (D) 0 4. If a,b,c are three noncoplanar nonzero vectors, then a abc a bc a a ca b is equal to b c a a c a b b a b c c 5. Let r be a vector perpendicular to a b c, where a b c then + m + n is =. If r b c mc a ma b, If a,b,c are any three vectors in space then c bc a c b a is 3 a b c 0 a b c 7. If a,b,c are the noncoplanar vectors, then a b c a c a b is equal to 0 a b c 8. If b is a unit vector, then a bb ba b is equal to ab a ba 3 a b c (D) a b c a FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

3 PET-XIII (EXTENDED)-018-MPC-3 9. Let a,b,c be three unit vectors such that a b c and respectively, then = 3, = =, = 4 4 b c and the angles between a,c and a,b be 3 =, = Let a,b and c be three vectors having magnitudes, 1, 1 and respectively. If aac b 0, the acute angle between a and b is If a,b,c are noncoplanar nonzero vectors then abac bcba c ac b is equal to a b c a b c 0 a b ca b c 1. If a,b,c are three noncoplanar nonzero vectors and r is any vector in space, then abr c bcr a c ar b is equal to a b c r 3 a b c r a b c r 13. If a,b,c be three vectors such that a b c = 4, then ab bc c a is equal to b c b c b c is equal to b c b c b c 15. If AB b and AC c, then the length of the perpendicular from A to the line BC is b c b c b c b c 1 b c b c FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

4 PET-XIII (EXTENDED)-018-MPC The equation of the tangent to the curve y = e x at the point where the curve cuts the line x = 1 is x + y = e e(x + y) = 1 y + ex = The equation of the tangent to the curve y = be x/a where it cuts the y-axis is x y 1 a b x y a b 1 x y a b If the tangent to the curve x y a at any point on it cuts the axes OX and OY at P and Q respectively, then OP + OQ is a a 1 a c 19. If the line joining the points (0, 3) and (5, ) is a tangent to the curve y =, then the value of c is x The curve x a y n n = touches the line x y n n b a = at the point b (b, a) (a, b) (1, 1) (D) 1 1, b a 1. The sum of the intercepts made on the axis of coordinates by any tangent to the curve x y is equal to 4 8. The area bounded by the axes of reference and the normal to y = log e x at the point (1, 0) is 1 unit unit 1 unit 3. The normal to the curve x + y = 1 at the point (, ) cuts the curve again at, 9 9, 9 9 (, ) 4. Two cyclists start from the junction of two perpendicular roads, their velocities being 3v meter/minute and 4v meter/minute. The rate at which the two cyclists are separating is 7 v m/min 5v m/min v m/min FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

5 PET-XIII (EXTENDED)-018-MPC-5 5. A stick of length a cm rests against a vertical wall and the horizontal floor. If the foot of the stick slides with a constant velocity of b cm/s, then the magnitude of the velocity of the middle point of the stick when it is equally inclined with the floor and the wall, is 6. If y = b cm/ s x 0 t t 1 b cm / s ab cm/ s dt, then the rate of change of y with respect to x when x = 1, is On the curve x 3 = 1y the abscissa changes at a faster rate than the ordinate. Then x belongs to the interval (, ) ( 1, 1) (0, ) 8. A balloon is pumped at the rate of a cm 3 / minute. The rate of increase of its surface area when the radius is b cm, is a 4 b cm /min a b cm /min a b cm /min 9. x and y are the sides of two squares such that y = x x. The rate of change of the area of the second square with respect to that of the first square is (1 + x )x x 3x + 1 (x 3x + 1) 30. Let the equation of a curve be x = a( + sin ), y = a(1 cos ). If changes at a constant tate k, then the rate of change of the slope of the tangent to the curve at = 3 is k 3 k 3 k 31. Two identical charged spheres suspended from a common point by two massless strings of length are initially a distance d (d << ) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. The rate of change in velocity is so slow that the charged spheres may be considered to be in the state of equilibrium at all times. As a result the charges approach each other with a velocity v. Then, v as a function of distance x between them, is v x 1/ v x 1 1/ v x (D) v x FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

6 PET-XIII (EXTENDED)-018-MPC-6 3. The figure given below shows a charge + Q held on an insulating support S and enclosed by a hollow spherical conductor. O represents the centre of the spherical conductor and P is a point such that OP = x and SP = r. The electric field at point P will be 33. Capacity of an isolated sphere of radius r is increased n times when it is enclosed by an earthed concentric sphere of radius R. The ratio of their radii is: n n1 n n1 n n 1 (D) n 1 n1 34. In the given arrangement of parallel plates each plate has area A and distance between two consecutive plates is d. The thickness of the plates is negligible compared to the spacing between plates. Equivalent capacitance of the structure between X and Y is 40A 50A 70A d d d Y 70A (D) d K=5 K=3 K=6 X 35. All values of capacitances are in micro farads. The equivalent capacitance between A and B is 0 F 3 9 F 48 F (D) 0 FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

