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IIT JEE Class 12 2019 : Science

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FIITJEE ALL INDIA TEST SERIES PART TEST II JEE (Advanced)-2020 PAPER 1 TEST DATE: 17-11-2019 Time Allotted: 3 Hours Maximum Marks: 183 General Instructions: The test consists of total 54 questions. Each subject (PCM) has 18 questions. 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 Two Sections: Section-A & Section-B. 1. Section-A (01 7, 19 25, 37 43) contains 21 multiple choice questions which have one or more than one correct answer. Each question carries +4 marks for correct answer and 2 marks for wrong answer Partial Marks +1 for each correct option provided no incorrect option is selected. Section-A (08 13, 26 31, 44 49) contains 18 questions. Each of 2 Tables with 3 Columns and 4 Rows has three questions. Column 1 will be with 4 rows designated (I), (II), (III) and (IV). Column 2 will be with 4 rows designated (i), (ii), (iii) and (iv). Column 3 will be with 4 rows designated (P), (Q), (R) and (S). Each multiple choice question with 4 options has only one correct answer and carries +3 marks for correct answer and 1 mark for wrong answer. 2. Section B (14 18, 32 36, 50 54) contains 15 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. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 Physics 2 PART I SECTION A (One or More than one correct type) This section contains 07 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 1. A square conducting loop ABCD and a rectangular conducting loop EFGH are placed on the same plane as shown in the figure. The loop ABCD is placed symmetrically with respect to EFGH such that its central line is at a distance d from the loop EFGH. Side length of small loop ABCD is much smaller than the length a and width d of the bigger loop EFGH. A source is applied on loop ABCD, such that it sets up a current I = kt in it. Here k is a positive constant and t is time. Then choose the correct option(s). E F d >> A B a >> d a >> C D G H d (A) (B) (C) (D) 2. If the current in the loop ABCD is in clockwise sense then the induced current in the loop EFGH due to this current is in anticlockwise sense. If the current in the loop ABCD is in clockwise sense then the induced current in the loop EFGH due to this current is in clockwise sense. 2k emf induced in the loop EFGH due to current in the loop ABCD is 0 . 4 d 3 0 2k emf induced in the loop EFGH due to current in the loop ABCD is . 4 d A thin walled non-magnetic spherical shell with wall thickness d and radius R (R >> d) is placed in a uniform magnetic field dB0 B B0 j , which slowly changes as , where is a dt positive constant. Electrical resistivity of the material of the shell is . Then choose the correct option(s). (A) Induced magnetic moment of the shell is towards j direction (B) Induced magnetic moment of the shell is towards j direction (C) (D) d B R 3 4 dR 2 2 4 Induced magnetic moment of the shell is dR 3 Induced magnetic moment of the shell is FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com y x 3 3. AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 A metallic disc of radius a mounted on a rigid axle is rotating with a constant angular velocity inside a long solenoid of inductance L whose two ends are connected to the rotating disc by two brush contacts as shown. The total resistance of the whole circuit is R. Then R P metallic disc of radius a a long uniform solenoid of N turns and length Q Brush (A) (B) (C) (D) 4. 0Ni a2 , when current in the coil is i. 2 Current in the coil can increase or decrease with time depending upon the value of . R min for increasing the current in the coil always is 2 0Na2 The induced emf between terminals P and Q is min for increasing the current in the coil always is 2 R 0Na2 A solenoid of radius r is made of thin metallic wire rings with resistance of each ring R. The rings have been put in a uniform way on a very long glass cylinder which has vacuum inside it. The solenoid and glass cylinder are glued to each other. The number of rings per unit length is n and the planes containing the rings are perpendicular to the symmetry axis of the cylinder. At a moment the cylinder starts rotating around its symmetry axis with an angular acceleration . The e magnetic field B at the centre of the cylinder (after a long time) is ( is specific charge of m electron). 