02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Question Paper

Sri Chaitanya IIT Academy., India. A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI A right Choice for the Real Aspirant ICON Central Office – Madhapur – Hyderabad Sec: Sr.Super-60& All Jee-Main Date: 02-05-2021 Max.Marks:300 Time: 10.00Am to 01.00 GTM-22

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Test Syllabus PHYSICS : Total Syllabus CHEMISTRY : Total Syllabus MATHEMATICS :Total Syllabus Sec: Sr.Super-60 & All Space for Rough Work Page 2

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P PHYSICS Max Marks: 100 (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases. 1. A tube filled with water and closed at both ends uniformly rotates in a horizontal plane about the OO ' axis. The manometers A and B fixed in the tube at distances r1 and r2 from rotational axis indicate pressures p1 and p2 , respectively. Determine the angular velocity  of rotation of the tube. (density of water is  ) p1 p2 O AB r1  O' r2  1)   2 p2  p1  2)   2 p2  p1  r22  r12  r22  r12  2 r22  r12 4)   2 p2  p1 3)   r1r2 p1  p2 2. A particle of mass 4m is projected from the ground at some angle with horizontal range is R. At the highest point of its path it breaks into two pieces of masses m and 3m. respectively, such that the smaller mass comes to rest. The larger mass finally falls at a distance x from the point of projection, where x is equal to 1) 2R 2) 7R 3) 5R 4) R 3 6 4 3. A quantity X is given by 0 L V , where 0 is the permittivity of the free space, L is t the length, V is potential difference, and t is the time interval. The dimensional formula for X is the same as that of 1) Resistance 2) Charge 3) Voltage 4) Current Sec: Sr.Super-60 & All Space for Rough Work Page 3

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 4. System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass 2m and m just after string is cut will be 2m m 1) g upwards, g downwards 2) g upwards, g downwards 2 2 3) g upwards, 2g downwards 4) 2g upwards, g downwards 5. The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a  g is imparted to the projectile 4 due to wind, then its horizontal range and maximum height will be 1)  R  H , H 2)  R  H  , 2H 3)  R  2H , H 4)  R  H , H  2  2 6. Charges Q,2Q and 4Q are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii R , R and 2R respectively, as shown in figure. If magnitudes of the 2 electric fields at point P at a distance R from the center of spheres 1,2 and 3 are E1, E2 and E3 respectively, then P PR P R R Q 2Q 4Q R/2 2R Sphere 1 Sphere 2 Sphere 3 1) E1  E2  E3 2) E3  E1  E2 3) E2  E1  E3 4) E3  E2  E1 Sec: Sr.Super-60 & All Space for Rough Work Page 4

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 7. A piece of conducting wire of resistance R is cut into 2n equal parts. Half the parts are connected in series to form a bundle and remaining half in parallel to form another bundle. These bundles are then connected to give the maximum resistance. The maximum resistance of the combination is 1) R 1  1   2) R 1 n2  3) R 4) R  n  1 2  n2  2 2 1 n2  n   8. A moving coil galvanometer of resistance 100 is used as an ammeter using a resistance 0.1  . The maximum deflection current in the galvanometer is 100A. Find the minimum current in the circuit so that the ammeter shows maximum deflection. 1) 100.01 mA 2) 1000.1 mA 3) 100.1 mA 4) 1.01 mA 9. A square conducting loop of side L is situated in gravity free space. A small conducting circular loop of radius r r  L is placed at the center of the square loop, with its plane perpendicular to the plane of the square loop. The mutual inductance of the two coils is (current passing through square loop is i ) 1) 2 20I r2 2) 20I r2 L L 3) 0 4) 2 20I r 3L 10. An alternating e.m.f. of 200 V and 50 cycles is connected to a circuit of resistance 3.142 and inductance 0.01 H . The lag in time between the e.m. f . and the current is 1) 1.5 ms 2) 2.5 ms 3) 3.5 ms 4) 2ms 11. A system of identical cylinders and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. The velocity of lower and upper plates are V and 2V, respectively, as shown in figure. Then the ratio of angular speeds of the upper cylinders to lower cylinders is 2v v 1) 1/3 2) 3 3) 1 4) 2 Sec: Sr.Super-60 & All Space for Rough Work Page 5

