JEE (Advanced), 2016HALF COURSE TEST – VII ALL INDIA INTEGRATED TEST SERIES FIITJEE Students From All Programs have bagged 33 in Top 100, 77 in Top 200 and 205 in Top 500 All India Ranks. FIITJEE Performance in JEE (Advanced), 2015: 4551 FIITJEE Students from All Programs have qualified in JEE (Advanced), 2015. FIITJEE Paper 1 Time Allotted: 3 Hours Maximum Marks: 246 Pl ea s e r ea d t h e i n s t r u c t i o n s c a r ef u ll y . Yo u a r e a l l o t t ed 5 m i n u t es s p ec i f i c a ll y f o r t h i s p u r p o s e. Yo u a r e n o t a l l o wed t o l ea v e t h e E xa m i n at i o n Ha l l b ef o r e t h e en d o f t h e t es t . INSTRUCTIONS A. General Instructions 1. 2. 3. 4. 5. Attempt ALL the questions. Answers have to be marked on the OMR sheets. This question paper contains Three Parts. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. Each part is further divided into three sections: Section-A, Section-B & Section-C Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work. 6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed. B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your Enrolment No. and write your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts. 1. Section – A (01 – 07) contains 7 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and – 1 mark for wrong answer. Section – A (08 – 11) contains 4 multiple choice questions which have one or more than one correct answer. Each question carries +3 marks for correct answer. There is no negative marking. Section-A (12 – 16) contains 2 paragraphs. Based upon paragraph, 2 and 3 multiple choice questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer and – 1 mark for wrong answer. 2. Section – B (01 – 02) contains 2 Matrix Match Type questions containing statements given in 2 columns. Statements in the first column have to be matched with statements in the second column. Each question carries +8 marks for all correct answer. For each correct row +2 marks will be awarded. There may be one or more than one correct matching. No marks will be given for any wrong matching in any question. There is no negative marking. 3. Section-C (01 – 06) contains 6 Numerical based questions with answers as numerical value from 0 to 9 and each question carries +3 marks for correct answer. There is no negative marking. Name of the Candidate Enrolment No. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 2 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Useful Data PHYSICS Acceleration due to gravity g = 10 m/s2 Planck constant h = 6.6 1034 J-s Charge of electron e = 1.6 1019 C Mass of electron me = 9.1 1031 kg Permittivity of free space 0 = 8.85 1012 C2/N-m2 Density of water water = 103 kg/m3 Atmospheric pressure Pa = 105 N/m2 Gas constant R = 8.314 J K1 mol1 CHEMISTRY Gas Constant R Avogadro's Number Na Planck’s constant h 1 Faraday 1 calorie 1 amu 1 eV = = = = = = = = = = 8.314 J K1 mol1 0.0821 Lit atm K1 mol1 1.987 2 Cal K1 mol1 6.023 1023 6.625 1034 Js 6.625 10–27 ergs 96500 coulomb 4.2 joule 1.66 10–27 kg 1.6 10–19 J Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8, N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16, Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56, Pb=82, U=92. Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com Two cars A and B are moving towards each other with same speed 25 m/s. (B). A particle is moving along the x axis is acted upon by a single force F = F0e–kx. where F0 and k are constants. (C) and (D). FIITJEE House.. Wind is blowing with speed 5 m/s in the direction of motion of car A. The particle is released from rest at x = 0. The car A blows horn of frequency 300 Hz and the sound is reflected from car B. The wavelength of the reflected sound received by the driver of car A is (velocity of sound in air = 330 m/s) 25 31 (A) m (B) m 36 36 35 37 (C) m (D) m 36 36 3. Under the normal atmospheric pressure and the temperature of 300 kelvin. It will attain a maximum kinetic energy of : F F (A) 0 (B) 0k k ke kF0 (C) k (D) kekF0 e Space for rough work FIITJEE Ltd. Sarvapriya Vihar. The length of the air column if the temperature