SPL Module-1

Class (XII) - [SPJ 2023 - Module - I] 18. The ratio of close packed atoms to tetrahedral holes in cubic close packing is A) 1 : 1 B) 1 : 2 C) 1 : 3 D) 2 : 1 19. In a metal oxide, the oxide ions are arranged in hexagonal close packing and metal ion occupy 2 rd of 3 the octahedral voids. The formula of the oxide is A) MO B) M2O3 C) MO2 D) M2O 20. In a crystal system, anions ‘B’ are in ccp arrangement. Cations ‘A’ occupy 50% of octahedral voids and 50% tetrahedral voids. Its formula of representation is A) A2B3 B) A3B2 D) AB2 D) AB3 21. An alloy of copper, silver and gold is found to have copper constituting the ccp lattice. If silver atoms occupy the edge centres and gold is present at body centre, the alloy will have the formula A) Cu4Ag2Au B) Cu4Ag4Au C) Cu4Ag3Au D) Cu2AgAu 22. A metal crystallizes in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach distance between two atoms in metallic crystal will be A) 2 2 a B) 2 a a D) 2a C) 2 23. An element has a bcc structure with a cell edge of 288pm. The density of the element is 7.2g/cm3. How many unit cells are present in 208g of the element? A) 28.88×1023 unit cells B) 30.32×1023 unit cells C) 12.08×1023 unit cells D) 24.16×1023 unit cells 24. Tl Al(SO4)2. xH2O is bcc with a = 1.22 nm. If the density of the solid is 2.32 g/cc, then the value of ‘x’ is (atomic wt : Tl = 204, Al = 27, S = 32, O = 16, H = 1) A) 2 B) 4 C) 47 D) 70 25. A face centred cubic element (atomic mass - 60) has a cell edge length of 400 pm. What is its density? A) 6.2 g cm–3 B) 24.8 g cm–3 C) 12.4 g cm–3 D) 3.1 g cm–3 26. The total number of unit cells in 78g of potassium if it crystallizes in bcc lattice is A) 6.022 1022 B) 6.02 1023 C) 3.011022 D) 4.11023 27. A compound forms HCP structure. What is the total number of voids in 0.5 mol of it A) 9.033 × 1023 B) 6.022 ×1023 C) 3 ×1023 D) 6 × 1022 51

Class (XII) - [SPJ 2023 - Module - I] 28. How many unit cells are present in 39 g of potassium that crystallises in body - centred cubic structure A) NA B) NA C) 0 .5NA D) 0.75NA 4 29. Gold crystallises in ccp structure. The number of unit cells in 1g of gold is about (Atomic mass 197) A) 3.06 1021 B) 1.511021 C) 7.64 1020 D) 3.82 1019 30. Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is 3 43 1 33 A) 2 B) 3 2 C) 2 D) 4 2 31. A metal has an fcc lattice. The edge length of the unit cell is 404 pm. The density of the metal is 2.72 g cm–3. The molar mass of the metal is : (NA Avogadro’s constant = 6.02 × 1023 mol–1) A) 30 g mol–1 B) 27 g mol–1 C) 20 g mol–1 D) 40 g mol–1 32. KCl crystallizes in the same type of lattice as does NaCl and CsF in the CsCl type of structure. The molar mass of CsF is twice that of KCl and the ‘a’ value for KCl is 1.5 times that of CsF. The ratio of the densities of CsF to that of KCl is A) 2.05 B) 1.69 C) 3.2 D) 4.51 33. KCl crystallizes in NaCl structure, if  Na  0.5 and  Na  0.70 , the ratio of the edge length of a unit  Cl K cell of KCl to that of NaCl is A) 1.18 B) 2.18 C) 1.14 D) 2.14 34. Co-ordination number of Na+ and Cl– in NaCl crystal is A) 8 and 8 B) 4 and 4 C) 6 and 6 D) 8 and 4 35. What happens to the co-ordination number in a crystal lattice as pressure increases? A) increases B) decreases C) remains same D) either increase or decrease 36. Which of the following fcc structure contains cations in alternate tetrahedral voids? A) KCl B) ZnS C) NaCl D) Na2O 37. The range of radius ratio for an octahedral arrangement of ions in an ionic solid is A) 0–0.155 B) 0.155–0.225 C) 0.225–0.414 D) 0.414–0.732 52

Class (XII) - [SPJ 2023 - Module - I] 38. Which one of the following defects in the crystals lowers its density? A) Frenkel defect B) Schottky defect C) F-centres D) Interstitial defect 39. At room temperature, the number of Schottky defects per cm3 in NaCl crystal is A) 102 B) 106 C) 108 D) 1012 40. Excess of K makes KCl ‘P’ colour Excess of Na makes NaCl ‘Q’ colour Zinc oxide is heated it becomes ‘R’ colour Excess of Li makes LiCl ‘S’ colour Identify P,Q,R,S A) P-yellow , Q-yellow , R- pink , S- violet B) P-pink , Q-yellow , R- yellow , S- violet C) P-pink , Q-yellow , R- violet , S- yellow D) P-violet , Q-yellow , R- yellow , S- pink Single correct 41. If AgCl is dopped with 0.001 mol percent of CdCl2, the number of cation vacancies per mol of AgCl will be A) 6.02 1023 B) 6.02 1021 C) 6.02 1018 D) 3.011018 42. Cations are present in the interstitial sites in A) Frenkel defect B) Schottky defect C) Vacancy defect D) Metal deficiency defect 43. Which one of the following elements should silicon be doped with so as to give p-type semiconductor? A) Germanium B) Arsenic C) Selenium D) Boron Multiple Answer Type 44. From the following statements which one is correct A) Long range order is the arrangement of constituent particles in a regular and periodically repeating pattern B) At sufficiently high temperature, intermolecular forces bring the constituent particles so close that they cling to one another and occupy fixed positions. C) Quartz can be converted into glass by heating into high temperature and readily cooled in room temperature. This is because quartz contain both long range and short range order. D) Anisotropy of crystalline solids is due to different arrangement of particles in different direciton 53

Class (XII) - [SPJ 2023 - Module - I] 45. Which of the following statements is/are correct? A) The co-ordination number of each type of ion in CsCl crystal is 8 B) A metal that crystallises in B.C.C. structure has co-ordination number equal to 12 C) In fcc lattice, the body centre is the octahedral void  D) The length of unit cell in NaCl is 552 pm rNa  95 pm; rCl  181 pm 46. From the following compound/s can act as p-type semiconductor : A) Germanium is doped with Arsenic B) Silicon is doped with Gallium C) Cu1.8O D) Germanium is doped with Silicon Numerical & Integer Type 47. AgI crystallises in zinc blende structure with I– ions at lattice points. What percentage of tetrahedral voids is occupied by Ag+ ions? 48. Zinc crystallises in hcp lattice. Its coordination number is 49. How many of the following crystal defects can account for cationic vacancies in NaCl? (assume that all anionic sites are occupied) i) Frenkel ii) Schottky iii) Impurity defect due to crystallisation of molten NaCl containing a little amount of SrCl2 iv) Non stoichiometric defect arising when crystals of NaCl are heated in an atmosphere of sodium vapour Matrix match Type 50. Match List 1 with List II and select the correct answer using the codes given below the lists: 1. Ionic solids a. Cu, Rb, brass 2. Covalent solids b. Ar, solid CO2, ice, P4O10, I2, P4 3. Molecular solids c. Diamond, SiC, SiO2(quartz), AlN, Si, graphite 4. Metallic solids d. glass, (quartz glass), rubber, plastics 5. Amorphous solids e. NaCl, (NH4)3PO4, LiBr A) 1-e, 2-c, 3-b, 4-d, 5-a B) 1-e, 2-c, 3-b, 4-a, 5-d C) 1-a, 2-d, 3-e, 4-b, 5-c D) 1-e, 2-c, 3-d, 4-b, 5-a 54

Class (XII) - [SPJ 2023 - Module - I] LEVEL- I 1. Number of atoms present in a fcc unit cells is A) 1 B) 2 C) 4 D) 6 2. Which of the following is not a characteristic features of poly crystalline solid : A) They appear amorphous B) They have micro crystalline structure C) Individual crystals are randomly oriented D) Individual crystals are isotropic 3. A atoms at the corners, B atoms on the alternate face centre. Find the formula of crystal. A) A3B2 B) A2B3 C) AB D) AB3 4. Examples of unit cell with crystallographic dimensions a  b  c,     900 ,   120 is A) ZnO B) SnO2 C) CaCO3 D) TiO2 5. A solid element ‘X’ forms cubic crystal, in which the atoms occupy each corner, two atoms on each body diagonal and also one atom at each edge centre. The effective number of ‘X’ atoms in the unit cell is A) 12 B) 4 C) 8 D) 28 6. AB is an ionic solid. If the ratio of ionic radius of A+ and B– is 0.52. What is the co-ordination number of B? A) 2 B) 3 C) 6 D) 8 7. CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct A) rCs  rCl  3a B) rCs  rCl  3a 2 C) rCs  rCl  3 a D) rCs  rCl  3a 2 8. A solid AB has NaCl type structure with edge length 580.54 pm. The radius of A+ is 100 pm. The radius of B– is A) 178.12 pm B) 332.2 pm C) 190.2 pm D) 200 pm 9. The appearance of violet colour when solid KCl is heated in K vapour is generally due to A) Vacancy defect B) Schottky defect C) Frenkel defect D) F-centres 55

Class (XII) - [SPJ 2023 - Module - I] 10. Which of the following arrangements shows schematic alignment of magnetic moments of ferrimagnetic substances? A) B) C) D) LEVEL - II 1. An element crystallises in fcc lattice having edge length 400 pm. What is the maximum diameter of atom which can be placed in interstitial site without distorting the structure A) 117 pm B) 130 pm C) 135 pm D) 140 pm 2. Sum of the fractions of the total volume occupied by atoms present in a simple cube and fcc is A)  6 B)  2   1 2   2 1 6 C) D) 6 8 3. In NaCl at room temperature number of Schottky defect per 1016 ions is A) 1 B) 1022 C) 1016 D) 106 4. A compound alloy of gold and Cu crystallises in a cubic lattice in which the gold atoms occupy at the corners of a cube and the copper atoms occupy the centres of each of the cube faces. What is the empirical formula of this compound. A) AuCu3 B) Au3Cu C) Au2Cu3 D) AuCu 5. In a close packed structure, it is found that lattice has oxide ions and half of the octahedral voids are occupied by ions of ‘A’ and one-eighth of the tetrahedral voids are occupied by ions of B. If the charge of B is +2 find that of A? A) +3 B) +2 C) +4 D) +1 6. The distance between an octahedral and tetrahedral void in fcc lattice would be A) 3 a B) 3a C) 3a D) 3a 2 3 4 7. CsCl is bcc type structure. Find the density of unit cell has edge length is equal to 5.54Ao . GMM = 170g; NA = 6 × 1023 A) 3.33 g/cm3 B) 1.7 g/cm3 C) 4.7 g/cm3 D) 8.2 g/cm3 8. Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of lithium will be A) 152 pm B) 75 pm C) 350 pm D) 200 pm 9. The cubic unit cell of a metal (molar mass = 63.55 g mol–1) has an edge length of 362 pm. Its density is 8.92 g cm–3. The type of unit cell is A) primitive B) face centred C) body centred D) end centred 56