0 nmr 2 (A) eR 0nmr 2 (B) eR 2 0nmr 2 (C) eR 4 0nmr 2 (D) eR FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 5. 6. During the melting of a slab of ice at 273 K at the atmospheric pressure. (A) Positive work is done by the ice-water system on the atmosphere. (B) Positive work is done on the ice-water system by the atmosphere. (C) The internal energy of the ice-water system increases. (D) The internal energy of the ice-water system decreases. An electric dipole having dipole moment P 3i 4 j 10 9 Cm is placed in a uniform electric field E 60i 80 j N/C. (A) (B) (C) (D) 7. 4 Electric field applies zero net force on the dipole Electric field energy of the dipole in the electric field is 5 10 7 J. The dipole is in stable equilibrium in the electric field. The dipole is in unstable equilibrium in the electric field. A charged particle of charge q and mass m is entering at origin with a velocity v i in a uniform magnetic field B k which is extended upto infinite at right of the line L. Select the correct option(s) mv Given that 1 meter. and v = 1 m/s. qB y (B) 30 x q, m (A) L Velocity of the particle makes an angle 60 with x-axis while it is coming out of the magnetic field. 1 3 The co-ordinates of point of exit is m, m 2 2 (C) 3 1 The co-ordinates of point of exit is m, m . 2 2 (D) Time spent by the particle in the magnetic field is sec. 3 (Matching type - Single Correct Option) This section contains SIX questions of matching type. The section contains TWO tables (each having 3 columns and 4 rows). Based on each table, there are THREE questions. Each question has FOUR options (A), (B), (C), and (D). ONLY ONE of these four options is correct. Answer questions 8, 9 and 10 by appropriately matching the information given in the three columns of the following table. Here P, V, T , U have usual meaning of pressure, volume, temperature, density and Internal energy of gas. Column 1 P Column 3 A B V (I) Column 2 (i) C WAB 0 (P) UAB 0 T CA Rectangular Hyperbola FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 5 AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 A B (II) C (ii) WAB 0 (Q) UBC 0 (iii) WBC 0 (R) UAB 0 (iv) WCA 0 (S) UCA 0 T CA Rectangular Hyperbola U A V B (III) C V CA Rectangular Hyperbola P B 2P0 (IV) P0 C A V0 2V0 V 8. In a cyclic process W AB and UAB are both non zero values and have same sign. (A) (I) (ii) (R) (B) (II) (i) (P) (C) (III) (i) (P) (D) (IV) (ii) (R) 9. In a cyclic process QBC must be positive. (A) (I) (iii) (Q) (B) (II) (iii) (Q) (C) (III) (iii) (Q) (D) (IV) (iii) (Q) 10. In a cyclic process, W any path + Uany path < 0 (any path means any of AB or BC or CA) (A) (I) (ii) (R) (B) (II) (iv) (S) (C) (III) (iv) (S) (D) (IV) (i) (R) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 6 Answer questions 11, 12 and 13 by appropriately matching the information given in the three columns of the following table. Column 1 is having charged systems, Column 2 is having variation of electric field for any charged system of column 1 and Column 3 is having variation of electric potential (taking potential at infinity to be zero) for any charged system of column 1 Column 1 Column 2 Column 3 R2 R1 2Q +Q P1 (I) (i) (P) Point charge at center = Q and charge on thick conducting shell = 2Q R2 V E R1 R1 Q R2 R1 r E R2 r V P1 (II) (ii) (Q) Two thin conducting shell, out of which inner shell is having charge Q and outer shell is uncharged R2 R1 (III) P1 (IV) Q P1 R2 r R1 R2 r (R) R1 R2 r E R1 +Q R1 V (iii) Two thin uncharged conducting shell and Point charge at centre =Q R2 r E R1 +Q R2 (iv) V (S) R1 R2 R1 R2 r r Point charge at center = Q, Charge on thick conducting shell = +Q In each charged system Q = 1 C, R1 = 10 cm, R2 = 20 cm. Each of the shells or spheres are conducting. Variation of electric field and potential is given as a function of radial distance r. point P1 in each figure is at distance r = R1 + (where 0) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 