rises to 330 Kelvin will be: 100 (A) cm (B) 11 cm 11 (C) 10 cm (D) 12 cm vacuum air column l0 2. New Delhi -110016.3 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Physics PART – I SECTION – A Straight Objective Type This section contains 7 multiple choice questions numbered 1 to 7. Each question has 4 choices (A). Kalu Sarai. At the middle of the mercury barometer tube there is a little column of air with the length l0 and there is vacuum at the top as shown.fiitjee. Fax 26513942 website: www. l0 = 10 cm. 29-A. 26569493.com . out of which ONLY ONE is correct 1. Ph 46106000. Neglect expansion of the tube. The average power developed by the man is in elevator ref. The maximum possible value of for satellite to move in the elliptical orbit is: (A) 2 (B) 2 1 (C) 2 + 1 (D) 2 1 6. 29-A. At some point it is given an impulse along its direction of motion. It has velocity v at t = 0.36 × 10 J/kg. Sarvapriya Vihar.4 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 4. its speed becomes v 0). New Delhi -110016. frame : m(g a)h 1 (A) (B) m(g + a) (v + at0) t0 2 mgh 1 (D) mg (v + at0) t0 2 A thermally insulated vessel contains some water at 0°C. Space for rough work FIITJEE Ltd. Fax 26513942 website: www. The maximum percentage amount of water that will be solidified in this manner will be : (A) 86. It is given Latent heat of 5 5 vaporization of water at 0°C = 21 × 10 J/kg and latent heat of freezing of water = 3.. It now goes into an elliptical orbit. An elevator is moving upward with an acceleration a.36% (C) 7. First 10 cm piece of a uniform meter strick is cut and kept on the other end as shown in figure.2% (B) 33. This results in some water getting frozen. The vessel is connected to a vacuum pump to pump out water vapour. causing its velocity to increase times (that is. Find the shift in the x-coordinate of center of mass (A) 5 cm (B) 10 cm (C) 9 cm (D) 45 cm 5. Kalu Sarai. A satellite is in a circular orbit very close to the surface of a planet with speed v 0. A man inside the elevator lifts a body of mass m through a height h in interval t = 0 to t = t0. 26569493.fiitjee.6% (C) 21% (D) 24. FIITJEE House.com . Ph 46106000. Sarvapriya Vihar. (B). Space for rough work FIITJEE Ltd. Each question has 4 choices (A).com . 26569493. As a wave propagates : (A) The wave intensity remains constant for a plane wave (B) The wave intensity decreases as the inverse of the distance from the source for a spherical wave (C) The wave intensity decreases as the inverse square of the distance from the source for a spherical wave (D) Total power of the spherical wave over the spherical surface centered at the source decreases with distance. Fax 26513942 website: www. (use g = 10 m/s (A) The block starts slipping over the surface (B) The friction force on the cube by the surface is 5 N. out of which ONE OR MORE is/are correct 8. (D) The contact force exerted by the surface on the cube is 925 N 2kg F=40N z y x An ideal monoatomic gas undergoes a processes in which P = 3V3. 29-A.4. A solid cube of mass 5 kg is placed on a rough horizontal surface. then pressure must also decrease. Kalu Sarai. heat will have to be supplied to the gas. Then in the time interval from 2 t = 0 to t = seconds. (C) and (D) for its answer. Ph 46106000. in xy-plane as shown. At t = 0 the system is at rest as shown.5 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Multiple Correct Choice Type This section contains 4 multiple choice questions. FIITJEE House. The other end of the string is pulled by a constant force F = 40 N. pick up the correct statement (s) : (g = 10 m/s2) 10 (A) tension in the string is 40 N (B) work done by gravity is – 20 J (C) work done by tension on block is 80 J (D) None of these 10. 