Class (XII) - [SPJ 2023 - Module - I] 10. Which one of the following statements are correct in context of point defects in a crystal? A) AgCl has anion Frenkel defect and CaF2 has Schotky defect B) AgCl has cation Frenkel defect and CaF2 has anion Frenkel defect C) AgCl as well as CaF2 have anion Frenkel defect D) AgCl as well as CaF2 have Schottky defect LEVEL - III Single correct 1. Location of octahedral voids in fcc lattice is A) 12 edge centers and 1 body centre B) 2 on each body diagonal C) 1 on each body diagonal D) 8 corners and 6 face centers 2. From the following, which one is correct matching : A) CrO2 - Antiferromagnetic B) F-centre contain NaCl - Paramagnetic C) MnO2 - Ferromagnetic D) MgFe2O4 - Diamagnetic 3. How many nearest neighbours does potassium have in BCC lattice? A) 8 B) 6 C) 12 D) 2 Numerical(Round off to two decimal points)/Integer type 4. In a compound AB, the ionic radii of A+ and B– are 88pm and 200pm respectively. What is the co- ordination number of A+? 5. A compound A+B– has rock-salt type structure. The formula mass of AB is 6.023y amu and the closest approach distance of A+ and B– in the crystal is y1/3 nm. Calculate the density of the lattice in Kg.m3? 6. A metal crystallises into two cubic phases, face centred cubic (fcc) and body centred cubic (bcc), whose unit cell lengths are 3.5 and 3.0 A0 respectively. Calculate the ratio of densities of fcc and bcc. 7. Packing efficiency in percentage of the 2D hexagonal close packing is (area based calculation). More than one correct 8. The correct statement(s) regarding defects in solid is (are) A) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion B) Frenkel defect is a dislocation defect C) Trapping of an electron in the lattice leads to the formation of F-centre D) Schottky defects have no effect on the physical properties of solids 57

Class (XII) - [SPJ 2023 - Module - I] 9. ZnO the heated. Then which of the following are correct A) Colour changes from yellow to white B) It loses O2 C) Zn2+ and electrons occupy interstitial site D) It is metal excess defect due to anion vacancy 10. Which of the following are correct A) Cu2+, O2, Fe3+ and Cr3+ are paramagnetic B) H2O, NaCl and C6H6 are diamagnetic C) Fe, Co, Ni, CrO2 and Gd are ferromagnetic D) MnO, Fe3O4, MgFe2O4 and ZnFe2O4 are ferrimagnetic 11. From the following select the correct statement/s A) In ccp arrangement, co-ordination number of atom is 12 is due to one atom is surrounded by 6 atoms in a plane and three atom on above and below the plane in symmetric manner B) In ccp arrangement both tetrahedral void and octahedral voids are present C) In ccp arrangement unit cell exactly similar to fcc D) In ccp arrangement ABAB pattern is following Matrix Match Type Question 12. Column-I Column-II 1) Rock salt NaCl p) Anion occupy the void having co-ordination number 4 2) CsCl q) Number of atoms in one unit cell = 4 3) ZnS r) Anions occupy the ccp arrangement 4) CaF2 s) Cations occupy the void having co-ordination number 4 t) Number of atoms in unit cell = 1 A) 1 q, r; 2  t; 3  q, r,s; 4  q, p B) 1  p, q; 2  r; 3  q, r; 4  s C) 1  r; 2  s; 3  q, r; 4  p D) 1  t; 2  s; 3  r; 4  q 58

Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 02 SOLUTION QUESTIONS [HOMEWORK] 1. Which of the following is a solid in solid solution A) glucose in water B) camphor in N2 C) copper dissolved in gold D) Amalgam of mercury with sodium 2. From the following, select the temperature independent concentration A) Molarity B) Normality C) Molality D) Volume % 3. 5L of a solution contains 25 mg of CaCO3. What is its concentration in ppm? (mol.wt of CaCO3 is 100) A) 25 B) 1 C) 5 D) 2500 4. The volume of water to be added to 100 cm3 of 0.5 N H2SO4 to get decinormal concentration is A) 400 cm3 B) 450 cm3 C) 500 cm3 D) 100 cm3 5. 60 ml of N H2SO4 , 10 ml of N HNO3 and 30 ml of N HCl are mixed together. The strength of the 5 2 10 resulting mixture is A) 0.1 N B) 0.2 N C) 0.3 N D) 0.4 N 6. What will be the volume of 0.01 M HCl required to completely react with 4g NaOH A) 100 ml B) 10 ml C) 1000 ml D) 10, 000 ml 7. Which of the following has highest Henry’s constant (KH/k bar) at 293 K A) Ar B) CO2 C) HCHO D) CH4 8. Vapour pressure of liquid depend only on A) Surface area of liquid B) Temperature C) Nature of liquid D) Both 2 and 3 59

Class (XII) - [SPJ 2023 - Module - I] 9. Which of the following graph is a correct representation of Henry’s law? A) B) C) D) 10. On adding a solute to a solvent having vapour pressure 0.80 atm, vapour pressure reduced to 0.60 atm. Mole fraction of solute is A) 0.25 B) 0.75 C) 0.50 D) 0.33 11. The boiling point C6H6, CH3OH, C6H5NH2 and C6H5NO2 are 80°C, 65°C, 184°C and 212°C respec- tively. Which will show highest vapour pressure at room temperature A) C6H6 B) CH3OH C) C6H5NH2 D) C6H5NO2 12. The vapour pressure of pure benzene and toluene at a particular temperature are 100 mm and 50 mm respectively. Then the mole fraction of benzene in vapour phase in contact with equimolar solution of benzene and toluene is A) 0.67 B) 0.75 C) 0.33 D) 0.50 13. A solution containing components A and B follows Raoult’s law when A) A–B attraction force is greater than A–A and B–B B) A–B attraction force is less than A–A and B–B C) A–B attraction force remains same as A–A and B–B D) Volume of solution is different from sum of volume of solute and solvent 14. A mixture of components A and B will show -ve deviation when A) Vmix  0 B) Hmix  0 C) A–B interaction is weaker than A–A and B–B interactions D) A–B interaction is stronger than A–A and B–B interactions 60

Class (XII) - [SPJ 2023 - Module - I] 15. A non ideal solution was prepared by mixing 30 ml chloroform and 50 ml acetone. The volume of mixture will be A) >80 ml B) <80 ml C) =80 ml D)  80 ml 16. A binary liquid solution is prepared by mixing-n-heptane and ethanol. Which one of the following state- ments is correct regarding the behaviour of the solution? A) The solution is non-ideal, showing negative deviation from Raoul’ts law B) The solution is non-ideal, showing positive deviation from Raoul’ts law C) n-heptane shows positive deviation while ethanol shows negative deviation from Raoul’ts law D) It is an ideal solution 17. A mixture of two completely miscible non-ideal liquids which distill as such without change in its composition at a constant temperature as though it were a pure liquid. This mixture is known as A) binary liquid mixture B) azeotropic mixture C) eutectic mixture D) ideal mixture 18. Raoul’ts law becomes a special case of Henry’s law when A) KH  p10 B) KH  p10 C) KH  p10 D) KH  p10 19. The system that forms maximum boiling azeotrope is A) Carbon disulphide - Acetone B) Benzene - Toluene C) Acetone - Chloroform D) n-Hexane - n-heptane 20. Which one of the following binary mixtures forms an azeotrope with minimum boiling point type? A) acetone-ethanol B) H2O - HNO3 C) benzene-toluene D) n-hexane-n-heptane 21. A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm Hg at 300 K. The vapour pressure of propyl alcohol is 200 mm Hg. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm Hg) at the same temperature will be A) 360 B) 350 C) 300 D) 700 22. Colligative properties depend on A) The nautre of the solute particles dissolved in solution B) The number of solute particles in solution C) The physical properties of the solute particles dissolved in solution D) The nature of solvent particles 23. The vapour pressure of water at 20°C is 17.5 mm Hg. If 18g of glucose (C6H12O6) is added to 178.2 g of water at 20°C, the vapour pressure of the resulting solution will be A) 17.324 mm Hg B) 15.750 mm Hg C) 16.500 mm Hg D) 17.500 mm Hg 61

Class (XII) - [SPJ 2023 - Module - I] 24. Calculate the boiling point of a 5% solution of cane sugar (C12H22O1A). Kb of H2O = 0.52 K kgmol–1 A) 375.01 K B) 373.08 K C) 374.12 K D) 376.12 K 25. A 0.5 molal solution of ethylene glycol in water is used as coolant in a car. If the freezing point constant of water be 1.86°C per mole, the mixture shall freeze at A) 0.93°C B) –0.93°C C) 1.86°C D) –1.86°C 26. A solution of urea (mol mass 56 g mol–A) boils at 100.18°C at the atmospheric pressure. If Kf and Kb for water are 1.86 and 0.512 K kg mol–1 respectively, the above solution will freeze at A)0.654°C B) –0.654°C C) 6.54°C D) –6.54°C 27. In the depression of freezing point experiment, it is found that i) The vapour pressure of the solution is less than that of pure solvent ii) The vapour pressure of the solution is more than that of pure solvent iii) Only solute molecules solidify at the freezing point iv) Only solvent molecules solidify at the freezing point A) i, ii B) ii, iii C) i, iv D) i, ii, iii 28. When mercuric iodide is added to the aqueous solution of potassium iodide, the A) freezing point is raised B) freezing point is lowered C) freezing point does not change D) boiling point does not change 29. A solution of 1 molal concentration of a solute will have maximum boiling point elevation when the solvent is A) Ethyl alcohol (Kb = 1.2C) B) Acetone (Kb = 1.80) C) Benzene (Kb = 2.6D) D) Chloroform (Kb = 3.8) 30. Camphor is often used in molecular mass determination in Rast method because A) it is readily available and cheap B) it has a very high cryoscopic constant C) it is volatile D) it is a solvent for organic substances 31. Osmotic pressure is 0.0821 atm at temperature of 300 K. Find concentration in mole/litre A) 0.033 B) 0.066 C) 0.33 × 10-2 D) 3 32. The osmotic pressure of a 5% (w/v) solution of cane sugar at 150°C is A) 2.45 atm B) 5.078 atm C) 3.4 atm D) 4 atm 62