7 11. Electric field at point P1 is 900 AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 KV for a charged system. Choose the correct option for that m charged system. (A) (III) (i) (Q) (B) (III) (iv) (S) (C) (II) (iv) (Q) (D) (II) (i) (P) 12. Electric potential of a conducting shell (thin or thick) is 45 KV for a charged system. Choose the correct option for that charged system. (A) (I) (ii) (R) (B) (I) (ii) (P) (C) (III) (i) (R) (D) (III) (i) (P) 13. Electrical potential energy stored in outside space (from r = R2 to (r ) is 2.25 10-2J (A) (I) (ii) (Q) (B) (II) (iv) (S) (C) (III) (i) (P) (D) (III) (i) (S) SECTION B (Single digit integer type) This section contains FIVE questions. The answer to each question is a single Digit integer ranging from 0 to 9, both inclusive. 14. A conducting rod is initially at 0 C temperature. Now Steam Melting ice Insulation chamber chamber one end A is kept at melting ice chamber (0 C) and (100 C) (0 C) the other end B is kept at steam chamber (100 C). XY A B The surface of the rod is well insulated from the outer environment so that heat is only flowing along the length of the rod as shown is the figure. The cross-sectional area of the rod is 1 cm 2 and length of the rod is 1 m. Thermal conductivity of the rod is 500 W/m-K. Density of the rod is 8000 kg/m3. Specific heat capacity of the rod is 500 J/kg-K. A small cylindrical element xy (of length 1 cm and cross-sectional area same as that of rod) is examined. It is observed that temperature gradient of the end X is 5 C/m and average temperature of xy part of the rod is rising at 0.05 C/sec. What is the temperature gradient (in C/m) of end Y of the element? 15. A point charge q = 8.85 10 9 C is placed at (0, d, 0) where d = 1m. An insulating surface ABCA is on the x-z plane, which is bounded by a quarter circle AB and two equal length straight line BC and CA as shown in the figure. Electric flux through the surface ABCA in Nm2/C is (nearest integer) C2 Take 0 8.85 10 12 Nm2 y q(0, d, 0) B (d, 0, 0) x A z C (d, 0, d) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 8 16. Chandrayan-1, the lunar mission launched by India in 2008, had all gold wiring. A particular instrument on board the mission, was operating at the same temperature as the space surrounding the Chandrayan at 3 K. Instrument specifications demanded that no wire in the instrument should offer a resistance more than 7 m . All the instruments on Chandrayan were fabricated in ISRO lab at room temperature of 30 C. If the radius of all wires in the instrument was 0.1 mm (as measured in ISRO lab). If the maximum allowable length (as measured in ISRO 1 22 lab) of any wire is approximately meter then find . Take . (Assume that resistivity 7 and length of gold wire change linearly with temperature) You can use these properties of gold. Resistivity at room temperature = 2.2 10 8 m Temperature coefficient of resistivity = 0.0032 K 1 Linear thermal expansion coefficient = 1.5 10 5 K 1. 17. The network shown consists of an infinite number of cells of emf 1 and 2 with corresponding internal resistances r1 and r2 respectively A resistor R = 1 is connected to the end of the network. If the values of the emfs and internal resistances are 1 = 1.0 V, 2 = 2.0 V, r1 = 4 and r2 = 6 . If the current flowing through the resistor R is I ampere, then find 10 I. 1 18. r1 1 r1 2 2 r2 r2 A thin non conducting disc of mass M = 2 kg, charge Q = 2 10 2C 1 and radius R m is placed on a frictionless horizontal plane with 6 its centre at the origin of the coordinate system. A non uniform, radial magnetic field B B0 r exists in space, where B0 = 10 T and the disc is rotated with an angular velocity x 102 rad/sec about an axis passing through its centre and perpendicular to its plane, as shown in the figure. At what value of x the disc will lift off from the surface. R y B B0r x w FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 9 Chemistry AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 PART II SECTION A (More Than One Correct Type) This section contains 7 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 19. CHCl3 NaOH N H Product (s) formed is/are (A) CHO N H (B) Cl N (C) CHO N (D) N H CHO 20. Which of the following statement is/are correct? (A) Cellulose nitrate is a natural polymer. (B) Vulcanization increases rigidity by restricting the movement of the polymer chains. (C) HDPE is a linear polymer whereas LDPE is a branched polymer. (D) Cellulose is an example of an unbranched polysaccharide. 