11. (C) The friction force acts in xy-plane at angle 127° with the positive x-axis in clockwise direction. An external force F 3iˆ 4ˆj 20kˆ N is applied on 2 the cube. 9. (C) For expansion. (A) If volume increases then temperature will also increase (B) If temperature of the gas decreases. Choose the correct statements.fiitjee.. The friction coefficient between the surface and the cube is 0. (D) If temperature increases then work done by gas is positive. A block of mass 2 kg is hanging over a smooth and light pulley through a light string. New Delhi -110016. Ph 46106000.1 mm) cos 0. (B).8 2 (C) Pex = (225 N/m2) sin (y + 1 cm) cos 2(200t) 0.8 where y is measured from the top of the tube in meters and t in second. whose equation is given by longitudinal displacement 2 (y + 1 cm) cos 2(400) t = (0. 29-A.8 2 (D) Pex = (225 N/m2) cos (y + 1 cm) sin 2(200t) 0.6 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Comprehension Type This section contains 2 paragraphs.fiitjee. 26569493. (C) and (D) out of which ONLY ONE is correct Paragraph for Questions 12 and 13 In an organ pipe (may be closed or open) of 99 cm length standing wave is setup. 12.8 Space for rough work FIITJEE Ltd.com . 13. New Delhi -110016. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered.8 2 (B) Pex = (125 N/m2) cos (y + 1 cm) sin 2(400t) 0. Kalu Sarai.. Fax 26513942 website: www. Here 1 cm is the end correction. FIITJEE House. Each of these questions has four choices (A). Sarvapriya Vihar. The air column is vibrating in (A) First overtone (C) Third harmonic (B) fifth harmonic (D) Fundamental mode Equation of the standing wave in terms of excess pressure is – (Bulk modulus of air B = 5 × 105 N/m2) 2 (A) Pex = (125 N/m2) sin (y + 1 cm) cos 2(400t) 0. . Net external force on any system is equal to the product of the mass of the system and the acceleration of the center of the mass of the system. A m 2l sphere of mass hits the rod elastically with horizontal speed v0 at a 4 3 m 4 2 distance from O. The maximum angular deflection of the rod from the vertical after the collision is 5 v 20 3 v 20 (A) cos 1 1 (B) sin1 1 16 g 16 g 3 v 20 (C) cos 1 1 16 g 15. 14.7 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Paragraph for Question Nos. 14 to 16 O A rod of mass m and length l is free to rotate in a vertical plane about fixed horizontal axis O passing through one end as shown in the figure. force exerted by O. For the rod alone. Before collision. the rod is at rest in vertical position. Similar conclusion can be drawn for the sphere. New Delhi -110016.com . 3 If we consider the sphere and the rod as a system. Kalu Sarai. Ph 46106000. 5 v 20 (D) sin1 1 16 g The velocity of the sphere just after collision is 2v 0 (A) 7 2v (C) 0 7 v0 2 v (D) 0 2 (B) Magnitude of the impulse on the rod exerted by the axis O during the collision is 3mv 0 (A) zero (B) 8 3mv 0 3 (C) (D) mv 0 14 7 Space for rough work FIITJEE Ltd.fiitjee. Sarvapriya Vihar. then gravity and force due to axis O are external forces. gravity and impact force are all external forces. 16. 29-A. 26569493. Fax 26513942 website: www. FIITJEE House. B-q. FIITJEE House. p q r s t A p q r s t B p q r s t C p q r s t D p q r s t Match the following : A block P of mass m placed on smooth horizontal surface and connected with a spring. B-r. Then match the matrix. Column – I (A) Friction force on the block Q. 29-A. New Delhi -110016. q. The blocks oscillates without slipping on each other. Another block Q of same mass is placed on the block P.. D) in column I have to be matched with statements (p. s. The answers to these questions have to be appropriately bubbled as illustrated in the following example.com . A-s. r. Kalu Sarai. Ph 46106000.8 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – B (Matrix-Match Type) This section contains 2 questions. then the correctly bubbled 4 4 matrix should be as follows: 1. 