7 PET-XIII (EXTENDED)-018-MPC The equivalent capacity of the combination shown in figure is C C 3 C (D) C 37. A capacitor of capacitance 1 F withstands a maximum voltage of 6 kv, while another capacitor of capacitance F, the maximum voltage 4 kv. If they are connected in series, the combination can withstand a maximum of 6 kv 1 kv 10 kv (D) 9 kv 38. Two spherical conductors A and B of radii a and b (b> a) are placed concentrically in air. B is given a charge +Q and A is earthed. The equivalent capacitance of the system is: ab 40 b a 4 0b (D) 4 0 (a b) b 40 b a 39. Six metallic plates each with a surface area of one side A, are placed at a distance d from each other. The alternate plates are connected to points P and Q as shown in figure. The capacitance of the system is: 0 A d 50A d 60A d 0 (D) A 5d 40. A F capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch S is turned to position, is : 0% 0% 75% (D) 80% FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

8 PET-XIII (EXTENDED)-018-MPC The charge deposited on 4 F capacitor in the circuit is: 6 x 10 6 C 1 x 10 6 C 4 x 10 6 C (D) 36 x 10 6 C 4. A network of six identical capacitors, each of value C, is made as shown in the figure. The equivalent capacitance between the points A and B is: 4C 3 3C 4 3C (D) 3C 43. Three capacitors are connected with the source of electromotive force E as shown in the figure. Then, the energy drawn from the source is 1 CE 3 CE 1 CE 3CE (D) A charge +q is fixed at each of the points x = x 0, x = 3x 0, x = 5x 0, on the x axis and a charge q is fixed at each of the points x = x 0, x = 4x 0, x = 6x Here x 0 is a positive Q constant. Take the electric potential at a point due to a charge Q at a distance r from it to be. 40r Then, the potential at the origin due to the above system of charges is qe q qloge (D) 4 x 8 x log 4 x e 45. Electric potential is given by : V = 6x 8xy 8y + 6yz 4z. Electric field at the origin is 6i ˆ 8j ˆ 6i ˆ 8j ˆ ˆ i ˆ j (D) zero 46. Two identical small balls, each of mass, are suspended by two light inelastic conducting threads each of length l from the same fixed point support.if the distance (d) between two balls is very less then d is equal to 0 0 FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

9 PET-XIII (EXTENDED)-018-MPC If in the electric field of a point charge q, a charge is carried from A to B and A to C the work done in case I is greater than work done in case II the work done in case II is greater than work done in case I the work done in both the cases is same but not zero (D) the work done in both the cases is same and zero A C q B 48. Two small balls having equal positive charge Q on each are suspended by two insulating strings at equal length L meter, from a hook fixed to a stand. The whole set up is taken in a satellite into space where there is no gravity. Then the angle between two strings and tension in each string is kq kq kq kq 0,,, (D), L L 4L L 49. A small hole is drilled along the diameter of a solid non conducting sphere of radius R. Charge Q is uniformly distributed throughout the volume of the sphere. What minimum speed v 0 be imparted to a particle of charge q and mass m at A so that it reaches the diametrically opposite point B? The groove is frictionless. Qq 4 Rm 0 Qq Rm 0 (D) Qq 3 Rm 0 Qq 8 Rm 0 B x x x x x x x x x x x x x R x x x x x x x x x O v 0 A x q, m x x x x x x x x x x x x x x x x x x x 50. A thin non conducting spherical shell of radius R has charge density and uniformly distributed in two hemi spherical halves. Find the dipole moment due to the configuration. R 3 R 3 8R 3 (D) 4 R Consider the charge configuration and a spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to q 3 only positive charges all the charges (D) +q 1 and q 1 +q 1 q R + + q FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

PET-XIII (EXTENDED)-018-MPC-10 5. A system of two electric dipoles, each of dipole moment having magnitude P are arranged in the configuration shown in figure.

