S_(12)=3(S_(8)-S_(4))

If S_(1) and S_(2) are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_(3) and S_(4) are the foci of the conjugate hyperbola,then the area of quadrilateral S_(1)S_(3)S_(2)S_(4) is 24 (b) 26 (c) 22 (d) none of these

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

If S_(1), S_(2), S_(3),….., S_(n) are the sum of infinite geometric series whose first terms are 1,3,5…., (2n-1) and whose common rations are 2/3, 2/5,…., (2)/(2n +1) respectively, then {(1)/(S_(1) S_(2)S_(3))+ (1)/(S_(2) S_(3) S_(4))+ (1)/(S_(3) S_(4)S_(5))+ ........."upon infinite terms"}=

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(0),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

If S_(r)=alpha^(r)+beta^(r)+gamma^(r) then show that det[[S_(2),S_(1),S_(2)S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)det[[S_(1),S_(2),S_(3)S_(2),S_(3),S_(4)]]=(alpha-beta)^(2)(beta-gamma)^(2)(gamma-alpha)^(2)

The order of increasing O.N. of S in S_(8), S_(2) O_(8)^(-2), S_(2) O_(3)^(-2), S_(4) O_(6)^(-2) is given below -

The order of increasing oxidation number of S in S_(8),S_(2)O_(8)^(-2),S_(2)O_(3)^(2-),S_(4)O_(6)^(-2) is given below -

The order of increasing oxidation number of S in S_(8),S_(2),O_(8)^(-2),S_(2)O_(3)^(2-),S_(4)O_(6)^(-2) is given below -

The sets S_(1), S_(2), S_(3), …………. are given by S_(1) = {2/1} , S_(2) = {3/2, 5/2} , S_(3) = {4/3, 7/3, 10/3} , S_(4) = {5/4, 9/4, 13/4, 17/4} ,........ . Then the sum of the set S_(25) is