" (i) "(2^(30)+2^(29)+2^(28))/(2^(31)+2^(30)-2^(29))=(7)/(10)

Prove that (2^(30)+2^(29)+2^(28))/(2^(31)+2^(30)-2^(29))=(7)/(10)

PRove that (2^(30)+2^(29)+2^(28))/(2^(31)+2^(30)-2^(29))=(7)/(10)

Sum of last 30 coefficients in the binomial expansion of (1+x)^(59) is a) 2^(29) b) 2^(59) c) 2^(58) d) 2^(59)-2^(29)

(21)/(x^(2))-(29)/(x)-10=0

If ((n),(r)) denotes nC_r , then Evaluate 2^15((30),(0))((30),(15))-2^14((30),(1))((29),(14))+2^13 ((30),(2))((28),(13))...............-((30),(15))((15),(0))

Show that ""^(30)C_(0) +""^(30)C_(1)+""^(30)C_(2) +…+ ""^(30)C_(14) =2^(29)-(1)/(2) (""^(30)C_(15))

If ((n),(r )) "denotes " ""^nC_r then (a) Evalutae : 2^(15)((30),(0))((30),(1))-2^(14)((30),(1))((29),(14))+2^(13)((30),(2))((28),(13)).......-((30),(15))((15),(0)) ( b) Prove that : Sigma_(r=1)^(n) ((n-1),(n-r))((n),(r))=((2n-1),(n-1)) ( c) Prove that : ((n),(r))((r),(k))=((n),(k))((n-r),(r-k))

If the value of the sum 29(.^(30)C_(0))+28(.^(30)C_(1))+27(.^(30)C_(2))+…….+1(.^(30)C_(28))-(.^(30)C_(30)) is equal to K.2^(32) , then the value of K is equal to

If the value of the sum 29(.^(30)C_(0))+28(.^(30)C_(1))+27(.^(30)C_(2))+…….+1(.^(30)C_(28))+0.(.^(30)C_(29))-(.^(30)C_(30)) is equal to K.2^(32) , then the value of K is equal to