21. Which of the following transformation(s) is/are possible by aq. NaOH in presence or absence of heating (A) CH2OH CH2OH O HCHO excess OH HOH2C (B) Ph O Ph HCOO Na CH2OH OH Me Me FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 10 (C) O O O (D) Br OH NO 2 NO 2 NO 2 NO 2 22. OH Which of the following is/are correct about the above drawn compound? (A) It gives positive Br2 water test. (B) It gives positive Na-metal test. (C) It gives negative iodoform test. (D) It does not give turbidity with Lucas reagent at room temperature. 23. SCl2 H2C CH2 P Which of the following statement(s) is/are correct regarding P ? (A) P on treatment with sodium ethoxide produces divinyl sulphide. (B) It is a chemical warfare agent. (C) Rate of hydrolysis of P is much more than its corresponding ether analogue. (D) On complete hydrolysis it produces HCl and diol. 24. Which of the following acids undergo decarboxylation just on heating? (A) COOH CH2 (B) CO 2H CO 2H (C) O HO 2C (D) O C O OH FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 11 25. AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 How many of the following statements is/are correct? (A) -D-(+)-glucopyranose and -D-(+)-glucopyranose are diastereomers (B) D-Glucose and D-Mannose are diastereomers (C) Maleic acid and Fumaric acid are diastereomers (D) Dextro form and Meso form of tartaric acid (2,3-dihydroxybutanedioic acid) are diastereromers. (Matching type - Single Correct Option) This section contains SIX questions of matching type. The section contains TWO tables (each having 3 columns and 4 rows). Based on each table, there are THREE questions. Each question has FOUR options (A), (B), (C), and (D). ONLY ONE of these four options is correct. Answer Q. 26, Q. 27 and Q. 28 by appropriately matching the information given in the three columns of the following table. (I) Column 1 Orlon (i) (II) Buna-N (ii) (III) Dacron (iii) (IV) ABS (iv) Column 2 High impact resistance and mechanical toughness Have good resistance to stains, chemicals Resistant to the action of petrol, lubricating oil Crease resistant 26. Which of the following is only correct combination? (A) (I) (iv) (S) (B) (II) (iii) (P) (C) (IV) (i) (P) (D) (I) (iv) (S) 27. Which of the following is only correct combination? (A) (IV) (i) (R) (B) (II) (ii) (Q) (C) (III) (iv) (Q) (D) (I) (ii) (P) 28. Which of the following is only correct combination? (A) (II) (ii) (S) (B) (III) (ii) (R) (C) (IV) (i) (P) (D) (I) (ii) (Q) (P) Column 3 Elastometer (Q) Homopolymer (R) Terpolymer (S) Thermoplastic or thermoset depend on the chemical structure FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 12 Answer Q. 29, Q. 30 and Q. 31 by appropriately matching the information given in the three columns of the following table. Column 1 O (I) Column 2 E1CB involved during the reaction Column 3 (P) One product (ii) Proceeds via six membered cyclic TS (Q) Three products (iii) Proceeds via five membered cyclic TS (R) Four products (iv) Butterfly type transition state (S) Two products (i) C12 OH H2C C14 OH O (II) R2 CH2I2 Zn Cu Et2 O R1 Br (III) 14 NaNH2 liq. NH 3 (IV) N 2 2 ii 160o C, i H O Product s not containing N 29. Which of the following is only correct combination? (A) (III) (ii) (R) (B) (II) (iv) (S) (C) (IV) (i) (P) (D) (I) (iii) (S) 30. Which of the following is only correct combination? (A) (III) (i) (S) (B) (II) (i) (P) (C) (IV) (ii) (P) (D) (I) (iii) (R) 31. Which of the following is only correct combination? (A) (III) (iv) (S) (B) (IV) (iii) (Q) (C) (IV) (ii) (S) (D) (I) (ii) (P) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 13 AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 SECTION B (Single digit integer type) This section contains FIVE questions. The answer to each question is a single Digit integer ranging from 0 to 9, both inclusive. 