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Evaluate the following : (i) 1+.^(20)C...

Evaluate the following :
`(i) 1+.^(20)C_(1)+^(20)C_(2)+^(20)C_(3)+....+^(20)C_(19)+^(20)C_(20)`
`(ii) ^(10)C_(1)+^(10)C_(2)+^(10)C_(3)+.....+^(10)C_(9)`
`(iii)^(25)C_(1)+^(25)C_(3)+^(25)C_(5)+.....+^(25)C_(25)`
`(iv) ^(18)C_(2)+^(18)C_(4)+^(18)C_(4)+^(18)C_(6)+....+^(18)C_(18)`

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1.^(20)C_(1)-2.^(20)C_(2)+3.^(20)C_(3)-...-20.^(20)C_(20)

Evaluate the following: ""^(19) C_(17) + ""^(19) C_(18)

Knowledge Check

  • The value of .^(20)C_(10)+.^(20)C_(1)+.^(20)C_(2)+.^(20)C_(3)+.^(20)C_(4)+.^(20)C_(12)+.^(20)C_(13)+.^(20)C_(14)+.^(20)C_(15) is

    A
    `2^(19)-((.^(20)C_(10)+.^(20)C_(9)))/(2)`
    B
    `2^(19)-((.^(20)C_(10)+2xx.^(20)C_(9)))/(2)`
    C
    `2^(19)-(.^(20)C_(10))/(2)`
    D
    none of these

  • The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

    A
    `-.^(20)C_(10)`
    B
    `1/2 .^(20)C_(10)`
    C
    0
    D
    `.^(20)C_(10)`

  • The value of 1^(1).^(20)C_(1)+2^(2).^(20)C_(2)+3^(2).^(20)C_(3)+….+(20)^(2).^(20)C_(20) is

    A
    `210xx2^(17)`
    B
    `420xx2^(17)`
    C
    `420xx2^(18)`
    D
    `210xx2^(18)`

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