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MathsMediumMCQ2018 ยท 16 Apr Online

Q81.Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 โˆ’9x2 + 12x + 5 in the interval [0, 3] . Then M โˆ’m is equal to (1) 9 (2) 4 (3) 1 (4) 5 + C , ( C is a constant of integration), then the ordered pair

What This Question Tests

This question requires finding the absolute maximum and minimum values of a cubic function within a given closed interval by evaluating the function at critical points and interval endpoints.

Concepts Tested

Absolute maximum and minimum valuesCritical pointsFirst derivative testEvaluating function at endpoints

Formulas Used

f'(x) = 0 for critical points

๐Ÿ“š NCERT Sections This Tests

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5.29 Amongst the following ions which one has the highest magnetic moment value? (i) [Cr(H2O)6]3+ (ii) [Fe(H2O)6] 2+ (iii) [Zn(H2O)6]2+ 5.30 Amongst the following, the most stable complex is (i) [Fe(H2O)6]3+ (ii) [Fe(NH3)6] 3+ (iii) [Fe(C2O4)3]3โ€“ (iv) [FeCl6] 3โ€“ 5.31 What will be the correct order for the wavelengths of absorption in the visible region for the following: [Ni(NO2)6] 4โ€“, [Ni(NH3)6] 2+, [Ni(H2O)6] 2+ ? Answers to Some Intext Questions 5.1 (i) [Co(NH3)4(H2O)2]Cl3 (iv) [Pt(NH3)BrCl(NO2)]โ€“ (ii) K2[Ni(CN)4] (v) [PtCl2(en)2](NO3)2 (iii) [Cr(en)3]Cl3 (vi) Fe4[Fe(CN)6]3 5.2 (i) Hexaamminecobalt(III) chloride (ii) Pentaamminechloridocobalt(III) chloride (iii) Potassium hexacyanidoferrate(III) (iv) Potassium trioxalatoferrate(III) (v) Potassium tetrachloridopalladate(II) (vi) Diamminechlorido(methanamine)platinum(II) chloride 5.3 (i) Both geometrical (cis-, trans-) and optical isomers for cis can exist. (ii) Two optical isomers can exist. (iii) There are 10 possible isomers. (Hint: There are geometrical, ionisation and linkage isomers possible). (iv) Geometrical (cis-, trans-) isomers can exist. 5.4 The ionisation isomers dissolve in water to yield different ions and thus react differently to various reagents: [Co(NH3)5Br]SO4 + Ba2+ ยฎ BaSO4 (s) [Co(NH3)5SO4]Br + Ba2+ ยฎ No reaction [Co(NH3)5Br]SO4 + Ag+ ยฎ No reaction [Co(NH3)5SO4]Br + Ag+ ยฎ AgBr (s) 5.6 In Ni(CO)4, Ni is in zero oxidation state whereas in NiCl42โ€“, it is in +2 oxidation state. In the presence of CO ligand, the unpaired d electrons of Ni pair up but Clโ€“ being a weak ligand is unable to pair up the unpaired electrons. 5.7 In presence of CNโ€“, (a strong ligand) the 3d electrons pair up leaving only one unpaired electron. The hybridisation is d 2sp 3 forming inner orbital complex. In the presence of H2O, (a weak ligand), 3d electrons do not pair up. The hybridisation is sp 3d 2 forming an outer orbital complex containing five unpaired electrons, it is strongly paramagnetic. 5.8 In the presence of NH3, the 3d electrons pair up leaving two d orbitals empty to be involved in d2sp3 hybridisation forming inner orbital complex in case of [Co(NH3)6]3+. In Ni(NH3)6 2+, Ni is in +2 oxidation state and has d 8 configuration, the hybridisation involved is sp 3d 2 forming outer orbital complex. 5.9 For square planar shape, the hybridisation is dsp 2. Hence the unpaired electrons in 5d orbital pair up to make one d orbital empty for dsp2 hybridisation. Thus there is no unpaired electron. Chemistry 140 Reprint 2025-26

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1.27 If the solubility product of CuS is 6 ร— 10โ€“16, calculate the maximum molarity of CuS in aqueous solution.