26569493. (exclude the equilibrium position) (C) Friction force will be maximum on Q. C-q and D-s. (exclude the equilibrium position) (B) Friction force at the block Q when both block going right from equilibrium position. The two blocks are pulled by a distance A and released. When both block coming towards equilibrium position form left. C. Each question contains statements given in two columns which have to be matched. (exclude the equilibrium position) (s) at extreme position Q P (q) towards left (r) at equilibrium position (t) none of these Space for rough work FIITJEE Ltd. t) in column II. Column – II (p) towards right (D) Friction force on P when both block is coming towards the equilibrium position from right. If the correct match are A-p. Fax 26513942 website: www. Statements (A. B. Sarvapriya Vihar.fiitjee. C-p. each of length . (q) 70C A cylindrical and thermal resistor of inner radius R and outer radius 8R is in steady state with its inner surface maintained at 100C and its outer surface maintained at 10C(heat flow is radially outwards). Assume that L is very large in comparison to R and the lateral surface of the cylinder is thermally insulated from the surroundings. Sarvapriya Vihar. B and C. The temperature of the co-axial cylindrical interface of radius 2R in steady state is T. has the two base radii as 6R and 3R respectively and the perpendicular distance between its. T is the temperature of the interface between resistor B and C in the steady state. Match the following columns. is in steady state with its inner surface maintained at 100C and its outer surface maintained at 10C(heat flow is radially outwards). FIITJEE House.9 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 2. The temperature of the concentric spherical interface of radius 3R in steady state is T. 3K0 and 6K0 respectively are joined in series such that there is one dimensional heat flow from left end (temperature 100C) to the right end (temperature 10C). two bases is 3L. 29-A. cross-sectional area A and thermal conductivity 2K0. In the steady state(heat flows from left end to the right end) the temperature of the interface at a distance of 2L from the left end is T. 26569493. The two bases are maintained at 100C and 10C. New Delhi -110016.fiitjee. (r) 55C L (s) 25C (t) none of these B 2K0 C 6K0 3K0 100C 10C T Three homogenous thermal resistors A. Find T. Ph 46106000. Fax 26513942 website: www. (B) 5R 10C 100C 2R 3R T (C) 100C 2R 10C T R 8R (D) 2L A 6R B b 3R 100C 10C T A homogeneous thermal resistor whose outer surface is the frustom of a solid cone.com .. Column – I A (A) (p) Column – II (Temperature T in steady state) 50C A spherical annular thermal resistor of thermal conductivity K and inner and outer radii 2R and 5R respectively. Kalu Sarai. Space for rough work FIITJEE Ltd. 2 kJ. 26569493. if the correct answers to question numbers X. Friction is negligible everywhere. The container has a heating element (a resistor R) which is generating heat at the rate of P. New Delhi -110016. The appropriate bubbles below the respective question numbers in the ORS have to be darkened.com . a body of mass m is hung from the other end and the system is released. What is the minimum power P (in watt) that must be generated as heat in the steady state in resistor R so that the amount of liquid water in the container neither increases nor decreases with time ? (Neglect other losses of heat.fiitjee. Water at temperature 20º C flows from a tap T into a heated container C. such as conduction from the container to the air and heat capacity of container) For water. For example. then the correct darkening of bubbles will look like the as shown 1. 9 and 2. 2.. At what minimum ratio m/M will the cylinder tilt? X Y Z W 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 h/2 h M m Space for rough work FIITJEE Ltd. 29-A. The rate of water in flow from trap is F = 0. Sarvapriya Vihar. respectively. diameter h/2 and mass M and with a homogeneous mass distribution is placed on a horizontal table.m–3.3 MJ. that may be varied. Z and W (say) are 6.16 cc/minute. Kalu Sarai. ranging from 0 to 9. Fax 26513942 website: www. specific heat c = 4. density p = 1000 kg. 0. A cylinder of height h. latent heat of vaporisation L vap=2. Y.kg–1 . Ph 46106000.10 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – C Integer Answer Type This section contains 6 questions. The answer to each of the questions is a single-digit integer.kg –1 K–1. FIITJEE House. The heat generated is sufficient so that the water in the container is boiling and getting converted into steam at a steady rate. One end of a string running over a pulley is fastened to the top of the cylinder. The accelerations of A. is