Calendar: 1878-1879 Page 600

598 GENERAL LITERATURE AND SCIENCE 10 Show that the number of combinations of η things taken at time is the same as the number taken η at time From company of soldiers mustering 100 picket of 10 is to be selected in how many ways can this be done so as always to include two particular men 11 Find the sum of the coefficients of the terms in the expan- sion of -j- and shew that the middle term of is equal to 2BjM- Lf 12 What is the logarithm of 5832 to the base Given 10g30103 and log107 845098 find the logarithm of to the base 1000 13 The angles of triangle are as the numbers ex- press them in degrees grades and circular measure 14 Prove the following cos Λ sm2 Λ י -ל tanM sec2A cosec2 sec2 -f- cosec2 sinM coseA sin4 cos 15 Determine the values of the trigonometrical ratios for angles of 405 and 1050 and find all the angles between and 900 which satisfy the relation tan 16 Give geometrical proofs for the expansions of sin and cos Deduce the values of sin 2A cos 2A sin3 cos3 17 Solve the equations sin θ cos 'tan20 4sin20 sin θ sin θ tan θ 3tan 343