# Calendar: 1890-1891 Page 803

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WARNEFORD SCHOLARSHIPS cxli How many different hands at whist can be dealt con- taining no card higher than What fraction is this of the whole number of hands that can be dealt 10 Prove the Binomial Theorem for positive fractional index lv- Expand Η-1 χ in each case giving the general term -Crigonomctn antl &rit1 nuttc Candidates for Warneford Scholarship and Sambrooke Exhibition omit Questions 1-5 Define the cosecant of any angle and find cosec 30 cosec 90 cosec 180 cosec 210 Prove that cos 2A cos 2A sin 2A and deduce cos 2j Obtain another formula by changing cos 2A into 45 Obtain an expression for the tangent of half an angle of triangle in terms of the sides Prove that the area £ ύ2 c2 a2 tan In triangle ABC AP is perpendicular to and Μ is the point of contact of the incircle with AC prove that BM2 sin cos 2C Extract the fourth root of cos 2Θ -f sin 20 Write down all the fourth roots Explain your method of dividing one number by another modihcations 01 the divisors 2779 70 י Divide 854321 by each of these divisors Prove without finding the result that the cost of things at £b each is the same as that of things at £4 each 57 many

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