v than v/10 is equal to …………….11 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 3. Ph 46106000. B and C at any instant are A 1 m/sec 2. A small block is projected on the block with velocity v1 = 25 m/s at an angle = 37° relative to the ground. External force acting on the system is (m 1 = 1kg. Calculate the time taken (in seconds) by the particle to reach from the point A to B . Kalu Sarai. FIITJEE House.fiitjee. What is 2 maximum area (in m ) on ground that can be sprinkled? The speed of water form nozzle is 1/ 4 400 2 m / s (g = 10 m/s ) 5. directed as m1 shown in the figure.com . Shown in the figure is a system of three particles connected by two springs. 29-A. If velocity of block (in m/s) relative to ground after time t = 10 sec. The 1/v versus displacement graph of a particle is shown in the figure. The coefficient of friction between the block and the board is = 0. 26569493. 1/v (s/m) B 4 2 A 0 2 x (m) Space for rough work FIITJEE Ltd. where v is the speed of the particle. Sarvapriya Vihar. Fax 26513942 website: www. A horizontal board is being moved with a constant velocity v0 on a smooth horizontal plane. 2 m/sec 2 and (1/2) m/sec2. 6. 4.3... m 2 = 2kg and m 3 = 4kg) a3 a2 a1 B C m2 m3 In a lawn a water sprinkler is sprinkling water in all the possible directions while rotating. New Delhi -110016. respectively. The particle is moving in a straight line along positive x-axis. (B)..com . Agaq 2NH3aq Ag NH3 2 aq What is the relationship between Kc and Ksp(AgCl)? 2 2 K sp NH3 1 (A) K c Ag NH3 Cl 2 (C) K c 4. FIITJEE House. Sarvapriya Vihar.7 (B) 49 (D) 37. Fax 26513942 website: www. New Delhi -110016. Kalu Sarai. Ph 46106000. Ag NH3 Cl 2 K sp Ag NH3 2 (D) K c 2 NH3 Cl K sp Cl Ag NH3 NH3 2 2 The shape of XeOF2 is similar to (A) T (C) (B) K c K sp NH3 (B) (D) Space for rough work FIITJEE Ltd. out of which ONLY ONE is correct 1. Find the equivalent weight of H3PO4 in the following reaction: Ca OH 2 2H 3PO 4 Ca H2PO 4 2 2H2 O (A) 98 (C) 32. Each question has 4 choices (A). (C) and (D). 29-A.fiitjee. Which one of these does have greatest second ionization energy? (A) B (B) C (C) Sr (D) Ba 3.12 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Chemistry PART – II SECTION – A Straight Objective Type This section contains 7 multiple choice questions numbered 1 to 7. 26569493.2 2. Sarvapriya Vihar. Each question has 4 choices (A). The reaction is (A) non-spontaneous. Fax 26513942 website: www. Which of the following carbocation will be relatively more stable than benzyl carbocation? (A) (B) CH2 Ph2CH (C) (D) CH3 C Ph CH3 Space for rough work FIITJEE Ltd. For the following reaction: CO g 1 O2 g CO2 g at 298K 2 The standard entropy change is 0. The values of standard Gibbs free energy of formation of CO2 and CO are 394. endothermic (B) non – spontaneous. (B).. out of which ONE OR MORE is/are correct 8.13 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 5. Find de – Broglie wavelength of the electron in the first Bohr’s orbit: (A) 3 10 10 m (B) 4 10 10 m (C) 3 10 11m (D) 4 10 11 m 6.4 and 137. endothermic (D) spontaneous.fiitjee.com . 29-A. New Delhi -110016. FIITJEE House. CH3 H3C CH2 C (A) (C) HBr / H2 O2 CH CH3 (B) CH3 H3C CH2 C H3C CH Br CH Br CH3 CH2 CH3 CH2 CH3 CH3 H3C CH2 C CH3 Br CH3 (D) H3C CH2 CH C CH3 Br 7. Ph 46106000. (C) and (D) for its answer. exothermic (C) spontaneous. Kalu Sarai. 26569493. exothermic Multiple Correct Choice Type This section contains 4 multiple choice questions.2 kJ mol1 respectively.094 kJ mol1. Now select the correct statement (s) among the following: (A) the mass of Cl2 generated is 42. Fax 26513942 website: www.5 mm Hg.6 mm (D) 64. FIITJEE House. 12. (C) and (D) out of which ONLY ONE is correct Paragraph for Question Nos. After 30 minutes from the start of the decomposition in a closed vessel. What is the pressure of the vessel before the beginning of decomposition of N2O5? (A) 223.8 mm (B) 233. An inert gas with partial pressure 10 mm Hg has always been present in vessel during decomposition of N 2O5. On complete decomposition the total pressure is 594. New Delhi -110016. KOH NaOI 3 2 2 B C D E A NaBH . Which of the following is correct about the given reaction sequence? H3 O Hg OCOCH / THF. Sarvapriya Vihar. 