# Calendar: 1863-1864 Page 531

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GENERAL LITERATURE AND SCIENCE 531 If χ and be the sides of right angled triangle convert the result into geometrical theorem 11 14 The sum of η terms of an arithmetic series is-- find the fifth term 15 The sum of geometric series is 255 the first and last terms are respectively and 128 Find the common ratio and the number of terms 16 Five four-oars have to be made up the number of men is exact but five of them can only steer In how many ways can the crews be chosen 17 Find the greatest term in the expansion of Λ 18 If the price of pure whisky be 16 per gallon and its specific gravity be 75 that of water being unity what should he the price of mixture of whisky and water the specific gravity of which is 19 The seventh power of an integer diminished by the in- teger is multiple of 42 20 The number of solutions of ax by in positive in- teeers cannot exceed ab Ex χ 4- 7y 250 21 If in the preceding question one value of χ and one of can be found show that general solution can be obtained Ex Zx 7y 250 25 25 22 If 4-c -f c- varies as a2 then β2 IP c2 or varies as 23 Three white and two red balls are arranged in line show that the probability that the first and last balls shall be white

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