10 PET-XIII (EXTENDED)-018-MPC A system of two electric dipoles, each of dipole moment having magnitude P are arranged in the configuration shown in figure. The electrostatic interaction energy of this system of two dipoles is 5 kp 7kp kp (D) None of these a a 4a 53. A particle of mass m and charge Q is placed in an electric field E which varies with time t as E = E 0 sin t. It will undergo simple harmonic motion of amplitude QE m 0 QE m Variation of electrostatic potential along x-direction is shown in the graph. The correct statement about electric field is x component at point B is maximum x component at point A is towards positive x- axis x component at point C is along negative x- ax is (D) x component at point C is along positive x-axis 55. The figure shows a nonconducting ring which has positive and negative charge non uniformly distributed on it such that the total charge is zero. Which of the following statements is true? The potential at all the points on the axis will be zero. The electric field at all the points on the axis will be zero. The direction of electric field at all points on the axis will be along the axis. (D) If the ring is placed inside a uniform external electric field then net torque and force acting on the ring would be zero. 56. A short dipole p î is placed at origin in x- y plane. The locus of equipotential surface around the dipole if a constant electric field E î also exists through out the space is 1 k 40 x y z E kp x y z E kp / 3 1/ 3 x (D) none kp y E / 3 QE m 0 (D) QE 0 m FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

11 PET-XIII (EXTENDED)-018-MPC A wheel having mass m has charges +q and -q on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of uniform vertical electric field E = mg q mg q mgtan q (D) none 58. The surface charge density of a sphere of radius r is. It is placed at a point A. The electric field intensity at B due to this sphere is E. Another charged sphere of radius r is placed at B. If the intensity at the centre of A and B is E then the surface charge density of B is 7 3 (D) 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 potential difference appears between the two cylinders when a charge density is given to the inner cylinder. A potential difference appears between the two cylinders when a charge density is given to the outer cylinder. 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. 60. Two rods of length L each and charge density and are kept at angle to each other. Find dipole moment. L sin j L cos ˆj L tan ˆ j (D) L sin ˆj ˆ FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

12 PET-XIII (EXTENDED)-018-MPC For the non stoichiometric reaction A + B C + D, the following kinetic data were obtained in three separate experiments, all at 98 K. Initial rate of Initial concentration Initial concentration formation of C (mol L S ) 0.1 M 0.1 M 1. x M 0. M 1. x M 0.1 M.4 x 10 3 The rate law for the formation of C is : dc k A B dt dc k A dt dc k A B dt (D) dc k A B dt 6. The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be : (R = JK 1 mol 1 and log = 0.301) 48.6 kj mol kj mol kj mol 1 (D) 53.6 kj mol The rate of a chemical reaction doubles for every 10C rise of temperature. If the temperature is raised by 50C, the rate of the reaction increases by about 10 times 4 times 3 times (D) 64 times 64. A reactant forms two products : k 1 A B, Activation energy k A C, Activation energy Ea If 1 Ea 1 / RT k1 ke Ea 1 / RT k k1e E a 1 E a Ea, then k 1 and k are related as : Ea / RT 1 Ea / RT k1e k k e (D) k 65. The time for half life period of a certain reaction A products is 1 hour. When the initial concentration of the reactant A, is.0 mol L 1, how much time does it take for its concentration to come from 0.50 to 0.5 mol L 1 if it is a zero order reaction? 4h 0.5 h 0.5 h (D) 1 h FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

13 PET-XIII (EXTENDED)-018-MPC Consider the reaction, A + B products. When concentration of B alone was doubled, the half life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is (assume concentration in mol/l and time in second) L mol 1 s 1 no unit mol L 1 s 1 (D) s A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will remain unchanged triple increase by a factor of 4 (D) double 68. Rate of a reaction can be expressed by Arrhenius equation as : E / RT k Ae In this equation, E represents the energy above which all the colliding molecules will react the energy below which all colliding molecules will react the total energy of the reacting molecules at a temperature, T (D) The fraction of molecules with energy greater than the active activation energy of the reaction. 69. What is the effect of a tenfold increase in pressure on K p in the reaction? 3 N g 3H NH g At equilibrium : a tenfold increase no change a tenfold decrease (D) equal to K c mole each of H and I are reacted in an evacuated vessel at 445C, to establish the equilibrium H + I HI. The equilibrium constant of the reaction is 64. Then the amount of H remaining unreacted at equilibrium is (D) The equilibrium constant of the reaction is K 1, that for HIg H g I g H g I g HI g nhg & nig nhi g is K 3. Then the wrong statement is : K 1 K 1 K 1 K1 (D) K K n 3 K1 1 1 is K and that for n 3 K FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