12 to 13 The decomposition of N2O5 is according to the equation: 2N2O5 g 4NO2 O2 g is a first order reaction. Each of these questions has four choices (A). H O Br2 / h alc. Ph 46106000..com . H2SO4 gives (B) Compound (B) can not exhibit position isomerism Compound (A) can exhibit position isomerism Chlorine gas is prepared in laboratory by the reaction: K 2Cr2O7 HCl KCl CrCl3 Cl2 H2O If a 61.14 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 9. Kalu Sarai.5 mm Hg. Which of the following molecules/species contains atleast one atom with sp3 hybridization? 2 (A) ClO2 (B) SO3 3 (C) BO3 (D) H3PO3 10.6 mm Space for rough work FIITJEE Ltd. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered.8 mm (C) 243.63 g (B) equivalent weight of K2Cr2O7 is 49 g (C) equivalent weight of HCl is 85.15 g/ml and containing 30% HCl by mass.16 g (D) the stoichiometric coefficient of HCl is 14 Comprehension Type This section contains 2 paragraphs. 26569493.8 mm 13. OH F 4 (A) (B) (C) (D) 11. What is the pressure of NO2 after 30 minutes? (A) 67. 29-A.3 g sample of 96% K2Cr2O7 is allowed to react with 320 ml of hydrochloric acid solution having density 1.fiitjee.6 mm (C) 65.6 mm (B) 66. Molecular weight of (F) is nth multiple of weight of a methyl radical (where n = positive integer) Compound (C) on heating with conc. the total pressure is found to be 294.8 mm (D) 253. (B). What is the molecular formula of isomer of any of these molecules? (A) C5H10 (B) C5H12 (C) C5H14 (D) C4H10 15. hence 6 C atoms Space for rough work FIITJEE Ltd. 14 to 16 Study following molecules before answering questions: CH3 H H3C H CH3 CH3 H H H3C CH3 H H3C 14. 26569493. Fax 26513942 website: www. H CH3 (B) 2 (D) 4 One of the seven cyclic isomers is missing. New Delhi -110016.. Ph 46106000. Kalu Sarai.15 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Paragraph for Question Nos. 29-A. What is the number of C atom constituting the cyclic ring? (A) 3 member ring. hence 4 C atoms (C) 5 member ring.com . hence 3 C atoms (B) 4 members ring.fiitjee. FIITJEE House. hence 5 C atoms (D) 6 member ring. The number of pairs of diastereomers are (A) 1 (C) 3 16. Sarvapriya Vihar. com .5 (r) (D) 3 (s) (t) Match the following: Column – I (Quantity) (A) (B) (C) (D) Degree of dissociation Pre-exponential factor equation) Rate of reaction Activation energy (Arrhenius + p q r s t A p q r s t B p q r s t C p q r s t D p q r s t Column – II (Molecule) N2 N2 CO O2 He2 Column – II (Dimensions) (T = Time. 2. s. 29-A. C-p. Sarvapriya Vihar. If the correct match are A-p.. t) in column II. Match the following column – I and column – II: Column – I (bond Order) (A) 0 (p) (B) 1. Ph 46106000. W = mass) (p) T1 (q) L0T0 (r) (s) M0L 0 M1L 3T1 (t) W1L2T2 Space for rough work FIITJEE Ltd. 26569493. then the correctly bubbled 4 4 matrix should be as follows: 1. B. B-q. C-q and D-s. New Delhi -110016. q. The answers to these questions have to be appropriately bubbled as illustrated in the following example. L = length. Statements (A.16 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – B (Matrix-Match Type) This section contains 2 questions. C. FIITJEE House. D) in column I have to be matched with statements (p. A-s. M = mol.fiitjee. B-r. Each question contains statements given in two columns which have to be matched. Kalu Sarai.5 (q) (C) 2. r. Fax 26513942 website: www. Sarvapriya Vihar. Fax 26513942 website: www. The number of pure sigma bonds in Cr2O72 will be. If a mixture of 3 mol of H2 and 1 mole of N2 is completely converted in to NH 3. 26569493. Y.. 3. ranging from 0 to 9.fiitjee.45 g requires 40 ml of N/2 KOH solution. The pH of blood stream is maintained by a proper balance of H2CO3 and NaHCO3 concentration. FIITJEE House. Z and W (say) are 6. (MW = 90) 5.4 is x mL. 0. New Delhi -110016. then the correct darkening of bubbles will look like the as shown X Y Z W 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1. Ka for H2CO3 in blood is 4 107. if the correct answers to question numbers X.com . 