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 12. The string of a simple pendulum is replaced by a uniform rod of length L and mass M while the bob has a mass m. It is allowed to make small oscillations. Its time period is 1) 2  2M  L 2) 2 2M  3m L  3m  g 3M  2m g 3) 2  M m L 4) 2  2m  M  L  M  3m  g    3M  2m  g 13. Two tanks A and B contain water at 300C and 800C , respectively, calculate the amount of water that must be taken from each tank respectively to prepare 40 kg of water at 500C . 1) 24 kg, 16 kg 2) 16 kg, 24 kg 3) 20 kg, 20 kg 4) 30 kg, 10 kg 14. A cyclic process ABCD is shown in the following P  V diagram. Which of the following curves represents the same process? P AB C D V P B P B A A C C D D T T O O B 2) 1) C T P B P A A DC D 3) T 4) Sec: Sr.Super-60 & All Space for Rough Work Page 6

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 15. A factory is served by a 220 V supply line. In a circuit protected by a fuse marked 10 A, the maximum number of 100 W lamps in parallel that can be turned on is 1) 11 2) 22 3) 33 4) 66 16. ABCD is right-angled prism with other angles as 600 and 300. Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face AC. For total internal reflections, maximum refractive index of the liquid is (nearly) A 600 300 B 600 C 1) 1.4 2)1.3 3) 1.2 4) 1.6 17. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b, respectively. When a current I passes through the coil, the magnetic field at the center is 1) 0NI 2) 20NI 3) 0 NI  ln b 4) 2 0I a  ln b b a a a a 2b b  18. A massless rod of length L is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that BO is equal to ' x' . Further it is observed that the frequency of 1st harmonic in AB is equal to 2nd harmonic frequency in CD, ' x' is AC O D BL xm 1) L 2) 4L 3) 3L 4) L 55 4 4 Sec: Sr.Super-60 & All Space for Rough Work Page 7

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 19. A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle  . A pin is located at a distance l below the pivot point. When the pendulum swings down, the string hits the pin as shown in figure. The maximum angle  which the string makes with the vertical after hitting the pin is  Pin L L l  Pin M M 1) cos1  L cos   l  2) cos1  L cos   l   Ll   Ll  3) cos1  L cos   l  4) cos1  L cos   l   Ll   Ll  20. A projectile is fired vertically upwards from the surface of the earth with a velocity kve where ve is the escape velocity and k 1. If R is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be (neglect air resistance) 1) 1  k 2 2) k 2R  3) R 1 k 2 4) R R 1 k2 1 k2 (NUMERICAL VALUE TYPE) This section contains 10 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, 0.33, 30, 30.27, 127.30). Attempt any five questions out of 10. Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 21. The isotope 12 B having a mass 12.014 u undergoes   decay to 12 C. 162C has an 5 6  excited state of the nucleus 12 C * at 4.041 MeV above its ground state. If 12 B 6 5 decays to 12 C *, the maximum kinetic energy of the   particle in units of MeV is ( 6 1u  931.5 MeV / c2, where c is the speed of light in vacuum). Sec: Sr.Super-60 & All Space for Rough Work Page 8

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 22. Magnetic field at the center (at nucleus) of the hydrogen like atoms (atomic number  z ) due to the motion of electron in nth orbit proportional to zx then xy is______ ny 23. In YDSE, the thickness (in m ) of a glass slab is x   1.5 should be placed before the upper slit S1 so that the central maximum now lies at a point where 5th bright fringe was lying earlier (before inserting the slab). Wavelength of light used is 5000 A0 . Then x _______ 24. A closed and an open organ pipe of same length are set into vibrations simultaneously in their fundamental mode to produce 2 beats. The length of open organ pipe is now halved and of closed organ pipe is doubled. Now find the number of beats produced. 25. A carrier wave of peak voltage 14V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be ____ volts 26. A 27 mW laser beam has a cross-sectional area of 10mm2 . The magnitude of the maximum electric field in this electromagnetic wave is given x 10 y v / m . Then xy is___[ 0  9 1012 SI units, C  3108m / s ] 27. A small bar magnet placed with its axis at 300 with an external field of 0.06T experience a Torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is x 102 Joule . Then x is______ 28. A horizontal force F is applied at the top of an equilateral triangular block having mass m. The minimum coefficient of friction required to topple the block before translation will be   1 , then 2x is______ x F A aa B aC 29. A spherical drop of capacitance 12F is broken into eight drops of equal radius. What is the capacitance of each small drop in F ? 30. An element of atomic number 9 emits K X  ray of wavelength  . Find the atomic number of the element which emits K X  ray of wavelength 4 . Sec: Sr.Super-60 & All Space for Rough Work Page 9