14 PET-XIII (EXTENDED)-018-MPC A 1000 ml vessel contains M each of P, Q, R and S at equilibrium. If 1 M each of P and Q are taken out, the value of equilibrium constant for P + Q R + S at the same temperature would be 1 1 (D) Two moles of PCl 5 were heated to 7C in a closed two litre vessel, and the extent of dissociation at equilibrium was found to be 40%. The equilibrium constant K p of the reaction is 0.67 atm atm atm (D) atm 74. In the dissociation of AB as AB g ABg Bg, the equilibrium concentration of AB is 400 mm and equilibrium constant is 100 mm. The initial concentration of AB was 600 mm 00 mm 400 mm (D) 800 mm 75. Reactants A and B are mixed in the molar ratio 1 : 1.5 to establish the equilibrium A B C D. At equilibrium the concentrations of A and B are found to be equal. The equilibrium constant K C for the reaction is (D) 76. For a reaction to proceed in the backward direction, conditions for reaction quotient is Q C > K C Q C < K C Q C = K C (D) Q C = The ratio of K p to K C for the equilibrium reaction NH Cls NH g HCl g I atm mol I 1 atm 1 mol I atm mol (D) 1.6 x 10 3 I atm mol at 300 K is 78. AB 3 (g) is dissociates as AB 3 (g) AB (g) + 1 B (g). When the initial pressure of AB 3 is 800 torr and the total pressure developed at equilibrium is 900 torr. What fraction of AB 3 (g) is dissociated? 10% 0% 5% 79. The yield of product in the reaction low temperature and high pressure low temperature and low pressure A g B g C g QkJ will be higher at high temperature and high pressure (D) high temperature and low pressure FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

15 PET-XIII (EXTENDED)-018-MPC For which one of the following gaseous equilibria will an increase in pressure increase the yield of the product?( all are in the gaseous state) HI H + I SO + O SO 3 H O + CO H + CO (D) H + Br HBr 81. In which of the following K p is less than K C.(all are in the gaseous state) N O 4 NO HI H + I SO + O SO 3 (D) N + O NO 8. In the reaction H (g) + Cl (g) HCl(g) K p = K c K p K c K p > K c (D) K p < K c 83. For the equilibrium reaction A(g) + B(g) C(g) + D(g) the equilibrium constant (K c ) is given by the expression K c = [C][D] [C] [D] [A] [B] [C] [D] K c = K c = (D) K c = [A][B] [A] [B] [C] [D] [A] [B] 84. N + 3H NH K.cals. The effect of increase in pressure increases the rate of forward reaction increases the rate of backward reaction produces no change in the reaction (D) results in an increase in the volume 85. The equilibrium concentration of C H 4 in the following gas phase reaction can be increased by C H 4 (g) + H (g) C H 6 (g) H = 3.7 K. cal removal of C H 6 removing H decrease in temperature (D) increase in pressure 86. Consider the reaction A 1 0.5s 1.0s B. If the reaction is started with one molar solution of A, then concentration of B at equilibrium is 0. M 0.5 M 0.5 M (D) 0.75M FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

16 PET-XIII (EXTENDED)-018-MPC Ammonium hydrogen sulphide dissociates according to the equation NH HS S NH g H S g 4 3. If the observed pressure of the mixture is 1.1 atmosphere at C, what is the equilibrium constant K p of the reaction? atm atm 1 atm (D) atm 88. PCl 5 dissociation a closed container as : PCl g PCl g Cl g 5 3 If total pressure at equilibrium of the reaction mixture is P and degree of dissociation of PCl 5, the partial pressure of PCl 3 will be : P. 1 P. 1 P. 1 (D) P What is the equilibrium constant expression for the reaction. P s 5O g P O s? PO 4 10 K PO 4 10 c K 5 c P4 O 5 P 4 O 5 Kc O (D) 1 Kc 5 O 90. The chemical equilibrium of a reversible reaction is not influenced by : catalyst pressure temperature (D) concentration FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

17 PET-XIII (EXTENDED)-018-MPC-17 FIITJEE PET XIII (EXTENDED) MAINS_ANSWERS DATE: MATHEMATICS PHYSICS 1. A. A 3. C 4. A 5. C 6. C 7. C 8. C 9. C 10. D 11. B 1. A 13. B 14. A 15. B 16. D 17. A 18. B 19. C 0. B 1. A. C 3. A 4. B 5. A 6. C 7. A 8. C 9. B 30. D 31. A 3. A 33. B 34. BONUS 35. B 36. B 37. D 38. D 39. B 40. D 41. C 4. A 43. B 44. D 45. A 46. BONUS 47. C 48. C 49. A 50. B 51. C 5. C 53. B 54. D 55. A 56. A 57. B 58. D 59. A 60. D CHEMISTRY 61. B 6. D 63. C 64. A OR C 65. C 66. A 67. C 68. A 69. C 70. A 71. D 7. B 73. C 74. A 75. B 76. A 77. C 78. C 79. A 80. B 81. C 8. A 83. D 84. A 85. B 86. A 87. A 88. A 89. D 90. A FIITJEE Limited. 97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad Ph :

FIITJEE PET III (REG_1 ST YEAR)

FIITJEE PET III (REG_1 ST YEAR) MAINS DATE: 4.06.017 Time: 3 hours Maximum Marks: 360 INSTRUCTIONS: Instructions to the Candidates 1. This Test Booklet consists of 90 questions. Use Blue/Black ball Point