`.^(5)C_(0)+.^(5)C_(1)+.^(5)C_(2)+.^(5)C_(3)+.^(5)C_(4)+.^(5)C_(5)=`……………

""^(15)C_(0)*""^(5)C_(5)+""^(15)C_(1)*""^(5)C_(4)+""^(15)C_(2)*""^(5)C_(3)+""^(15)C_(3)*""^(5)C_(2)+""^(15)C_(4)*""^(5)C_(1) is equal to :

""^(15)C_(0)*""^(5)C_(5)+""^(15)C_(1)*""^(5)C_(4)+""^(15)C_(2)*""^(5)C_(3)+""^(15)C_(3)*""^(5)C_(2)+""^(15)C_(4)*""^(5)C_(1) is equal to :

C_(1)+2.5C_(2)+3.5^(2)C_(3)+----1=

Given are six 0' s, five 1' s and four 2's . Consider all possible permutations of all these numbers. [A permutations can have its leading digit 0 ]. How many permutations have the first 0 preceding the first 1 ? (a) "^(15)C_(4)xx^(10)C_(5) (b) "^(15)C_(5)xx^(10)C_(4) (c) "^(15)C_(6)xx^(10)C_(5) (d) "^(15)C_(5)xx^(10)C_(5)

Prove that .^(15)C_(3) + 2 xx .^(15)C_(4) + .^(15)C_(5) = .^(17)C_(5)

^5C_(1)+^(5)C_(2)+^(5)C_(3)+^(5)C_(4)+^(5)C_(5) is equal to 30 b.31c.32d.33

Which of the following compounds will exhibit tautomerism and which do not? Give reasons. (1) CH_(3)COCH_(3) (2) C_(6)H_(5)COC_(6)H_(5) (3) C_(6)H_(5)COCH_(3) (4) C_(6)H_(5)CHO (5) MeCCOCHMe_(3)

(C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+....=

Prove that .^(35)C_(5) + sum_(r=0)^(4^((39-r))) C_(4) = .^(40)C_(5)