Class (XII) - [SPJ 2023 - Module - I] 33. The osmotic pressures of equimolar solutions of urea, BaCl2 and AlCl3 will be in the order A) AlCl3 > BaCl2 > urea B) BaCl2 > AlCl3 > urea C) urea > BaCl2 > AlCl3 D) BaCl2 > urea > AlCl3 34. Which one of the following pairs of solutions can we expect to be isotonic at the same temperature? A) 0.1 M urea and 0.1 M NaCl B) 0.1 M urea and 0.2 M MgCl2 C) 0.1 M NaCl and 0.1 M Na2SO4 D) 0.1 M Ca(NOC)2 and 0.1 M Na2SO4 35. 1.0 molal aqueous solution of an electrolyte X3Y2 is 25% ionised. The boiling point of the solution is (Kb for H2O = 0.52 K kg mol) A) 375.5 K B) 374.04 K C) 377.12 K D) 373.25 K 36. Which of the following is the correct example of solid solution in which the solute in in gas phase? A) Copper dissolved in gold B) Camphor in nitrogen gas C) Hydrogen in palladium D) All of these 37. The mole fraction of helium in a saturated solution at 0°C is 1.2 × 10–6. Find the pressure of helium above the solution. Henry’s law constant is 6.8 × 10–6 atm–1 A) 1.176 atm B) 0.716 atm C) 0.176 atm D) 0.567 atm 38. Arrange the decreasing order of solubility of gases in water at 298 K A) Ar > CO2 > HCHO > CH4 > CH2 = CH–Cl B) HCHO > CH4 > CH2 = CH – Cl > CO2 > Ar C) CH2  CH  CH4  HCHO  CO2  Ar Cl D) HCHO  CH2  CH  CO2  CH4  Ar Cl 39. At a given temperature, total vapour pressure (in torr) of a mixture of volatile compounds A and B given by PTotal = 120 – 75 XB. Hence, vapour pressure of pure A and B respectively (in torr) are A) 120, 75 B) 120, 195 C) 120, 45 D) 75, 45 40. On freezing an aqueous solution of sodium chloride, the solid that starts separating out is A) ice B) sodium chloride C) solution D) none of these 41. The correct representation of van’t Hoff factor in relative lowering of vapour pressure A) P  nB B) P  in B PA0 in A  nB PA0 inA  inB C) P  in B D) P  in B PA0 in B  nA PA0 nA  nB 63

Class (XII) - [SPJ 2023 - Module - I] Matrix match 42. For a solution containing 25% ethanol, 25% acetone, 25% acetic acid and 25% H2O Column I Column II A. EtOH p. 0.5 B. acetone q. 0.15 C. AcOH r. 0.155 D. H2O s. 0.195 A) A  s; B  r;C  q; D  p B) A  r; B  s;C  q; D  p C) A  r; B  s;C  p; D  q D) A  p; B  q;C  r; D  s 43. Column-I Column-II 1) Least freezing point p) 1% sucrose 2) Same osmotic pressure q)1% NaCl 3) Highest boiling point r) 1% CaCl2 4) Lowest vapour pressure s) 1% glucose t) 1% fructose A) 1  q; 2  r, s; 3  p, q, t; 4  p, q, r, t B) 1  q, r; 2  r, s, t; 3  p, s, t; 4  p, q, r, t C) 1  q; 2  s, t; 3  q; 4  q D) 1  r; 2  r, s, t; 3  r; 4  r Numerical type questions 44. Certain substance A tetramerises in water to the extent of 80%. A solution of 2.5g of A in 100 g of water lowers the freezing point by 0.3oC. The molar mass of A in g is 45. Vapour pressure of a pure liquid X is 2 atm at 300 K. It is lowered to 1 atm on dissolving 1 g of Y in 20 g of liquid X. If molar mass of X is 200 g. What is the molar mass of Y in g? More than one correct type questions 46. In which of the following solution have solid solvents A) 24 carat gold B) Amalgam C) Dissolved gases in minerals D) Aerated drinks 47. Which of the following binary liquid solutions is ideal and obeys Raoult’s law? A) Acetone & chloroform B) C6H6 + C7H8 C) Ethanol + Cyclohexane D) C6H5Cl + C6H5Br 64

Class (XII) - [SPJ 2023 - Module - I] LEVEL- I Single correct type questions 1. The amount of sugar required to prepare 2L of its 0.1 M aqueous solution is A) 68.4 g B) 17.1 g C) 34.2 g D) 136.8 g 2. 50 mL of 0.5 M oxalic acid is needed to neutralise 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is A) 4 g B) 2 g C) 5 g D) 10 g 3. Which of the following statement/s is/are CORRECT with respect to Henry’s law constant (KH)? I) KH is a function of nature of the gas II) KH of N2 is 76.48 kbar at 303 K and 88.84 kbar at 293 K III) Highly soluble gases have low KH at the given temperature and pressure IV) KH has a unit of pressure or (pressure)–1 A) I, IV only B) I, II, III only C) II, III, IV only D) I, III, IV only 4. Liquids A and B form an ideal solution in the entire composition range. At 350K, the vapor pressures of pure A and pure B are 7×103 Pa and 12×103 Pa, respectively. The composition of the vapor in equilibrium with a solution containing 40 mol percent of A at this temperature is: A) XA  0.37; XB  0.6 B) XA  0.28; XB  0.72 C) XA  0.76; XB  0.24 D) XA  0.4; XB  0.6 5. Elevation in the boiling point for 1 molal solution of glucose is 2K. The depression in the freezing point for 2 molal solution of glucose in the same solvent is 2K. The relation between Kb and Kf is A) Kb = 0.5 Kf B) Kb = 2 Kf C) Kb = 1.5 Kf D) Kb = Kf 6. Example of a solid solution is : A) Camphor in Nitrogen gas B) Ethanol dissolved in water C) Oxygen dissolved in water D) Solution of hydrogen in palladium 7. A tooth paste contains 0.8  gmL–1 fluoride ion. Its concentrations in percent by mass is A) 0.8 B) 8 105 C) 8000 D) 800 8. The mole fraction of water in 20% aqueous solution of H2O2 is : A) 77/68 B) 68/77 C) 20/80 D) 80/20 65

Class (XII) - [SPJ 2023 - Module - I] 9. Solubility curves for some solid solutes in water are given in the diagram Select the CORRECT statement with respect to the solubility curves A) Solute D shows conversion of one hydrated form to another and the curve is a continuous solubility curve B) Solute C shows convertion of one hydrated form to another hydrated form and the curve is a discontinuous solubility curve C) The dissolution of B in water is an endothermic process D) The curve of solute A represents a continuous solubility curve 10. Vapour pressure of which of the following liquid is maximum at 298 K A) Water B) HF C) Ethanol D) Ammonia LEVEL- II Single correct type questions 1. At 20°C and 0.02 atm pressure, what is the solubility of oxygen in 1L of water. Given KH for oxygen is 4.6  104 atm A) 9 102 g B) 8 103 g C) 15104 g D) 8 104 g 2. Vapour pressure of C6H6 and C7H8 mixture at 50°C is given by P (mm Hg) = 179XB + 92, where XB is the mole fraction of C6H6. A solution is prepared by mixing 936 g benzene and 736 g toluene and if the vapours over this solution are removed and condensed into liquid and again brought to the temperature of 50°C, what would be mole fraction of C6H6 in the vapour state? A) 0.92 B) 0.16 C) 0.40 D) 0.76 3. The freezing point of a diluted milk sample is found to be -0.2°C, while it should have been -0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample? A) 2 cups of water to 3 cups of pure milk B) 1 cup of water to 3 cups of pure milk C) 3 cups of water to 2 cups of pure milk D) 1 cup of water to 2 cups of pure milk 4. Exactly 1.21 g of sodium salt of a saturated tricaboxylic acid is dissolved is 100 g of water and the resulting solution was found to begin freezes at –0.372° C. If a cryoscopic constant of water is 1.86 K kg mol–1, determine the molecular formula of the acid A) C3H4O3 B) C6H8O6 C) C4H6O4 D) C7H14O7 66

Class (XII) - [SPJ 2023 - Module - I] 5. The van’t Hoff factor i for an electrolyte which undergoes dissociation and association in solvent are respectively: A) greater than one and less than one B) less than one and greater than one C) less than one and less than one D) greater than one and greater than one 6. Which of the following aq. solutions at the same temperature are not isotonic with one another? A) 0.15 M urea B) 0.05 M CaCl2 C) 0.1M MgSO4 D) 0.15 M glucose 7. At a given temperature, total vapour pressure in torr of a mixture of volatile components A and B is given by PTotal  120  75XB hence, vapour pressure of pure A and B respectively (in torr) are A) 120, 75 B) 120, 195 C) 120, 45 D) 75, 45 8. Equal volumes of ethylene glycol (mol. mass = 62) and water are mixed. Kf of water = 1.86 K kg mol–1. The density of ethylene glycol is 1.11g/ml and that of water is 1g/ml.The depression of F.P produced is A) 0.0033 B) 0.0333 C) 0.333 D) 33.3 9. A 0.1 molal aquous solution of a weak acid is 30% ionised. If Kf for water is 1.86oC/m, the freezing point of solution will be A) –1.8oC B) –0.18oC C) –0.54oC D) –0.24oC 10. A 0.025M solution of monobasic acid had a freezing point of -0.060C. Calculate Ka for acid (Kf =1.86 K kg mol-1). Assume M=m A) 4×10-3 B) 3×10-4 C) 2×10-3 D) 3×10-3 LEVEL- III Single correct type questions 1. A solution of a non-volatile solute in water freezes at –0.30°C. The vapour pressure of pure water at 298 K is 23.51 mm Hg and Kf for water is 1.86 Kkgmol–1. Calculate vapour pressure of this solution at 298 K A) 23.51 mm Hg B) 24.62 mm Hg C) 23.44 mm Hg D) 22.16 mm Hg 2. Molecules of benzoic acid (C6H5COOH) dimerise in benzene.'w' g of the acid dissolved in 30g of benzene shows a depression in freezing point equal to 2K. If the percentage association of the acid to form a dimer in solution is 80, then w is: (Given that Kf=5 Kkgmol–1) A) 1.8 g B) 2.4 g C) 1.0 g D) 1.5 g 3. Which of the following binary liquid solutions is ideal and obeys Raoult’s law? A) Acetone & chloroform B) HCl & water C) Ethanol + Cyclohexane D) C6H5Cl + C6H5Br Numerical type questions 4. K2 HgI4  is 40% ionised in aqueous solution. Then the value of its van’t Hoff factor (i) is 67

