Calendar: 1874-1875 Page 550

550 GENERAL LITERATURE AND SCIENCE If cr be the coefficient of the rth term in the expansion of -f it an integer show that c32 etc if 11 be even and equal zero if η be odd Sr is the sum of terms of an arithmetic progression of which the first term is and the common difference also show that 51 "- 3g ax2 bx and i-3 a'x"- b'x have common quadratic factor show that c' c' a1c at b'c be' Enunciate the binomial theorem and prove it for positive integral index If be the coefficient of xT in -f- prove that 9T7 ן OT 1n I" No algebraical formula can represent prime numbets only The difference of the squares of any two prime numbers is divisible by 24 Find the greatest term in the binomial expansion of Find the greatest term in χ 20 when χ 10 bag contains white balls and 71 black ones If 2r balls be drawn find the chance that are white and black Also if any drawing whatever be made find the chance