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P CHEMISTRY Max Marks: 100 (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases. 31. Decreasing order of kinetic energy of photo-electron emitted on irradiating a metal surface with x  ray, uv , visible rays is 1) x  uv  visible 2) x  uv  visible 3) uv  visible  x 4) x  visible  uv 32. Correct statements in the following are OO || || a)CH3  C CH3 is liquid, NH2  C NH2 is solid b)Ethers are more soluble in H2O than alcohols c)order of melting point H2O  HF  NH3 CH2 OH CH2 OH CH3  OH  CH  OH CH2 OH d)order of viscosity CH2 OH 1) a,b,c 2) b,c, d 3) a,c,d 4) a,b,c,d 33. Order of Ionic character of the molecules NaF, KCl, NaCl, KBr is 1) NaF  NaCl  KCl  KBr 2) NaF  NaCl  KCl  KBr 3) KCl  NaCl  KBr  NaF 4) NaCl  NaF  KCl  KBr 34. Correct statement about H2O2 is a) H2O2 has non-planar structure b)urea can be added to H2O2 as stabiliser c) H2O2 acts as both oxidising & reducing agent d)10 volume H2O2 solution  10% H2O2 1) a,b,d 2) a,b,c,d 3) b,c, d 4) a,b,c 35. Order of  f H 0 of graphite, diamond, fullerene is 1) Diamond > Graphite > fullerene 2) Graphite > Diamond > fullerene 3) fullerene >Diamond > Graphite 4) fullerene > Graphite > Diamond Sec: Sr.Super-60 & All Space for Rough Work Page 10

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 36. When 3.2 g sulphur is vaporised at 4500C and 723 mm Hg pressure, the vapours occupy a volume of 780 ml what is the molecular formula of S-vapour 1) S2 2) S4 3) S6 4) S8 37. Acidified KMnO4 oxidises oxalic acid to CO2 . What is volume in lit  of 104 M KMnO4 required to completely oxidise 0.5 L of 102 M oxalic acid in acidic medium. 1) 125 2) 1250 3) 200 4) 20 38. At 600C , N2O4 is 50% dissociated. Calculate G0 at this temperature & 1 atm pressure. log1.33  0.1239 1) 789.98 KJ / mol 2) 403.98 KJ 3) 331.88 KJ 4) 504.89 KJ / mol 39. The solubilities of AgCl in water, 0.01M CaCl2, 0.01M NaCl, are denoted by S1, S2, S3 then relation 1) S1  S2  S3 2) S1  S3  S2 3) S1  S2  S3 4) S2  S1  S3 40. The following are some statements related to group 15 hydrides i) Reducign property increases from NH3 to BiH3 ii) Tendency to donate lone pair decreases from NH3 to BiH3 iii) Thermal stability of hydrides decreases from NH3 to BiH3 iv) Bond angle decreases from NH3 to BiH3 the correct statements are: 1) i,ii,iii and iv 2) i,iii and iv 3) i, ii and iv 4) i and iv 41. Geometry and hybridisation of Xe in XeOF4 molecule is 1) Square planar, sp3d 2 2) square pyramidal, sp3d 2 3) tetrahedral, sp3 4) octahedral sp3d 2 42. Arrange  I Ce3, II  La3  III  Pm3 and  IV Yb3 in increasing order of their ionic radii. 2) I  IV  III  II 1) IV  III  I  II 4) III  II  I  IV 3) IV  III  II  I Sec: Sr.Super-60 & All Space for Rough Work Page 11