Class (XII) - [SPJ 2023 - Module - I] 5. xg of a non-electrolytic compound (molar mass = 200 g) are dissolved in 1L of 0.05 M NaCl aque- ous solution. The osmotic pressure of this solution is found to be 4.92 atm at 27°C. Assume com- plete dissociation of NaCl and ideal behaviour of this solution. Then the value of x is 6. The freezing point of a 0.08 molal aqueous solution of NaHSO4 is –0.372°C. If Kf for water is 1.86 K kg mol–1, the dissociation constant for the reaction HSO4  H  SO42 is 7. The osmotic pressure of 0.1M monobasic acid if its pH is 2.0 at 25oC is xRT atm. Then x is More than one correct type questions 8. Which of the following solutions forms solution having negative deviation from Raoult’s law? A) CCl4  CHCl3 B) C6H6  C7H8 C) H2SO4  H2O D) C6H5  NH2  C6H5  OH 9. Which of the following represents application of Henry’s law? A) Soft drink industry B) Bends experienced by SCUBA divers C) Functioning of lungs D) Anoxia experienced by mountain climbers 10. Identify correct statement/s from the following A) Ethanol (bp = 351.3 K) and water (bp = 373 K) can form maximum boiling azeotrope B) HNO3 (bp = 359 K) and water (bp = 373 K) can form minimum boiling azeotrope C) An azeotropic solution of ethanol and water boils at 351.15 K D) An azeotropic solution of HNO3 and water boils at 393.5 K 11. The vapour pressure of a given liquid will remains unchanged if A) surface area of liquid is decreased. B) the volume of liquid in the container is decreased C) the volume of the vapour phase is increased D) the temperature is decreased Matrix match 12. Column-I Column-II 1) Ethanol + water p) separated by simple distillation 2) HCl + water q) can form maximum boiling azeotropes 3) Chlorobenzene + bromobenzene r) ΔGmix  ve 4) Acetone + chloroform s) can form a warm solution A) 1  r; 2  q, r, s; 3  p, r; 4  q, r, s B) 1  q, r; 2  r, s; 3  q, r; 4  r, s C) 1  r; 2  p, r; 3  q, r,s; 4  q, r, s D) 1  q, r; 2  p, r; 3  q, r; 4  p, s 68

Class (XII) - [SPJ 2023 - Module - I] CHAPTER - 03 ELECTROCHEMISTRY QUESTIONS [HOMEWORK] 1. The correct value of emf of cell is given by I) Ecell  EOPanode  ERPCathode II) Ecell  EOPanode  ERPCathode III) Ecell  ER.Panode  ERPCathode IV) Ecell  EOPanode  EOPCathode A) III & I B) I & II C) III & IV D) II & IV 2. The emf of the cell, Ni Ni2 1.0M  Ag 1.0M  Ag [ E0 for Ni2+ / Ni =-0.25 volt, E0 for Ag+ / Ag = 0.80 volt] is given by A) 0.55 volt B) -1.05 volt C) +1.05 volt D) - 0.55 volt 3. In an electrochemical cell, a salt bridge is used : A) to avoid mechanical contact of electrolyte solution in cathode and anodic half - cell B) to maintain electrical neutrality in the cells C) to avoid liquid junction potential D) all of these 4. The cell reaction for the given cell is Pt H2 || PH  2 || PH  3 | Pt H2 1atm 1atm A) Spontaneous B) Nonspontaneous C) in equilibrium D) Cannot predicted 5. Which of the following statements about the spontaneous reaction occuring in a galvanic cell is al- ways true ? A) E0  0, G0  0, and QK B) E0  0, G0  0, and QK cell cell C) E0  0, G0  0, and QK D) E0  0, G0  0, and QK cell cell 6. Electrode potential of H electrode is negative in A) Haq | H2g B) Haq | H2g C) Haq | H2g D) Haq | H2g 1M 1atm 2M 1atm 0.1M 1atm 2M 2atm 69

Class (XII) - [SPJ 2023 - Module - I] 7. The position of some metals in the electrochemical series in decreasing electropositive character is given as Mg > Al > Zn > Cu > Ag. What will happen if a copper spoon is used to stir a solution of aluminium nitrate? A) The spoon will get coated with aluminium B) An alloy of aluminium and copper is formed C) The solution becomes blue D) There is no reaction 8. For the cell reaction 2Fe3+ (aq) + 2I– (aq)  2Fe2+ (aq) + I2(aq) E = 0.24V at 298 K. The standard Gibbs energy 0 G of the cell reaction is: cell r A) –46.32 kJ mol–1 B) –23.16 kJ mol–1 C) 46.32 kJ mol–1 D) 23.16 kJ mol–1 9. In the electrochemical cell Mg(s) | Mg2 || Zn2 | Zn; E0  3.13 V . The correct plot of Ecell versus Mg2  log Zn2  will be represented as A) B) C) D) 10. In the electrochemical cell : Zn | ZnSO4 (0.01M) || CuSO4 (1.0M) | Cu, the emf of this Daniel cell is E1. When the concentration of ZnSO4 is changed to 1.0 M and that of CuSO4 changed to 0.01 M, the emf changes to E2. From the followings which one is the relationship between E1 and E2? (Given,  RT  0.059) F A) E1 = E2 B) E1 < E2 C) E1 > E2 D) E2 = 0  E1 70

Class (XII) - [SPJ 2023 - Module - I] 11. Saturated solution of KNO3 is used to make salt bridge because A) Velocity of K+ is greater than that of NO3 B) Velocity of NO3 is greater than that of K+ C) Velocity of K+ and NO3 are nearly the same D) KNO3 is highly soluble in water 12. The presence of H2 required to make the potential of H2 electrode zero in pure water at 298 K is A) 10–4 atm B) 10–14 atm C) 10–12 atm D) 10–10 atm 13. A hydrogen gas electrode is made by dipping platinum wire in a solution of HCl of pH=10 and by passing hydrogen gas around the platinum wire at one atm pressure. The oxidation potential of electrode would be? A) 1.18 V B) 0.059 V C) 0.59 V D) 0.118 V 14. For a cell involving one electron E = 0.59V at 298 K, the equilibrium constant for the cell reaction is: cell [Given that 2.303RT = 0.059 V at T = 298K] F A) 1.0 × 102 B) 1.0 × 105 C) 1.0 × 1010 D) 1.0 × 1030 15. Following limiting molar conductivities are given as o  x Scm2mol1 mH2SO4  o  yScm2mol1 mK2SO4  o  z Scm2mol1 m CH3COOK   0m in S cm2mol1 for CH3COOH will be B) x + y – z A) x – y + 2 z C) x – y + z D) x  y  z 2 16. The conductivity of electrolytic solutions depends on A) Size of the ions produced B) Concentration of electrolyte C) Temperature D) All of these 71

Class (XII) - [SPJ 2023 - Module - I] 17. Which of the following decreases on dilution of electrolyte solution A) Equivalent conductance B) Molar conductance C) Specific conductance D) Conductance 18. Cell constant has unit A) cm B) cm–1 C) cm2 D) mol/L 19. The electrical properties and their respective SI units are given below. Identify the wrongly matched pair Electrical property SI unit A) Specific conductance S m–1 B) Conductance S C) Equivalent conductance S m2 eq–1 D) Cell constant M 20. Which is correct regarding the plot of m versus C1/2 for electrolytes? A) Linear with positive slope for KCl B) Linear with positive slope for CH3COOH C) Non linear for NaCl D) Linear with negative slope for NaCl  21. 0 Molar conductivities  m at infinite dilution of NaCl, HCl and CH3COONa are 126.4, 425.9 and 91.0 S cm2 mol-1 respectively.  0 for CH3COOH will be: m A) 425.5 S cm2 mol-1 B) 180.5 S cm2 mol-1 C) 290.8 S cm2 mol-1 D) 390.5 S cm2 mol-1 22. Consider the statements S1 and S2: S1 : Conductivity always increases with decrease in the concentration of electrolyte. S2 : Molar conductivity always increases with decrease in the concentration of electrolyte. The correct option among the following is: A) Both S1 and S2 are correct B) S1 is wrong and S2 is correct C) S1 is correct and S2 is wrong D) Both S1 and S2 are wrong 72

Class (XII) - [SPJ 2023 - Module - I] 23. The value of A in Debye -Huckel Onsagar equation for a given solvent and temperature depend on A) Solubility B) The charge on the cation and anion produced on the dissociation of the electrolyte in the solution C) Viscocity D) density 24. Which one of the following graphs between molar conductivity m  versus C is correct? A) B) C) D) 25. The molar conductivity of a 0.5 mol/dm3 solution of AgNO3 with electrolytic conductivity of 5.76 × 10–3 S cm–1 at 298 K is A) 28.8 S cm2/mol B) 2.88 S cm2/mol C) 11.52 S cm2/mol D) 0.086 S cm2/mol 26. The limiting molar conductivities of HCl, CH3COONa and NaCl are respectively 425, 90 and 125 ohm–1 at 298K. The molar conductivity of 0.1M CH3COOH solution is 7.8 s cm2 mol–1 at the same temperature. Ionisation constant of acetic acid at the same temperature is A) 4 105 B) 4 104 C) 2 104 D) 2 105 27. On electrolysis, in which of the following, O2 would not be liberated at the anode? A) dilute H2SO4 with Pt electrodes B) aqueous AgNO3 solution with Pt electrodes C) dilute H2SO4 with Cu electrodes D) aqueous NaOH with a Fe cathodes & a Pt anode 28. Product of electrolysis depend on A) Nature of the electrolyte B) Temperature C) Nature of material being electrolysed and the type of electrode used D) None of these 29. During the electrolysis of molten sodium chloride, the time required to produce 0.10 mol of chlorine gas using a current of 3 amperes is A) 330 minutes B) 55 minutes C) 110 minutes D) 220 minutes 73

