Calendar: 1874-1875 Page 547

GENERAL LITERATURE AND SCIENCE 047 If -f- η η β a2 η b2 ma3 nb3 δ show that and έ are the roots of the equation ay β2 Xs ad βγ χ βδ y2 Sum η η 1-- -4- -4- &c to terms &c to η terms &c to terms 2x 2X2 2a &c to infinity From two towns 168 miles apart and Β set out to meet went miles the first day the second the third and so on Β went miles the first day the second the third and so on In how many days will they meet If be the digits of number beginning with the units prove that the number itself is divisible by 16 if 10b 4c isd is divisible by 16 Find the number of permutations of η things taken all together What is the number of things when the number of permutations is 5040 person wishes to make up as many different parties as he can out of 20 friends each party consisting of the same number how many must he invite at time 10 If the second term in the expansion of -f- he 240 the third term 720 and the fourth term 1080 find and 11 The middle term in the expansion of ג is gn 12 Find the least value of χ and show that if be any integer ifi η -f1 cannot be square number 13 Prove the formulse sin2 cos2 Λ sec -ii co ec2 sec cosec' sin sin cosB cos sin ιλ co tan2J --- -f- cos Μ Μ