# Calendar: 1875-1876 Page 583

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GENERAL LITERATURE AND SCIENCE 579 Extract the fourth root of 12 and shew that when η is positive integer x" is always divisible by χ Find the value to five places of decimals of 21 43I If χ β 13 a- Ja b3 shew that x3 Zbx 2a Solve the equations ry -f xz jf 39 411 χ τ2 5x 28 xl i2 84 xl 49 If ο and β be the roots of x2 ax -f construct the equation whose roots are a2 and β2 If prove that Λ Transform 22l248 from the scale of ten to the scale of five and 444'44 from the scale of five to that of ten Prove that the difference of two numbers consisting of the same digits is divisible by nine Sum twenty-one terms of an of which 30 is the middle term Shew also that the common difference of an is equal to the difference of the squares of the first and last terms divided by twice the sum of all the terms diminished by the first and last term 10 What is meant by the sum of an infinite number of terms of geometrical progression Write down the first five terms of the series of which the Mth term is 26- 34-and'find its sum to infinity 11 Find the number of permutations of η things taken to- gether and deduce tbe number of combinations of it things ן together In how many ways can ten persons form ring 12 If in the 7th and 8th terms are iu the same ratio as the 6th and 7th in find Write down the general term in the expansion of

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