# Calendar: 1899-1900 Page 819

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ENTRANCE EXHIBITIONS clXVll Solve the equations -a £ az cz £ φ- Obtain the relation between the numerical coefficients י י that -f- 2hxy Z2 may be perfect square Hence or otherwise prove that the product of and Λ 000ε bne il ifi ax 1xy ΛΎ man having miles to go walks at the rate of smiles per hour for hours and finishes his journey by train at the rate of miles per hour If he had walked all the way at Β the rate of -f- miles per hour he would have arrived at the same time Find the relation between ey tltAlso if 27 6J 30 find Prove that the ratio between two positive quantities is made to approach ratio of equality by adding positive quantity to each of its terms Find the ratios χ ζ if px qy vz qx -f- 92 Qz --- β Find the sum of 71 terms of the series fciifL Λ Λ β δ ί The Compound Interest on £A for years £1 for years £C for years are all equal find the relation between "V י M' 33 Assuming the Binomial Theorem for positive integral index prove it for positive fractional index If On 271 where is lj prove that vol Cn-2 jn-Z H" Gn-i f" Gn-2G2 2GV Cw- ί ρ JkJ ז io 0C0 bu 46 i5 "t It sls

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