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MathsMediumMCQ2020 ยท 02 Sep Shift 2

Q53.Let n > 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of the nearest stations is connected by a straight track only. Further, each pair of the nearest station is connected by blue line, whereas all remaining pairs of stations are connected by red line. If number of red lines is 99 times the number of blue lines, then the value of n is (1) 201 (2) 200 (3) 101 (4) 199

What This Question Tests

This problem involves applying combinations to count the number of blue and red lines based on a given condition and then solving the resulting algebraic equation to find the value of 'n'.

Concepts Tested

Combinations (nCr)Counting distinct types of connectionsSetting up and solving algebraic equations

Formulas Used

nCr = n! / (r! * (n-r)!)

nC2 = n(n-1)/2

๐Ÿ“š NCERT Sections This Tests

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5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26

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5.19 [Cr(NH3)6] 3+ is paramagnetic while [Ni(CN)4] 2โ€“ is diamagnetic. Explain why? 5.20 A solution of [Ni(H2O)6] 2+ is green but a solution of [Ni(CN)4] 2โ€“ is colourless. Explain. 5.21 [Fe(CN)6] 4โ€“ and [Fe(H2O)6] 2+ are of different colours in dilute solutions. Why?

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

๐Ÿ“‹ Question Details

Chapter
Permutation & Combination
Topic
Combinations and Counting Principles
Year
2020
Shift
02 Sep Shift 2
Q Number
Q53
Type
MCQ
NCERT Ref
Class 11 Maths Ch 7: Permutations and Combinations

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