29-A. The answer to each of the questions is a single-digit integer.17 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – C Integer Answer Type This section contains 6 questions. Which number of hydrogen will be having least bond energy with carbon in given below compound? H (2) H (5) H(1) H (3) H(4) 4. Kalu Sarai. What will be the value of x/10? 6. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. Calculate the number of protons present in an acid whose 0. Ph 46106000. 9 and 2. For example. The volume of 10 M NaHCO3 solution which is mixed with 10 mL sample of blood which is 4 M in H2CO3 in order to maintain a pH of 7. respectively. Number of possible cyclic alcohols with formula C 5H10O (excluding stereoisomer) is x than what is x/2? 2. what would be the ratio of the initial and final volume at same temperature and pressure? Space for rough work FIITJEE Ltd. Two consecutive sides of a parallelogram are 4x + 5y = 0 & 7x + 2y = 0. 4 are con-cyclic points. 2. 2.com . Kalu Sarai. 3 3 (B) y-axis (D) none of these.18 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Mathematics PART – III SECTION – A Straight Objective Type This section contains 7 multiple choice questions numbered 1 to 7. then equation of other diagonal is (A) x + 2y = 0 (B) 2x + y = 0 (C) x – y = 0 (D) none of these. Fax 26513942 website: www. 1 If mi . out of which ONLY ONE is correct 1. 4. Space for rough work FIITJEE Ltd. 3. Each question has 4 choices (A).. The curve x + y = 3axy is symmetric about (A) x-axis (C) y = x 3. Coefficient of xr in the expansion of (1 – 2x) –1/2 is 2r ! (A) (B) 2 r! (C) 2r ! r! 2 22r 2r ! 2 2r r! (D) none of these. (B). (C) and (D). FIITJEE House. If one diagonal is 11x + 7y = 9. New Delhi -110016. i = 1. 29-A. 26569493. Sarvapriya Vihar.fiitjee. Ph 46106000. then the value of m 1 m 2 m 3 m 4 is mi (A) 1 (B) – 1 (C) 0 (D) none of these. then the value of a0 + a 3 + a6 + . If w is a complex cube root of unity then w + w (A) – 1 (B) 0 (C) 9 (D) i..is 2 +2i . 26569493.. If 1 sin A = sin (A) first (C) third in the curve A A A – cos .19 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 1 3 9 27 . Ten persons. 9.com . is (A) a 1+ a 4 +a 7 + .. then could lie in quadrant 2 2 2 4 (B) second (D) fourth Space for rough work FIITJEE Ltd. If a. amongst whom are A. out of which ONE OR MORE is/are correct 8.fiitjee. Multiple Correct Choice Type This section contains 4 multiple choice questions.. remaining vertices is / are (A) -1+ i( 2 + 3 ) (C) -1+ i( 2 – 3 ) area that can be inscribed (B) –1– i( 2 + 3 ) (D) –1– i( 2 – 3 ) 10. c be three unequal positive quantities in H. 7! (D) none of these.. 29-A. FIITJEE House. New Delhi -110016. B and C to speak at a function. is 6.P. then 100 100 100 3 3 3 (A) a + c > 2b (B) a +c > 2b 5 5 5 2 2 (C) a + c > 2b (D) a + c > 2b2 11. Ph 46106000. 7. If (1+ x + x2) n = a 0 + a1 x + a 2x2 + …+a 2n x2n. (C) and (D) for its answer. 2 8 32 128 5. b. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is 10! (A) (B) 3! 7! 6 (C) 10P3 . n-1 (C) 3 (D) none of these... Kalu Sarai. (B). If 1 + a + a 2 + a3 + … + ax = (1 + a)(1 + a2)(1 + a4) then x is (A) 3 (B) 5 (C) 7 (D) 9.. One vertex of the triangle of maximum |z – 2 i| =2.. Sarvapriya Vihar.. Fax 26513942 website: www. (B) a2+ a5 +a8 + . Each question has 4 choices (A). 12 to 13 Read the following comprehension carefully: Let f(n) denotes the number of different ways the positive integer n can be expressed as the sum of 1’s and 2’s. f(3) = 3. Fax 26513942 website: www. The value of f(6) is (A) 6 (C) 13 (B) 11 (D) 15 f{f(6)} is equal to (A) 377 (C) 321 (B) 302 (D) 350 Space for rough work FIITJEE Ltd.. Kalu Sarai. New Delhi -110016. Sarvapriya Vihar. Based upon one of paragraphs 2 multiple choice questions and based on the other paragraph 3 multiple choice questions have to be answered. 13. Each of these questions has four choices (A). since 4 = 1 + 1 + 1 + 1 = 1 + 1 + 2 = 1 + 2 + 1 = 2 + 1 + 1 = 2 + 2. since 3 = 1 + 1 + 1 = 1 + 2 = 2 + 1 f(4) = 5.fiitjee.20 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Comprehension Type This section contains 2 paragraphs.com . FIITJEE House. (C) and (D) out of which ONLY ONE is correct Paragraph for Question Nos. 29-A. Note that order of the appearance of 1’s and 2’s is important. Now. (B). For example. Ph 46106000. 