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 43. Which of the following statement(s) is/are true or false? S1 :complexes having d 0 or d10 configuration of metal ions are always diamagnetic S2 : In organometallic compounds, carbon is bonded to metals directly S3 : In FeCO5 , the Fe  C bond possesses both  and  characteristics S4 : Extra stability of metal carbonyls is explained by synergic bonding 1) TTTT 2) FTFT 3) TTFF 4) FTTT 44. Which of the following pair of acid radicals can be distinguished by using dil. H2SO4 ? 1) C2O42 and NO3 2) NO3 and NO2 3) Cland Br 4) HCO3 and CO32 45.  f G0 vs T plot in the Ellingham diagram slopes downward for the reaction 1) Mg  1 O2  MgO 2) 2 Ag  1 O2  Ag2O 2 2 3) C  1 O2 CO 4) CO  1 O2 CO2 2 2 46. Conductivity & molar conductance of 0.01 M weak electrolyte AB are 3102ohm1 cm1 and 12 102 S cm2mol1respectly. find T f (depression in freezing point) for the 0.1 molal aqueous AB solution K f of water  1.86 1) 0.2604 2) 26.04 3) 18.6 4) 186 47. Rate of reaction at 400 K with catalyst is equal to rate of reaction at 500 K without catalyst. What will be the activation energy of reaction if the catalyst lower the activation energy by 20 KJ/mol 1) 120 KJ/mol 2) 80 KJ/mol 3) 100 KJ/mol 4) 20 KJ/mol 48. Match the following Column-I Column-II A) Milk p) Device to adsorb poisonous gases B) x  kp1/n q) Silicagel m C) For humidity control r) Emulsion D) Gas masks s) Freundlich adsorption isotherm 1) A  r, B  s,C  q, D  p 2) A  s, B  q,C  p, D  r 3) A  r, B  q,C  p, D  s 4) A  q, B  s,C  r, D  p Sec: Sr.Super-60 & All Space for Rough Work Page 12

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 49. At 1000C, benzene and toluene have vapour pressure of 1375 torr and 558 torr, Respectively. Assuming these two form an ideal solution, then calculate the mole fraction of Benzene in vapourphase at 1 atm and 1000C.? 1) 0.247 2) 0.753 3) 0.447 4) 0.553 50. Correct representation of edge lengths, Axial angles of trigonal 1) a  b  c,       900 2) a  b  c,       900 3) a  b  c,       900 4) a  b  c,       900 (NUMERICAL VALUE TYPE) This section contains 10 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, 0.33, 30, 30.27, 127.30). Attempt any five questions out of 10. Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 51. How many of the following are true: OO || || a) Acidic nature of R  C O  OH  R  C OH b) Acidic nature of oxalic acid > Butanoic acid c) Acidic nature of Sulphonic acid > carboxylic acid d) Amides are less basic than amines CH 2   e) Order of stability of free radical NH2 NH2 NH2  NH 2  NH2 f) Order of Basic strength NH2 CH  CH  CH  CH 2 CH  2 2 2 2    g) Order of stability NO2 Cl OMe CH3 Sec: Sr.Super-60 & All Space for Rough Work Page 13

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 52. How many of the following tests are correctly matched. a) Br2 / CCl4 (or) Br2 / H2O (or) alkaline KMnO4 ----- test for unsaturation b) Anhyd. ZnCl2  conc. HCl -----Test distinguishing 10,20,30 alcohols c) 2,4 D.N.P------- Test for carbonyl compounds. d) NaHCO3 --------- Test for carboxylic group e) carbyl amine test – identification test for 10 - amines f) NaOH -------- Test for amide group g) Hinsderg reagent test ------- Test for the separation of 10,20,30      amines 53. How many of the following are non – aromatic a) b) c) d) e) f) g) N h) i) 54. How many of the following essential amino acids. COOH COOH NH2 H H2N H a) H b) CH CH32 COOH COOH H2N H H2N H CH2 4 d) CH 2 c) NH2 COOH Sec: Sr.Super-60 & All Space for Rough Work Page 14