32. Cl CH CH Br HO 2C Cl CH A CHOH3 CO 2H B CH F If number of stereoisomers for (A) is 2x, and if number of stereoisomers are possible for (B) is 2y. Then value of x/y would be? 33. O H3C C i SOCl 2 OH ii KCN ' A ' iii H3O How many of the following statements is/are correct about A ? (1) It forms oxime with hydroxylamine (2) It can be prepared by the oxidation of propylene glycol by KMnO4. (3) It is stronger acid than propanoic acid (4) It forms phenyl hydrazone with phenyl hydrazine (5) It can be prepared by hydrolysis of , -dibrompropanoic acid (6) When it is heated with dil. H2SO4 in a sealed tube, decarboxylation takes place (7) When it is heated with conc. H2SO4, decarbonylation takes place (8) It gives positive result in the iodoform reaction (9) It decolourises bromine water and KMnO4 solution. 34. Nylon-2-nylon-6 is a biodegradable step growth polymer. It can be expressed as O NH CH2 x C NH CH2 y C O Value of y + x would be? 35. n How many of the following reaction is not possible or produce very poor yield? (i) NO 2 NO 2 CH3Cl Anhydrous AlCl3 CH3 (ii) NO 2 O NK + X i ii OH ,H O 3 O NH2 CO 2H CO 2H FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 14 NH2 (iii) NH2 CH3 Cl Anhydrous AlCl 3 CH3 (iv) OH OH Br Br Br2 CS 2 Br (v) O O R C O MnO H R (vi) C R O Li C OH i CO2 ii H2 O,H X (vii) Anhydrous AlCl 3 (viii) CH3 ONa 300 K (ix) Br NH2 NO 2 CF3 CO3H NH2 NO 2 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 15 36. AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 Protonation of carbonyl group forms a cation with significant charge on the carbon atom C O H C OH C OH How many of the following carbonyl compounds form an aromatic cation on protonation? 1. 2. O O 3. 4. O 5. O O 6. O O 7. 8. H B C O O 9. H O O FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 Mathematics 16 PART III SECTION A One OR More Than One Choice Type This section contains 07 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE OR MORE THAN ONE is/are correct 37. Let the ordered pair of integers (xi, yi) where i = 1, 2, ....., n satisfy the equation tan 1 x + tan 1 8 = tan 1 y + . For the polygon so formed in xy plane which of the following is/are 2 true? (A) It is a rectangle (B) It is not cyclic (C) It is symmetric about line y = x (D) It is symmetric about line x + y = 0 38. Let A = {xy = c| c R {0}}. Let EC = 0 represent locus of point Pc such that sum of slopes of normals drawn from it to xy = c is equal to sum of ordinates of feet of normals. Let F be the set of points of intersection of Ec = 0 with xy = c (for parameter c ), then (A) (1, 1) is an element of F (B) (2, 1) is not an element of F (C) (0, 0) is an element of Ec F c R {0} (D) F is a set of hyperbolas 39. Which of the following is/are correct with respect to angle bisectors of pair of lines 3x2 4y2 xy 12x + 16y = 0 (A) Angle bisector containing point (2, 1) is the obtuse angle bisector 40. (B) Equation of acute angle bisector is 3 2 5 x 4 2 5 y 20 0 (C) (D) Equation of obtuse angle bisector is 3 2 5 x 4 2 5 y 20 0 Angle bisectors are perpendicular with respect to each other For the curves 2x2 + y2 = 2 and y2 x2 = 2 which of the following is/are true? (A) Equation of a pair of common tangents is 4x2 + y2 4xy 6 = 0 (B) Equation of a pair of common tangents is 4x 2 + y2 + 4xy 6 = 0 5 (C) Length of common tangent is 3 (D) 41. Length of common tangent is 10 3 x 4 2 y 2 x 2 y2 1 and E 2 : 1 . If E2 rolls on E1, without slipping, then which of the 4 3 4 3 following is/are true? (A) Locus of centre of E2 is a polynomial of fourth degree (B) Locus of one of the focus of E2 is polynomial of third degree (C) Locus of centre of E2 is a closed curve (D) Locus of one of the focus of E2 is a closed curve Let E1 : FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 17 42. Let O be circumcenter of ABC and AO, BO, CO meet circumcircle of ABC in D, E, F respectively. If areas of ABC, DBC, EAC, FAB are , 1, 2, 3 and radius of their circumcircle are R, R1, R2, R3 respectively, then (where A, B, C and a, b, c have usual meaning) (A) 1 + 2 + 3 = (B) 1 + 2 + 3 = 2R2 sin A sin B sin C a b c 4 (C) 2 R1 R2 R3 R a b c abc (D) 2 R1 