Q62.Let ๐= ๐งโ๐ถ: ๐งโ1 = 1 and โ2 โ1๐ง+ ยฏ๐ง- ๐๐ง- ยฏ๐ง= 2โ2. Let ๐ง1, ๐ง2 โ๐ be such that ๐ง1 = max๐งโ๐ ๐ง and 2 ๐ง2 = min๐งโ๐ ๐ง. Then โ2๐ง1 โ๐ง2 equals: (1) 1 (2) 4 (3) 3 (4) 2
What This Question Tests
This question tests the ability to convert complex number conditions into geometric loci (circle and line), find their intersection points, and then determine the maximum and minimum modulus of these intersection points from the origin.
Concepts Tested
Formulas Used
|z-zโ|=R (equation of circle)
z=x+iy => z+zฬ=2x, z-zฬ=2iy
|z|=โ(xยฒ+yยฒ)
๐ NCERT Sections This Tests
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5.29 โ Amongst The Following Ions Which One Has The Highest Magnetic Moment Value?
Chemistry Class 11 ยท Chapter 5
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
๐ Question Details
- Chapter
- Complex Numbers
- Topic
- Locus of complex numbers, modulus, geometric interpretation
- Year
- 2024
- Shift
- 01 Feb Shift 1
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers
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