26569493. answer the following questions: 12. the rays of the beam strike an elliptical surface and get reflected. Fax 26513942 website: www. R. Now answer the following questions: 14. 26569493.. The eccentricity of the ellipse is equal to 1 (A) 3 2 (C) 3 (B) 1 3 1 (D) 2 15. The reflected rays form another convergent beam having equation x – y + 2(1 – ) = 0.fiitjee. R. FIITJEE House. Total distance travelled by an incident ray and the corresponding reflected ray is the least if the point of incidence coincides with (A) an end of the minor axis (B) an end of the major axis (C) an end of the latus rectum (D) none of these Space for rough work FIITJEE Ltd. 29-A. Further it is found that the foot of the perpendicular from the 2 2 point (2. 14 to 16 Read the following comprehension carefully: A coplanar beam of light emerging from a point source have equation x – y + 2(1 + ) = 0.21 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 Paragraph for Question Nos. Kalu Sarai. 2) upon any tangent to the ellipse lies on the circle x + y – 4y – 5 = 0. Sarvapriya Vihar.com . Ph 46106000. New Delhi -110016. The area of the largest triangle that an incident ray and the corresponding reflected ray can enclose with the axis of the ellipse is equal to (A) 4 5 (B) 2 5 (C) 5 (D) none of these 16. Match the following Column-I with Column-II (A) (B) (C) (D) 2. The codes for the Column(s) have choices (A).com . Column – I f(z) is a complex valued function f(z) = (a + ib)z where a. 26569493. b R 1 and |a + ib| = . Fax 26513942 website: www. n 2 x 2n .] denotes the greatest integer function) is 2 If 3x + 4y + z = 5. b 0) such that n 6 does not divide 6 n is A is the region of the complex plane {z: z/4 and 4/ z have real and imaginary part in (0. Sarvapriya Vihar. then minimum value of26(x 2 2 + y + z )is Column – II (p) 5 (q) 0 (r) 6 (s) 25 (t) 10 Match the following Column-I with Column-II Column – I Column – II sin cos x (A) cos sin x 1 (p) xR (q) R – n (B) (C) tan( sinx) (r) (D) ln(tanx) (s) (t) 6 x n. then [p] (where p is the area of the region A and [.22 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – B (Matching List Type) This section contains 2 multiple choice questions. FIITJEE House. New Delhi -110016. where x. Kalu Sarai. z R. It has the property that f(z) is always 2 equidistant from 0 and z. 1)}. Each question has matching Column(s). Ph 46106000. (C) and (D) out of which only ONE OR MORE is/are correct 1. 29-A.fiitjee. (B). 2n 2 2 x R n 8 Space for rough work FIITJEE Ltd.. y. then a – b = The number of all positive integers n = 2a 3 b (a. 1 If coefficient of x7 in ax 2 bx 4.. 4 11 1 is equal to coefficient of x–7 in ax 2 . 6. where and are the roots of 2x2 + 7x + c = 0 is …. x + by + 1 = 0 and x + y + c = 0 are concurrent then 11 3 3 7 . Z and W (say) are 6. a cos(B – C) + b cos(C – A) + c cos (A – B) = (abc) k then k is …… 5. Fax 26513942 website: www. Ph 46106000.. 9 and 2.fiitjee. New Delhi -110016. then ab = …. The value of ‘c’ for which 2 2 3. x 2. if the correct answers to question numbers X. The length of perpendicular from centre of second circle onto the line L is …. c are distinct and different from 1) Space for rough work FIITJEE Ltd.23 AIITS-HCT-VII (Paper-1)-PCM-JEE(Advanced)/16 SECTION – C Integer Answer Type This section contains 6 questions. Kalu Sarai.. respectively. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. 26569493. 0. b. bx 3 1 1 1 … 1 a 1 b 1 c (given a. FIITJEE House. Y. 29-A.com . The value of alogb x when a = 0. 4 8 16 1. For example.2 b = 5 . is …. The line L passes through the points of intersection of the circles x2 + y2 = 25 and 2 2 x + y – 8x + 7 = 0. The answer to each of the questions is a single-digit integer. In a ABC. Sarvapriya Vihar. ranging from 0 to 9.. then the correct darkening of bubbles will look like the as shown X Y Z W 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 . If the lines ax + y + 1 = 0.