Class (XII) - [SPJ 2023 - Module - I] 30. Using electrolytic method, if cost of production of 1L of oxygen at STP is Rs x. The cost of production of 10L of Hydrogen at STP will be A) 10x B) x/16 C) 10x/32 D) 10x/2 31. In the electrolysis of copper sulphate solution using copper electrodes, concentration of a Cu2+ ion in solution is A) Increases B) Decreases C) Remains same D) First increases then decreases 32. The weight of silver (at.wt. = 108) displaced by a quantity of electricity which displaces 5600 mL of O2 at STP will be A) 5.4 g B) 10.8 g C) 54.0 g D) 108.0 g 33. An aq. solution containing 1 mol per litre each of Cu (NO3)2, AgNO3, Hg(NO3)2 and Mg(NO3)2 is being electrolysed with inert electrodes. The Eo values are, Eo (Ag+ / Ag) = 0.80 V, Eo (Hg2+ / Hg) = 0.79V, Eo (Cu2+ / Cu) = 0.34 V and Eo (Mg2+ / Mg) = -2.37V. With increasing voltage, the sequence of deposition of the metals at the cathode is : A) Ag, Hg, Cu, Mg B) Mg, Cu, Hg, Ag C) Ag, Hg, Cu D) Cu, Hg, Ag 34. The electrolytic decomposition of dilute sulphuric acid with platinum electrode, cathode reaction is A) Reduction of H+ B) Oxidation of SO 2 4 C) Reduction of SO32 D) Oxidation of H2O 35. 3.8g of metal M is deposited at the cathode by passing 0.2F of electricity through the solution of metal chloride. The formula of the metal chloride (atomic mass of M =57) A) MCl B) MCl2 C) MCl3 D) MCl4 36. On electrolysis, in which of the following, O2 would not be liberated at the anode? A) dilute aqueous NaCl solution B) Molten NaCl C) dilute aqueous AgCl D) All of these 37. In a dry cell, at cathode reduction is takes place in A) NH  B) MnO2 C) Graphite D) ZnCl2 4 38. When a lead storage battery is discharged A) PbSO4 is formed B) Pb is formed C) SO2 is consumed D) H2SO4 is formed 74

Class (XII) - [SPJ 2023 - Module - I] 39. The cell potential of mercury cell approximately A) 1.5 B) 1.35 C) 2 D) 1.53 40. Among the following, select the antirusting material/s A) Alkaline solution of phosphate B) Alkaline solution of chromate C) Bisphenol D) All of these 41. The Gibb’s energy for the decomposition of Al2O3 at 5000C is as follows rG   960 kJ mol1 The potential difference needed for the electrolytic reduction of aluminium oxide (Al2O3) at 5000C is at least A) 4.5 V B) 3.0 V C) 2.5 V D) 5.0 V 42. S1 : Electrode potential of any electrode will change on changing any of its intensive properties 24 S2 : 3 Al2O3  3 Al + O2 ; E1 = xV; C3H8 + O2  3CO2 + 4H2O; E2 = xV Then G2 / G1  5 S3 :   of strong as well as weak electrolytes can be obtained by extra polation of graph b/w m m & C to C  O correct statements are: A) S1, S2 B) All C) S1 S2 S3 D) S2 S3 43. The standard emf of the cell Mg|Mg2+||Al3+|Al is 0.71 V at 298 K. Equilibrium constant of the reaction 3Mg2  2Al  3Mg  2Al3 is A) 1036 B) 1072 C) 10–72 D) 10–36 More than one correct 44. Given E0  0.80V, E0  2.37V Ag / Ag Mg2 / Mg E0  0.34V, E0  0.79V Cu2 / Cu Hg2 /Hg Which of the following statements is incorrect ? A) AgNO3(aq) can be stored in copper vessel B) Cu(NO3)2 (aq) can be stored in magnesium vessel C) CuCl2 can be stored in silver vessel D) HgCl2 can be stored in copper vessel 75

Class (XII) - [SPJ 2023 - Module - I] 45. Given A2  2e  A(s) Eo  0.10 B1 1e  B(s) Eo  2.71 X2(g)  2e  2x , Eo  1.08 Which of the following statement is true? A) X2(g) will oxidise both A and B B) A+2 will oxidise B C) The reaction 2x– (1M) + A+2 (1M)  X2 (1atm) + A(s) D) The oxidising power of A+2, B+1 and X2(g) is in the order B+1 < A+2 < X2 46. For the reduction of NO3 ion in an aqueous solution, Eo is + 0.96V, the value of Eo for some metal ions are given below Va2q  2e  V, Eo  1.19V Fe3aq  3e  Fe, Eo  0.04V Au 3  3e  Au, Eo   1.40 V  aq  Hg2aq  2e  Hg, Eo  0.86V The pair of metals that is/are oxidised by NO  in aqueous solution 3 A) V and Hg B) Hg and Fe C) Fe and Au D) Fe and V Numerical type 47. The molar conductivity of a 0.5 mol/dm3 solution of AgNO3 with electrolytic conductivity of 5.76 × 10–3 S cm–1 at 298 K is 48. A lead storage battery has initially 200 g Pb and 200 g PbO2 with excess of H2SO4. Theoretically how long could this cell deliver a current of 10 amp without recharging, if it is possible for completion of reaction 49. What is the emf of the following cell Pt; H2 (1 atm) | H+ (0.1 M) || Cl2 (1 atm) | Cl– (0.01 M) at 298 K ( E0 | Cl 1.36 V) Cl2 76

Class (XII) - [SPJ 2023 - Module - I] 50. Matrix match Column-II Column-I P) Temperature 1) Molar conductance Q) Concentration species involved 2) emf of a cell in operation R) Nature of substance involved 3) Electrode potential S) No of electrons lost or gained in the reaction 4) Standard reduction potential A) 1  PQRS; 2  PQ; 3  PQ; 4  PQRS B) 1  RS; 2  PQRS; 3  PQR; 4  S C) 1  PQR; 2  PQRS; 3  PQRS; 4  RS D) 1  PQR; 2  PQRS; 3  PQ; 4  RQ LEVEL- I 1. In Galvanic cell, which one is the correct statement i) Current flow from cathode to anode through external circuit ii) Current flow from anode to cathode through external circut iii) Electron flow from anode to cathode through external circuit iv) Electrons flow from cathode to anode through external circuit v) Cation move towards cathode and anions move towards anode through internal circuit A) ii, iii, iv B) i, iii, v C) v only D) i, iv, v 2. Nernst Equation for the electrode reaction Mn  ne  M(s) ................... is/are (aq) A) EMn /M  E0  RT ln 1 Mn /M nF Mn  B) EMn /M  E0  2.303 RT log 1  Mn /M nF  M n  C) E Mn /M  E0  0.0591 log reduced form  Mn /M n oxidised form  D) All of these 3. From the following, which one is the correct relation A) E0  G0 B) ln KC  G0 cell nF RT C) E0  2.303 RT log Kc D) All of these cell nF 77

Class (XII) - [SPJ 2023 - Module - I] 4. In which case Ecell – E0 is zero? cell A) Cu | Cu2 0.01M || Ag 0.01M | Ag B) Pt H2 | PH  1|| Zn2 0.01M | Zn C) Pt H2 | PH  1|| Zn2 1M | Zn D) Pt H2 | H 0.01M || Zn2 0.01M | Zn 5. For strong electrolyte,  0 can be find out by the relation Debye Huckel Onsagar equation. m Cm  0m  AC12 in which ‘A’ is the slope of the straight line graph the value of A changes when A) Solvent changes B) Temperature changes C) Charge on the cation and anion produced on dissociation D) All of these 6. 3 Faradays of current is passed through three electrolytic cells connected in series containing Ag+, Cu2+ and Al3+ respectively. The molar ratio in which the three metal ions are discharged at the elec- trodes is A) 1 : 2 : 3 B) 3 : 2 : 1 C) 6 : 3 : 2 D) 3 : 4 : 2 7. The specific conductance of 0.1M KCl at 298K is 0.024 ohm–1cm–1 and resistance of the cell containing this solution at the same temperature is 30 ohm. Cell constant is equal to A) 0.18 cm–1 B) 0.36 cm–1 C) 0.54 cm–1 D) 0.72cm–1 8. In the electrolysis of fused CaCl2, 2.8 litre of chlorine gas at NTP is produced at anode. Amount of calcium deposited at the cathode is A) 5g B) 2.5 g C) 10 g D) 15 g 9. Which of the following statements is/are correct with respect to lead storage battery i) It is one of the secondary cell with Pb act as anode ii) The electrolyte is used is 38% H2SO4 iii) PbO2 (s)  SO 2  4H  2e  PbSO4(s)  2H2O   ve electrode 4 ( aq ) iv) Pb(s)  SO42  PbSO4  2e ve electrode A) i, iii B) i, ii, iii C) i, ii, iv D) all are correct 78

Class (XII) - [SPJ 2023 - Module - I] 10. From the following, which one is the correct statement A) Rusting of iron is the miniature of electrolytic cell reaction B) Rust is poly hydrated ferric oxide (Fe3O4. xH2O) C) In order to prevent corrosion of iron, bis phenol is coated with iron D) The metal which is to be protected can be taken as anode LEVEL II 1. If pressure of hydrogen gas is increased from 1 atm to 100 atm keeping hydrogen ion concentration a constant at 1M, the voltage of hydrogen half cell at 298 K will be A) 0.059 V B) –0.059 V C) 0.59 V D) Zero 2. EMF of the cell Claq | Cl2 , Pt || Cl2g , Pt | Claq P atm P atm 1 2 will be positive if A) P1 > P2 B) P1 = P2 C) P1 < P2 D) EMF is independent of pressure 3. The equilibrium constant of the redox reaction : 2Fe3(aq)  2I(aq)  2Fe(2aq)  I2 (s) at 298 K is 1 × 108. If the standard reduction potential of I2 / I– is 0.54 V, what is the standard reduction potential of Fe3+ / Fe2+? A) 1.006 V B) -1.006 V C) 0.77 V D) -0.77 V 4. The emf of the cell Pt, H2g HA HCl H2g , Pt is 0.295V. Dissociation constant of the acid HA is 1atm 0.01M 1M 1atm A) 1104 B) 1106 C) 1108 D) 1105 5. The standard electrode potentials for the electrodes Mn2+ | Mn and Mn3+ | Mn2+ are –1.18V and 1.51V respectively. What is the potential of the electrode Mn3+ | Mn ? A) 0.33V B) 1.69V C) –0.28V D) +0.28V 6. The molar conductance of 0.01 M acetic acid is 1.65 ×10–3 Scm2 mol–1. The pH of the solution when  0 of CH3COOH is 3.92 × 10–3 Scm2 mol–1 is m A) 2.4 B) 3 C) 4.3 D) 0.54 cm–1 79

