Q81.Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x3 โ9x2 + 12x + 5 in the interval [0, 3] . Then M โm 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
Formulas Used
f'(x) = 0 for critical points
๐ NCERT Sections This Tests
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2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
5.29 โ Amongst The Following Ions Which One Has The Highest Magnetic Moment Value?
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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
1.27 โ If The Solubility Product Of Cus Is 6 ร 10โ16, Calculate The Maximum Molarity Of
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1.27 If the solubility product of CuS is 6 ร 10โ16, calculate the maximum molarity of CuS in aqueous solution.
๐ Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima
- Year
- 2018
- Shift
- 16 Apr Online
- Q Number
- Q81
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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