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P COOH COOH H2N H H2N H CH2 CH  OH C O e) CH3 f) NH2 55. A polymer contains 10 molecules with molecular mass 1000 and 10 molecules with molecular mass 10000 then calculate poly dispersity index (PDI) 56. Aspartame is ' x' times more sweeter than cane sugar then value of ' x' is 57. How many of the following would give positive test with tollen’s reagent. O O || || a) CH3  C H b) CH3  C OH O O || || c) H  C OH d) Ph  C H H3C OH H3C OCH3 C C e) H OC2H5 f) CH3 OCH3 O OH h) CH3  C  C  H g) O OH i) O 58. How many of the following will give positive Haloform test OH Ph b) CH3  CH  CH2  CH3 a) | Cl Sec: Sr.Super-60 & All Space for Rough Work Page 15

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P c) CH3  OH O O CH3 CH || d) OH e) CH3  C NH2 O O || || f) CH3  C Cl g) CH3  C OH OO || || h) CH3  C CH2  C OC2H5 i) O 59. How many of the following will give methane on reaction with CH3MgBr ? O C  OH a) H2O b) C2H5  OH O || c) C2H5  C OH d) e) HCN f) CH3  C  CH g) NH3 h) HCHO i) CH3  C  N j) CO2 60. How many of the following statements is/are correct about following reaction OO Ph  || || H i)CoHn3cOKOH product(s) C C II  I a) Order of the reaction is zero b) Hydride shift involves in rate determining step c) It is a disproportionation reaction d) Oxidation of carbon (I) take place e) Reduction of carbon (II) take place f) OH first attacks at carbon (I) g) OH first attacks at carbon (II) h) It is known as Cannizaro reaction i) malic acid is the final product of the reaction Sec: Sr.Super-60 & All Space for Rough Work Page 16

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P MATHS Max Marks: 100 (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases. 61. A man goes in for an examination in which there are 4 papers,each paper has 10 questions and each question carry one mark The number of ways of getting 20 marks on whole is 1) 750 2) 860 3) 881 4) 891 62. Thirty two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better – ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is 1) 16/31 2) 1/2 3) 17/31 4) 18/31 63. f : X  Y is a function where X  0,1,2,.........,9 , Y  0,1,2,.......,100 and f 5  5 . Then the probability that the function on the type f : X  B :where B  Y is of bijection in nature is 1) 100 10! 2) 101C 9.9! 3) 1 4) 100C9.9! r 1 r 9100cr 2 100 101  r10.100cr  r9.100Cr1 r 1 r 1 64. Period of x  2x  ........  nx  nn  1 x is 2 1) 1 2) 2 3) n 4) 3 rth r n 2 Lt tr n r1 65.  ______ Let the term tr is given by tr  4 then 1  r  r 1) 1 2) 1 3) 1 4) 1 4 23 66. z1, z2, z3 are complex numbers such that 2 1  1 . Then the points z1, z2, z3 and z1 z2 z3 origin are 1) collinear 2) concyclic 3) non concyclic 4) non coplanar Sec: Sr.Super-60 & All Space for Rough Work Page 17

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 67. If f  x  90x2  20x  1. Then sum of digits of f 111111 is 1) 11 2) 12 3) 13 4) 14 68. 404C4  303C4.4C1  202C4.4C2 101C4.4C 3  ______ 1) 1015 2) 1014 3) 2024 4) 2025 2 1 sin x3  69.  4 d 3 sin x  ______ 1 sin x3  1) sin1 1  3 sin x  c  2) sin1 3 sin x  c 1 Tan1  3 sin2 x 1  1 Tan1  3 sin x  2  2 3 sin x  2  2  3)  c 4)  c     1 70.   xsin xdx  ______ where [.] represents greatest integer function. 1 1) 1 2) 2 3) 4 4) 0  71. Differential equation representing the family of curves y  ex C1  C2x  C3x2 is 1) d3y  y0 2)  dy 3 1 0 dx3  dx  3) d3y  3 d2y  3 dy  y  0 4) None dx3 dx2 dx 72. If two distinct chords drawn from the point  p,q on the circle x2  y2  px  qy are bisected by x  axis  pq  0 . Then 1) p2  q2 2) p2  8q2 3) p2  8q2 4) p2  8q2 73. If the focus of the parabola  y  k 2  4 x  h lies between the lines x  y  1and x  y  3. Then 1) 0  h  k  2 2) 0  h  k  1 3) 1 h  k  2 4) 1 h  k  3 Sec: Sr.Super-60 & All Space for Rough Work Page 18