Class (XII) - [SPJ 2023 - Module - I] 7. Which of the following is/are true i) Specific conductance denotes conductance of 1 cm3 of a substance ii) Specific conductance as well as molar conductance of a solution of an electrolyte increases upon dilution iii) Limiting molar conductivity of a weak electrolyte cannot be determined by extrapolation of the plot of m against C iv) Conductance of metals is by movement of free electrons A) All B) i, ii, iv C) ii, iii, iv D) i, iii, iv 8. Select the correct statements I) Cathode reaciton in Ni-Cd cell is NiO2 (s)  2H2O   2e  Ni(OH)2  2OH(aq) II) The electrode used in Hg cell is mixture of ZnCl2 and NH4Cl III) Chemical reaction during rusting on iron is 2Fe(s)  O2 (g)  4H(aq)  2Fe(2aq)  2H2O IV) In electrical protection, metal used for preventing corrosion becomes anode A) I, II, III, IV B) II, III, IV C) I, III, IV D ) II, IV Numerical Type 9. When a quantity of electricity is passed through CuSO4 solution, 0.16g of copper gets deposited. If the same quantity of electricity is passed through acidulated water, then the volume of H2 liberated at STP will be (atomic weight of Cu = 64) A) 56 cm3 B) 4 cm3 C) 604 cm3 D) 8 cm3 10. The equivalent conductance of M/10 solution of weak monobasic acid is 8 Scm2 eq–1 and at infinite dilution is 400 Scm2 eq–1. The pH of the solution is A) 4 B) 2.7 C) 3.7 D) 4.5 LEVEL - III Numerical Type Questions 1. From the following molar conductivities at infinite dilution  0 for Ba(OH)2 = 457.6 ohm–1 cm2 mol–1 m  0 for BaCl2 = 240.6 ohm–1 cm2 mol–1 m  0 for NH4Cl = 129.8 ohm–1 cm2 mol–1 m Calculate  0 for NH4OH m 80

Class (XII) - [SPJ 2023 - Module - I] 2. The pH of 0.5L of 1M NaCl after electrolysis for 965second using 5A current (100% efficiency) is 3. An alloy of Pb-Ag weighing 1.08 g was dissolved in dilute HNO3 and the volume made upto 100 ml. A silver electrode was dipped in the solution and the emf of the cell set up, Pt,H2(g)|H(1M) ||Ag(aq) |Ag(s) was 0.62V. If E0 is 0.80 V. What is the percentage Ag in the alloy? (at 25°C 2.303 RT/F = 0.06) cell 4. 0.5 M NaOH solution offers a resistance of 31.6 ohm in conductivity cell at room temperature. What will be the approximate molar conductance of this NaOH solution, if the cell constant of the cell is 0.367 cm–1? More than one correct 5. Select the correct statements 1) Cathode reaction in Ni-Cd cell is NiO2(s)  2H2O  2e  Ni OH2  2OH  aq 2) The electrolyte used in Hg cell is mixture of ZnCl2 and NH4Cl 3) Chemical reaction during rusting of iron is 2Fes  O2(g)  4H   2Fea2q  2H2O aq 4) In electrical protection, metal used for preventing corrosion becomes anode. A) 1, 2, 3, 4 B) 2, 3, 4 C) 1, 3, 4 D) 2, 4 6. A cell Cu|Cu2+(1L of 1M) ||Ag+ (1L of 1M)|Ag. Operates for 1000s; steady current of 9.65A is with drawn then A) [Cu2+] = 1.1M B) [Ag+] = 0.8M C) [Cu2+] = 1.05M D) [Ag+] = 0.9M 7. Pb(s) | PbSO4 || PbI2 || Pb(s) which of the following expression represents the cell potential Saturated solutions Saturated solutions of the above cell at 25°C? A) Ecell  0.059 log10 Pb2 Cathode 2 Pb2 Anode B) Ecell  0.059 log10 Pb2 Anode 2 Pb2 Cathode C) Ecell  0.059 log10 Ksp PbI2  2 Ksp PbSO4  Ksp PbI2  / 4 13 Ksp PbSO4  12  D)Ecell 0.059 log10 2 81

Class (XII) - [SPJ 2023 - Module - I] 8. MnO4  8H  5e  Mn2  4H2O , If H+ concentration is decreased from 1M to 10-4 M at 250C, where as concentration of Mn2+ and MnO4 remain 1M. A) the potential decreases by 0.38 V with decrease in oxidising power B) the potential increases by 0.38 V with increase in oxidising power C) the potential decreases by 0.25 V with decrease in oxidising power D) the potential decreases by 038 V without affecting oxidising power Matrix Match 9. Column-I Column-II 1) Zn | Zn2 C || Zn2 (2C) | Zn P) Spontaneous cell reaction 2) H2 P  1atm | HCl1N || H2SO4 1N | H2, P  1 atm Q) Working cell representation R) By increasing concentration of cation 3) Cu | Cu2 0.01M || Ag 0.1M | Ag in cathodic compartment cell works  E0 Cu2 /Cu  0.34; E0  0.8 Ag /Ag 4) Zn Zn2 Cu2 Cu S) Concentration cells 101 M 102 M A) 1 PQR 2  PQ; 3  RS; 4  PQR B) 1 PQR 2  RS; 3  PQR; 4  PR C) 1 PQRS 2  RS; 3  PQR; 4  PQR D) 1 PQRS 2  PS; 3  PQR; 4  PS 82

Class(XII)[SPJ-2023 Module-I] MATHEMATICS CHAPTER - 01 RELATIONS FUNCTIONS AND BINARY OPERATION TEACHING POINTS Part I - Relations Introduction a) Relations definition b) Relation from set A to set B c) Relations on set A d) Domain and Range e) Number of relation Types of relations a) Reflexive b) Symmetric c) Transitive d) Equivalence e) Anti symmetric f) Partial ordered relation N.B: ,  inverse properties of above relation Part II - Functions 1) Graphs of functions a) Basic graph (functions) b) Simple transformation & graphs 2) Domain & Range 3) Types of functions a) one-one function b) many - one c) Onto d) Into e) Bijective function N.B Number of above functions should be explained 83

Class(XII)[SPJ-2023 Module-I] 4) Composite functions a) fog and gof (explanation) b) Properties of composite function 5) Invertable functions a) Inverse of an element b) Inverse of a function c) Properties of inverse with geometrical explanation 6) Even & Odd functions a) Analytical & Graphical approaches b) Properties 7) Periodic functions a) Algebraic functions and their fundamental periods b) Trigonometric function and its fundamental periods c) Properties of periodic function, Part III - Binary operation 1) Definition 2) Properties of Binary operation a) Commutative b) Associative c) Existence of identity (identity element) d) Existence of inverse (inverse of a element) 3) Number of Binary operation on a set Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Miscellaneous exercise 84

Class(XII)[SPJ-2023 Module-I] RELATIONS I. Cartesian product 1. A  B  (x, y) / x  A and y  B (a, b)  (c, d) (a, b)  (c, d)  a  c and b  d If A  B   then either one of A or B is null set 2. If n (A) = m and n (B) = n then n(A×B) = mn 3. If n(A  B) m then n (A  B)  (B A)  m2 4. A  B  B A(in general)but A  B  B A  A  B where A   and B   5. A  (B  C)  (A  B)  (A  C) and A  (B  C)  (A  B)  (A  C) and A  (B  C)  (A  B)  (A  C) 6. (A  B)  (C D)  (A  C)  (B  D) I. Relation 1. A relation from A to B is a subset of A ×B, If (x, y)  R means x related to y. ie., if xRy then (x, y) R . ie R = (x, y) / x  A, y  B If n(A) = m and n(B) = n then number relations from A to B = 2mn 2. Inverse relation If R :A  B then R1 : B  A R1  (y, x) /(x, y)  R Note : Dom (R) = Ran (R-1) and Ran (R) = Dom(R-1) 3. Relation on a set R :A  A is the relation on a set A  No. of relation on a set have n elements = 2n2 II. Types of relations 1. Reflexive If a R a a  A 2. Symmetric If a R b  b R a a, b  A 3. Transitive If a R b and b R c  aRc a, b, c  A 85

Class(XII)[SPJ-2023 Module-I] 4. Equivalence relation If R is equivalence then it is reflexive, symmetric and transitive. 5. Identity relation - IA : A A Let A be a set then the relation IA = (x, y) / x  A, y  A and x  y is called identity relation 6. Inverse relation If R : A  B then R1 : B  A R1  (y, x) /(x, y)  R 7. Void relation :- Let A be any set   A  A,  is called the void relation 8. Universal relation Let A be any set then A  A  A  A , A × A is called the universal relation III. Properties on relations Let R1 and R2 be two relations on a set A 1. If R1  R 2 and R1 is reflexive then R2 is reflexive. 2. If R1or R2 is reflexive then R1  R2 is reflexive 3. If R1 and R2 is reflexive then R1  R2 is reflexive 4. If R1 and R2 are symmetric then R 1 , R 1 , R1  R 2 , R1  R 2 , R1  R 2 and R2 - R1 are symmetric 1 2 5. If R1 and R2 are transitive then R1  R2 is transitive but R1  R2 is need not be transitive 6. If R1 and R2 are two equivalence relation then R1  R2 is need not be an equivalence relation. But R1  R2 is equivalence relation. 7. No. of possible relation from A  B  2O(A).O(B) 8. Congruent modulo m Let m be any fixed intiger then two intiger a and b are said to be congruence modulo m if a - b is divisible by m and is written as a  b (mod m). I. Function (mapping) A function from set A to set B is a relation R from A to B having the following properties. 1. Domain of R is A 2. If xRy and xRz then y = z ie., If R is a function from A to B then for each x  A there exists one and only y  B such that x R y Note : If f is a function from A to B is denoted as f : A  Band read as f from A to B II. Types of function 1. In to function : If f : A  B is an in to function then Ran (f)  B or Ran (f)  B Eg. 1) 2) 2. on to function (surjection) : If f : A  B is an on to function then Ran (f) = B Eg. 1) 2) 86

Class(XII)[SPJ-2023 Module-I] 3. one one function (injection) :- If f : A  B is a one one function then different elements in A have different images in B Eg. 1) 2) 4. many one function : If f : A  B is a many one function then different elements in A have same images in B Eg. 1) 2) 5. Bijection : A function which is both one one and on to 6. Inverse function : If f : A  B is a bijection then f-1exists and it denoted as f 1 : B  A 7. Identity function : IA : A  A and IA (a)  a a  A 8. Constant function : f : A  B is constant function then f(a) = k a  A where k is a constant and k  B III. Composition of functions If f : A  B and g : B  C then, g of : A  C is defined g of (x) = g(f(x)) x  A Note : 1. If f : A  B is a function and IA : A  A and IB : B  B are identity functions on A and B then IBof = f = fo IA 2. If f: A  A is a map then foIA = IA of = f 3. If f is a bijection from A to B and IA and IB are identity function on A and B then f of-1 = IB and f-1 of = IA 4. If f and g are bijections then g of is also a bijection 5. If A is a non empty set then f, g : A  A such that fog and gof = IA then f and g are bijections and g = f-1 6. If f : A  B and g : B  C are two bijections then gof : A  C is a bijection and (gof)-1 = f–1 og-1 87