R2 R3 R n 43. AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 2 Pia cos i ai th 2019 where Pi represents the i prime number i 1 (i.e., for example P1 = 2, P2 = 3, P3 = 5 .....) such that Pn < 2019 and ai R. If elements of set A be solution of the equation represented by ordered n-tuple (a1, a2, a3 ....., an), then (A) number of elements in set A is finite (B) if ai 9 i = 1, 2, ....., n, then number of element in set A is 25 (C) if ai 0 i = 1, 2, ....., n, then A is null set (D) if ai 9 i = 1, 2, ....., n, then A is singleton set (Matching type - Single Correct Option) This section contains SIX questions of matching type. The section contains TWO tables (each having 3 columns and 4 rows). Based on each table, there are THREE questions. Each question has FOUR options (A), (B), (C), and (D). ONLY ONE of these four options is correct. Answer Q.44, Q.45 and Q.46 by appropriately matching the information given in the three columns of the following table. Let P1 P2 P3 form an equilateral triangle. Let Pn + 3 be mid-point of Pn and Pn + 1 n N. Match the ratios of areas of triangle given in Column-1 and ratio of angles of triangle given in Column-2 to their respective values in Column-3 (I) Column 1 P2017 P2018 P2019 P2019 P2020 P2021 (i) Column 2 P2021 P2022 P2023 P2020 P2019 P2018 Column 3 (P) 1 (II) P2017 P2018 P2019 P2020 P2021 P2022 (ii) P2001 P2002 P2003 P2020 P2018 P2021 (Q) 2 (III) P2017 P2019 P2020 P2018 P2019 P2020 (iii) P2004 P2005 P2003 P2002 P2003 P2004 (R) 4 (IV) P2021 P2022 P2023 P2021 P2023 P2025 (iv) P2017 P2018 P2019 P2018 P2019 P2020 (S) 8 44. Which of the following combination is only CORRECT? (A) (I) (i) (Q) (B) (II) (iii) (P) (C) (I) (iii) (R) (D) (II) (i) (S) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 18 45. Which of the following combination is only CORRECT? (A) (III) (ii) (P) (B) (IV) (i) (R) (C) (III) (i) (P) (D) (IV) (iv) (R) 46. Which of the following combination is only CORRECT? (A) (II) (iv) (P) (B) (IV) (i) (Q) (C) (II) (ii) (R) (D) (IV) (iv) (P) Answer Q.47, Q.48 and Q.49 by appropriately matching the information given in the three columns of the following table. 3 Let inverse trigonometric functions be defined as follows: sin 1 x : 1, 1 , ; 2 2 3 1 cos 1 x : 1, 1 0, ; tan 1 x : R , ; cosec x : , 1 1, , 0 ; 2 2 2 2 cot 1x : R , 2 ; sec 1x : , 1 1, 0, . Match maximum value of expression in 2 Column-1 and minimum value of expression in Column-2 to corresponding values given in Column-3. (I) Column 1 sin x cos x (i) (II) sin 1 x sin 1 x (ii) tan 1 x tan 1 x 1 1 (III) cot 1 x cot 1 x 5 2 1 (IV) cosec 1 sin 1 x x Column 2 tan x cot 1 x 1 Column 3 0 (Q) 2 (P) 1 (iii) sec 1 cos 1 x x (R) 2 (iv) sec 1x cosec 1x (S) 5 2 47. Which of the following combination is CORRECT? (A) (I) (i) (P) (B) (I) (ii) (R) (C) (I) (i) (S) (D) (II) (i) (R) 48. Which of the following combination is CORRECT? (A) (II) (ii) (R) (B) (III) (iii) (S) (C) (IV) (iv) (P) (D) (I) (i) (Q) 49. Which of the following combination is CORRECT? (A) (III) (iv) (Q) (B) (IV) (ii) (P) (C) (II) (iv) (P) (D) (I) (ii) (Q) FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com 19 AITS-PT-II (Paper-1)-PCM-JEE(Advanced)/20 SECTION B (Single digit integer type) This section contains FIVE questions. The answer to each question is a single Digit integer ranging from 0 to 9, both inclusive. 50. If length of smallest path that can be traced from (0, 0) to 2 2 the curve x + y 2 2x + 1 = 0 is of the form 2 1, 1 without traversing inside a b ; a, b I, then value of a + b is equal to. 16 2 2 1 25 a2 b a 144 16b 2 . If maximum and minimum value of f(a, b) is 3 c and d respectively a, b R, then c d equals. 51. Let f a, b 52. If there are only two points on the curve 2x 2y 4x + 21 = 0 such that tangents drawn to x2 y 2 1 (a, b N) are perpendicular, then a + b equals. a2 b2 53. Number of solutions of the equation cosec2 x sec2 x tan2 x cot2 x sin2 x cos2 x + 3 = 0 x [ 2 , 2 ] is. 54. If maximum value of tan 1 x 2sin 1 x 3sec 1 x is 2 2 p where p, q are coprime integers, then q p q equals. FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 website: www.fiitjee.com

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