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P 74. r2 x2  r2 y2  1 will represents ellipse then ‘r’ lies in the interval r  6r  6  5 1) ,2  5, 2) 3, 3) 2,3 4) 1, 75. If radii of director circles of x2  y2 1 and x2  y2 1 are 2r and r respectively a2 b2 a2 b2 and ea ,eb are eccentricities of the ellipse and hyperbola respectively. Then 1) 2eb2  ea2  6 2) ea2  4eb2  6 3) 4eb2  ea2  6 4) eb2  2ea2  0 76. a,b R  a  b mod m where a,b  Z and m  Z  . Then the relation R is 1) Reflexive 2) symmetric 3) Transtive 4) Equivalence pbc 77. p  a;q  b, r  c and a q c  0. Then the value of p  q  r  _____ pa qb rc abr 1) 1 2) 2 3) 3 4) 4 78. One of the values of k for which the planes kx  4 y  z  0 , 4x  ky  2z  0 and 2x  2y  z  0 intersect in a straight line is 1) 0 2) 1 3) 2 4) 3 79. Let a line cut the sides PQ, PS and diagonal PR of a parallelogram at Q1, R1 and S1 respectively such that PQ1  1PQ, PR1  3PR, PS1  2PS . Then 1) 1  1  1 2) 1  1  1 1 2 3 1 2 3 3) 1  1  1 4) 1  1  1 1 2 3 1 2 3 80. For all natural numbers; n 1; 1  1  ......  1 n1 n 2 2n 1)  13 2)  13 3)  13 4)  13 24 24 14 24 Sec: Sr.Super-60 & All Space for Rough Work Page 19

Sri Chaitanya IIT Academy 02-05-2021_Sr.Super60 & All_Jee-Main_GTM-22_Q.P (NUMERICAL VALUE TYPE) This section contains 10 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, 0.33, 30, 30.27, 127.30). Attempt any five questions out of 10. Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 81. If f  x is a real number in 0,1 then the value of  f  x  Lt Lt 1 cos2m n!x when x is irrational and m,n N, is __ m n 82. Let f x  3  2 cos x; x    ,   where . denotes the greatest integer function. 2 2  The number of points of discontinuity of f  x is___________ 83. If 'a ' and 'b' are the numbers of points of non differentiability of f x  sin 1 x   and gx   2  ; x 0 (where [.] represents greatest integer function) 1  x2  respectively. Then the value of a  b is_______ 84. If 27a  9b  3c  d  0 . Then the equation 4ax3  3bx2  2cx  d  0 has atleast one real root lies between  and  . Then    is______. 85. If x, y  R and x2  y2  xy  1. Then the maximum value of x3 y  xy3 is______ 86.  is real root of 7 cos2 x  4cos x 1  0 if p cos2 2  q cos 2  r  0 where p,q,r are real constants. Then p  q  r  ____ 87. Number of real solutions of y  sin x, y  cos1cos x, 2  x  2 is________ 88. If each side of length 'a ' of an equilateral triangle subtends an angle of 600 at the top of a tower of ‘h’ metres height situated at the centre of the triangle. Then 3h2  _____ a2 89. A3,2, B2,5be two points.If the point P0,k  lies on y  axis such that PA  PB is maximum. Then k 1  _____ 5 90. Two lines x  3  y  1  z  6 and x  5  y  2  z  3 intersect at R. The reflection 1 3 1 7 6 4 of R on xy  plane is ,,  . Then       ________ Sec: Sr.Super-60 & All Space for Rough Work Page 20