Class(XII)[SPJ-2023 Module-I] IV. Number of functions 1. Number of functions from A  B is  O(B) O(A) 2. Number of one one function from A to B =  np m If n  m  Where O(A) = m and O(B) = n   0 If nm 3. If n(A) = m = n (B) then number of bijections from A to B = m ! n 4. If n(A) = m and n (B) = n where 1  n  m then number of on to functions from A to B is = (1)nr ncrrm r 1 5. The number of relation from A to B which are not functions = 2mn - nm where n(A) = m and n(B) = n BINARY OPERATIONS I. Definition Let S be a non empty set. A function f from S × S  S is a binary operation on S. Binary operations denoted by symbols like , ,  etc. II. Properties of binary operations Let  be a binary operation on S 1.  is said to be commutative if a  b = b  a ab S 2.  is said to be associative if (a  b)  c = a  (b  c) a, b, c S 3.  is said to be Binary operation with identity element. If  an element e S such that a  e = a = e  a a S 4. Let  be a binary operation with an element e then an an element a S such that a  a1 = e = a1  a then a1 is called an inverse of a. III. Number of Elements in Binary Operations 1. Let A be a set having ‘n’ elements. Then the number of Binary operations on A is nn2 2. Let n(A) = n, Then total number of commutative Binary operations on A is  n (n1)  n  2  3. Let n(A) = n. Then total number of Non-commutative Binary operations is nn2  n (n 1)   n  2  88

Class(XII)[SPJ-2023 Module-I] QUESTIONS [HOMEWORK] 1. Define a relation on NXN by (a,b) R(c,d) if ad =bc, then R is: A) not reflexive B) not symmetric C) not transitive D) an equivalence relation 2. The inverse relation of R : A  B is same as R, when: A) A = B B) A  B and R is transitive C) R is reflexive D) A = B and R is symmetric 3. On the set of all subsets of the real numbers, define a relation by ARB if A is subset of B. Then R is: A) an equivalence relation B) not reflexive C) not symmetric D) not transitive E) reflexive & symmetric 4. The range of the function for real x of y  2  1 3x is sin A) 1  y 1 B)  1  y 1 C)  1  y 1 D) 1  y 1 3 3 3 3 5. The range of the function f  x 7x Px3 is A) 1, 2, 3, 4 B) 1, 2, 3, 4, 5, 6 C) 1, 2, 3 D) 1, 2, 3, 4 6. Let function f : R  R be defined by f  x  2x  sin x for x  R . Then f is A) one-one and onto B) one-one but not onto C) onto but not one-one D) neither one-one nor onto 7. Let f(x) be a function where domain is 5,7 . Let g  x  2x  5 , then the domain of fog x is A) 4,1 B) 5,1 C) 6,1 D) 3,1 8. If f x  ax  c  y,  a  c , then f(y) equal to cx  a 1 C) 1 A) x B) x D) 0 9. A function f : R  R satisfies the condition x2f (x)  f (1 x)  2x  x4. Then f(x) is A) x2 1 B) x2 1 C) x2 1 D) x4 1 10. If f(x) f  1   f(x)  f  1  and f(4)  65 then f(6) is .......  x   x  A) 217 B) 317 C) 207 D) 247 89

Class(XII)[SPJ-2023 Module-I] 11. If f : R  R and g : R  R are defined by f (x)  2x  3 and g(x)  x2  7, then the values of x such that g(f (x))  8 are A) 1,2 B) -1,2 C) -1,-2 D) 1,-2 12. Define * on the set of real numbers by a * b = 1 + ab, then the operation * is: A) commutative but not associative B) associative but not commutative C) neither commutative nor associative D) both commutative and associative 13. Which of the following binary operations is commutative A) * on R given by a * b = a2b B) on R given by a b = ab b g b gC)  on P(S) the power set of a set S. given by AB  A  B  B  A D) a.b = ba 14. A is the set of all non - zero complex numbers of the form a + ib. The binary operation  is defined such that Z1  Z2 = Z1 Z2 where Z1, Z2 A. The inverse of a + ib A) a – ib B) a  i a2 b b2 a2  b2  C) a  i a 2 b b2 D) 1 + i0 E) 2 + i0 a2  b2  15. Let W denotes the words in the English dictionary. Define the relation by R  x, y  W  W / the words x and y have atleast one letter in common . Then R is A) reflexive, not symmetric and transitive B) not reflexive, symmetric and transitive C) reflexive, symmetric and not transitive D) reflexive, symmetric and transitive 16. For real numbers x and y, we write xRy  x  y  2 is an irrational number. Then the relation R is A) reflexive B) symmetric C) transitive D) an equivalence 17. Let R = {(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)} be relation on the set A = {3,6,9,12). The relation R is A) reflexive and transitive only B) reflexive only C) an equivalence relation D) reflexive and symmetric only E) symmetric 18. Let X be a family of sets and R be a relation on X defined by “A is disjoint B” The R is A) Reflexive B) Symmetric C) Transitive D) Equivalence 19. Let R be a relation in the set N of natural numbers defined by the relation nRm  n is a factor of m. Then relation R is A) Reflexive and symmetric only B) Symmetric and transitive only C) Reflexive and transitive only D) An equivalence relation 90

Class(XII)[SPJ-2023 Module-I] 20. Let A = {1, 2, 3} which of the following is not an equivalence relation on A. A) R1 = {(1, 2), (2, 1), (1, 1), (2, 2), (3, 3)} B) R2 = {(1, 1), (2, 2), (3,3 )} C) R3 = {(1,1), (2,2), (3,3), (2,3), (3,2)} D) R4 = {(1, 1), (2,2), (3,3), (3, 1), (1, 3)} E) R5 = {(1, 1), 2, 2), (3,3), (1, 2), (2, 1), (2, 3), (3, 2)} 21. Let R be a relation defined on S, the set of squares on a chess board, such that xRy, for x, y  S, if x and y share a common side. Then, which of the following is false for R : A) reflexive B) symmetric C) transitive D) not equivalence 22. Let A xR:xisnot a positive integer Defined a function f : A  R as f  x   2x then f is x 1 A) injective but not surjective B) not injective C) surjective but not injective D) neither injective nor surjective 23. Let N be the set of natural numbers and two functions f and g be defined as f , g : N  N such that  n  1 , if n is odd  2 , if n is even f  n    n  2  and g n   n  1n . Then f  g is A) both one-one and onto B) one-one but not onto C) neither one-one nor onto D) onto but not one-one 24. Let f :R R be defined by f  x   1 x 2 . Then the range of f is x A) 1,1 0 B)  1 , 1 C) R   1 , 1 D) R  1, 1 2 2  2 2  25. Let the function f : 0,   0, be defined by f x  1 1 . Then f is x A) injective only B) not injective but it is surjective C) both injective as well as surjective D) neither injective nor surjective 26. Let f  x  2x  x2, x  1, then the roots of the equation f  x  f 1  x is A) 1 B) 0,1 C) 1,1 D) 0 91

Class(XII)[SPJ-2023 Module-I] 27. The inverse of the function f (x)  ex  ex 2 is ex  ex A) f 1 (x )  1 log  x 1  B) f 1(x)  1 log  x 1  2  3x  2  3x  C) f 1(x)  1 log  x 1 D) f 1(x)  1 log  x 1 2  x  3  2  x  3  n 28. If f : R  R satisfies f  x  y  f (x)  f (y) for all x, y  R and f 1  7, then  f (r) is r 1 A) 7n(n 1) 7n C) 7 n 1 D) 7n(n 1) 2 B) 2 2  29.  x2  If f (x)  log x  1 x2  sin 3x    is an odd function  x 10,10, then  a  A) a > 100 B) a < 100 C) a > -100 D) a < -100 30. Define f :R  R by f (x)  Lt x2  3x  2 . Then f is: x2 x2 A) Not a function B) Neither one-one nor onto C) One-one D) Onto 31. Define f : R  R by  x2  3x, if x  3  f (x)   9, if 0  x  3 2x, if x is negative Then f is: C) Onto D) Bijection A) Not a function B) One-One 32. If f (x  3)  2x2  3x 1; then f (x 1) is: A) 2x2-11x+13 B) 3x2+11x-12 C) x2-11x+13 D) 3x2+11x-13 33. The value of the parameter  ; for which the function f (x)  1 x;   0 is the inverse of itself is: A) -2 B) 1 C) 2 D) –1 34. The period of the function f (x)  Sinx  Cosx is: A)  / 2 B)  C) 2 D)  / 4 92

Class(XII)[SPJ-2023 Module-I] 35. If f (x)  3x  2 then: 5x  3 A) f 1(x)  f (x) B) f 1(x)  f (x) C) f f (x)  x D) f 1(x)  1 f (x) 15 36. The function f : R  R defined by f (x)  x 1 x  2x  3 is: A) one-one onto B) onto but not one-one C) both one-one and onto D) neither one-one nor onto E) none 37. Which of the following is true when A is a subset of B: A) there is no one-one function from A to B B) there is no onto function from B to A C) there may be a one-one and onto function from B to A D) there is no function from B to A 38. Which of the following is true when A and B are finite sets and O(A) < O(B) : A) there is no onto function from A to B B) there is no one-one function from A to B C) there is a bijection from A to B D) no function from A to B can be either one-one or onto 39. A = [1, 2, 3, 4]. A binary operation is defined such that a « b = r where ‘r’ is the reminder obtained when ‘ab’ is divided by 5. Then the composition table is: 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 12 34 12 123 14 123 11234 B) 2 3 1 4 2 C) 2 2 1 4 3 D) 2 1 2 4 3 A) 2 2 4 1 3 3423 1 33 14 2 34 112 3 3 14 2 423 12 422 12 4 2 14 3 44321 40. If f is a polynomial function satisfying 2  f (x).f (y)  f (x)  f (y)  f (xy) x, y  R and of f (2)  5 then f (f (2)) A) 26 B) 36 C) 48 D) 72  41. The maximum value of the function f (x)  2x3 15x2  36x  48 on the set A  x / x2  20  9x is A) 7 B) 5 C) 12 D) 4 42. If f  x 1   x2 1 , then the value of f(2) is  x  2  x2 2 5 7 8 10 A) 11 B) 11 C) 11 D) 11 93

