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  Item Reference: KCLCAL-1898-1899-754

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cxxii FACULTY OF SCIENCE If the total cost of voyage of 63 miles at speed of 15 miles an hour be £32 116 and of one of 120 miles at 20 miles an hour be £102 find the cost of voyage of 100 miles at 12 miles an hour Explain what is meant by logarithm when it is not whole number Prove that oga xy loga logay Prove that 10g5 lies between and The sum of the two middle terms of an is and the sum of the series is 60 the last term exceeds the first by 37 find the first term 26 36 bum the series j-- to η r2 r3 terms ψ 10 Ascertain the relation that must subsist between in order that ax2 bx may be separable into real factors and shew that if it cannot be separated into real factors it always has the same sign as whatever be the value of Find the least value of 4x2 12x 13 11 What is meant by an identity as distinguished from an equation If aaWi bx cx dx identically where χ χ זג find the values of by Cj 12 Find the number of combinations of η things taken at time and prove that nCr -1O -j71-1 Cr-i In how many ways can the crew of an eight be selected and arranged out of 10 men of whom can row on the stroke side only on the bow side only and the remainder on either side 13 Establish the Binomial Theorem for positive integral exponent Expand 3δ to four terms and determine whether the 20th term is greater or less than the 19th if χ How many terms in the expansion of ax3 bx 100 will involve positive powers of 14 Prove that ן ן x2 ηφ -f χ -1 x2Y2
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