# Calendar: 1896-1897 Page 701

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FACULTY OF SCIENCE cxi 4th term and the wth term of each and where possible find the sum of η terms and the sum to infinity 32 ii ο 10 On what does the nature of the roots of quadratic depend Yj MvC ר י For what values of will the roots of the equation -3 -0 12מ be equal What will be the nature of the roots if have ίι value between the values found above -'' 11 Define logarithm give two examples and shew clearly why log is twice log whatever the base be Given log 3010300 log 4771213 find which is the greater 10J or 11v 12 Find the number of permutations of η things taking at time Find the number of arrangements that can be made of boys in row if certain of them are not to be all together 13 Write down the general term in the expansion of and hence find the 10th term in the quotient when unity is divided by 1- ע In the expansion of 11 η being positive integer the coefficients of the and 12th terms are equal the and 6th terms are equal and the 13th term is 364 Find the values of and 14 Solve the equations 4o r2 1g ϋ י ל י י and ascertain what you can without finding them as to the roots of iii at 15 Find the sum of the squares of the first η natural numbers and prove that the sum of η terms of the scries is Ί η η 13

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