Class(XII)[SPJ-2023 Module-I]  43. Let Z be the set of integers. If A  x  z :  2x2 x25x6 1 and B  x  z :| x 1|  | x  2 |  | x  3 | 6 then the relations from A to B which are not functions is A) 210 125 B) 215 125 C) 212 125 D) 125  243 . 44. If A  1, 2,3 then number of reflexive relation on A is A) 62 B) 64 C) 66 D) 68 The following figure shows the graph of a function f(x) with domain 3, 4 and range 1, 2 On basis of above information, answer the following questions 45. Figure (ii) represents the graph of the function A) f(x) B) f(x–2) C) f(x+2) D) f(x–1)+1 46. Figure (iii) represents the graph of the function A) f(x) B) f  x  C) f x  D) f  x  47. The domain and range respectively of A) f xare4,3and2,1 B) f x 1are3, 4and1, 2 C) f x  2are3, 4and2, 4 D) f x 1 1are4,3and1, 2 48. 2,5and2,1 are the domain and range respectively of function A) –f(x) B) –f(x–1) C) f x 1 1 D) f x 1 49. The number of solutions of figure (iii) and 2x  62  4y2  49 are A) 2 B) 4 C) 6 D) 1 94

Class(XII)[SPJ-2023 Module-I] 50. If n(A)  5 then number of equivalence relation on A is A) 50 B) 51 C) 52 D) 53 LEVEL - I 1. Let A  3, 6,9,12 and defined R  3,66,36,99,6 then R is A) Anti symmetric B) Reflexive C) Symmetric D) Transitive 2. Which of the Relation R on the set of real numbers is an equivalence relation. A) xRy if x  y B) xRy if x  y  0 C) xRy if x  y  10 D) xRy if xy  10  3. Given relation R  1,1,2,3 on the set A  1, 2,3 . The minimum number of ordered pairs to add in R so that R is an equivalence is A) 7 B) 5 C) 3 D) 2 4. The relation R in N×N,N is set of natural number, such that (a, b) R (c, d)  a + d = b + c is A) reflexive but not symmetric B) reflexive and symmetric but not transitive C) an equivalence relation D) symmetric and transitive only 5. The number of onto functions that can be defined from set A  a, b, c, d to set B  1, 2,3 is equal to A) 36 B) 24 C) 64 D) 81 6. If n  A  4 and n B  5 . The number of all possible injections from A to B in A) 9 B) 24 C) 120 D) 60 7. Given f (x)  log  1 x  and g(x)   3x  x2  ; Then f(g(x)) is equal to  1 x   1 3x2    A) f (x) B) 3f (x) C)  f (x)2 1 D) f (x) 8. If f : 1 ,     3 ,   where f (x)  x2 x 1 then f 1(x) is  2   4  A) 1  x3/4 B) 1  x 3/ 4 C) 2  x 1/ 4 D) 3  x 1/ 4 2 2 9. Let Z be the set of integers the operation  on Z defined by a  b = a + b + 1 for all a, b  Z is commutative and associative then the inverse of an integer a is A) –(a + 1) B) a + 1 C) a + 2 D) –(a + 2) 95

Class(XII)[SPJ-2023 Module-I] 10. Let z be the set of integers and ‘  ’ be a binary operation on Z defined as a  b = a + b - ab for all a, b  Z . The inverse of an element a  1  Z is: A) a B) a C) a 1 D) a2 a 1 1 a a a 1 LEVEL - II 11. Let S be the set of all real numbers. Then the relation R = {(a, b) : 1 + ab > 0} on ‘S’ is A) reflexive and symmetric but not transitive B) reflexive and transitive but not symmetric C) symmetric and transitive but not reflexive D) equivalence 12. Let x  y(mod 4) if 4 divides x - y, then the solution of the equation 8  x (mod 4) is given by A) {1,  5,  .......} B) {0,  4,  8.......} C) {2,  6,  .......} D) {3,  5,  7.......} 13. Let a relation R in the set N of natural numbers be defined as  x, y  R if and only if x2  4xy  3y2  0 for all x, y  N . The relation R is A) Reflexive B) Symmetric C) Transitive D) An equivalence relation 14. The set S : {1,2,3, ....,12} is to be partitioned into three sets A,B,C of equal size. Thus A  B  C  S, A  B  B  C  A  C   . The number of ways to partition S is A1) 12!/3!(4!)3 B) 12!/3!(3!)4 C) 12!/(4!)4 D) 12!/(4!)3 ob g t15. Let A  x : 1  x  1, x  R  B and S be the subset of A x B defined by S  x,y A  B; x2  y2  1 . This defines A) a one - one function from A into B B) a many - one function from A into B C) a bijective mapping from A into B D) not a function b g b g b g o b g b gt16. Let f x  x  1 2  1, x  1 , then the set S  x;f x  f 1 x is: SR|T|A) 0, 1, 3  i 3 , 3  i 3 VUW|| l qB) 0,1, 1 2 2 l qC) 0,1 D) {1, 1} 17. A is set of rational nos. p  0 , q, r, s A . Binary operation  is defined such that b gp,q  (r, s) = (pr, ps + q) .Then the inverse of (p, q) A) GHF 1 , q IKJ B) FHG 1 , q KJI C) GHF p, 1 KIJ D) HFG 1 , 1 JIK p p p p q p q 96

Class(XII)[SPJ-2023 Module-I] 18. Let f x  ax  b . Then fof(x) = x, if cx  d A) d = –a B) d = a C) a = b = c = d = 1 D) a = b = 1 19. Let A = {x1, x2, ....... x7} and B = {y1, y2, y3} be two sets containing seven and three distinct elements respectively. Then the total number of functions f: A  B that are onto, if there exist exactly three elements x in A such that f(x) = y2, is equal to A) 14.7C2 B) 16.7C3 C) 12.7C2 D) 14.7C3 20. The image of the interval [–1,3] under the mapping f :    given by f(x) = 4x3 – 12x is A) [8,72] B) [0,72] C) [–8, 72] D) [0,8] LEVEL - III 21. The function f :0,3  1, 29, defined by f  x  2x3 15x2  36x 1 is A) one-one and onto B) onto but not one-one C) one-one but not onto D) neither one-one nor onto 22. If f x  sin 2 x  sin2 x   / 3  cos x.cos x  / 3 and f  5 1 then g.f(x) =  4  A) 1 B) 0 C) sin x D) cos x 23. The inverse function of f x  82x  82x , x  1,1, is 82x  82x A) 1  log 8 e log e  1  x  B) 1 log e  1  x  4  1  x  4  1  x  C) 1  log8 e  log e  1  x  D) 1 log e  1  x  4  1  x  4  1  x  b g NLM e jQOP24. f x  sin log x  x2  1 is: A) even B) odd C) f x  f x D) f x  f x 25. Let f : 1,1  R be such that f(cos 4)  2 for    0,      ,   . Then the value(s) of 2  sec2   4   4 2  f  1  is (are)  3  A) 1 3 B) 1 3 C) 1 2 D) 1 2 2 2 3 3 97

Class(XII)[SPJ-2023 Module-I] 26. Let f (x )  sin   sin   sin x   for all x  R and g(x)   sin x for all x  R . Let (f  g)  x denote  6  2   2   f(g(x)) and g  f  x  denote g(f(x)). Then which of the following is (are) true? A) Range of f is  1 , 1 B) Range of fog is  1 , 1  2 2  2 2  C) lim f (x)   D) There is an x  R such that (gof)(x) = 1 x0 g(x) 6 27. Let f(x)  x  1  2 , then the range of C for which x  1  2  C has exactly two distinct real roots A) C = 0 B) C  2 C) C > 2 D) C = 2 Numerical Type 28. If f(x)  4x 2 then f  1   f  2   .....  f  49  is ....... 4x   50   50   50  29. If f be a real valued function with domain R such that f  x 1  f  x 1  2f  x  then period of f is 1 1 2 30. If g(x )   4 cos 4 x  2 cos 2x  cos 4x  x7 7 , then the value of g(g(100)) is equal to   31. If f be a real valued function with domain R such that f  x 1  f  x 1  2f  x  then period of f is Matrix match 32. A) If n A  3 then number of reflexive relation on A P:1 B) If n(A) = 4 then number of symmetric relations on A Q:210 C) If n(A) = 3 then number of bijection on A R: 26 D) If n(A) = 3 then number of identify function on A S:6 T:3 A) A  R, B  Q, C  S, D  P B) A  P, B  Q, C  S, D  R C) A  P, B  S, C  Q, D  R D) A  S, B  Q, C  R, D  P 98

Class(XII)[SPJ-2023 Module-I] CHAPTER - 02 INVERSE TRIGONOMETRIC FUNCTIONS TEACHING POINTS Section I 1. Revision for inverse function 1-1, onto and bijective function with diagram 2. Limitations to define inverse of trigonometric function - trigonometric functions are periodic and they are not bijective 3. Introduce restriction of a function for providing bijective function from a periodic function with suitable domain and range 4. Define inverse trigonometric function with corresponding domain and range 5. Graphs of all inverse trigonometric functions Section 2 1. Mechanism for simplifying Inverse Trigonometric Function. Generally   f 1  x is converted into x  f  and simplyfy the expression with trigonometric identities 2. Simplification of f 1 x 3. Simplification of f 1  1   x   4. Conversion of f 1 x into other Inverse Trigonometric Function 5. Sum and difference of two Inverse Trigonometric Function ie f 1  x  f 1  y Section 3 1. Different properties of inverse trigonometric function       2. Difference between f f 1  x  and f 1 f  x f f 1  x  is non-periodic f 1 f x is periodic 99

Class(XII)[SPJ-2023 Module-I]  3. Explain all Inverse Trigonometric Function. with f 1 f  x   x with domain of f1x  4. Explain all Inverse Trigonometric Function with f f 1  x  with principle domain and for all reals 5. General expressions with subdivision of domain for sin1 sin m and cos1 cos m  6. 2x2 1  x 2 2x Simplification of f 1 g x  for sum specified g(x) such a  1, 1  x 2 1 x2 etc 7. Simplification of f 1  x   g1  x, inverse trigonometric function with inequality Sections 4 & 5 Problem discussion - Level I * Selected NCERT * Selected Jeemain Problems * Selected Advanced level problems * Problem involving sum of consecutive differences Sections 6 & 7 Level II Level III Level IV I Two bijective functions f(x) and g(x) defined on A such that (fog) x  x  (gof)x, then ‘g’ is the inverse of ‘f’ and it is denoted as f-1. An invertible function y  f (x)  x  f 1(y). x  sin     sin1 x; x  cos ec    cosec1 x x  cos     cos1 x; x  sec     sec1 x x  tan     tan1 x; x  cot     cot1 x All periodic functions are manyone functions, so they are not bijective and hence they are not invertible. To define inverse trigonometric function, we forced to restrict the domain and range of them so that the restriction should be bijective.Restrictions for inverse trigonometric functions are given below. 100