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The greatest value of n for which the de...

The greatest value of n for which the determinant
`Delta = |(1,1,1),(.^(n)C_(1),.^(n+3)C_(1),.^(n+6)C_(1)),(.^(n)C_(2),.^(n+3)C_(2),.^(n+6)C_(2))|` is divisible by `3^(n)`, is

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The value of |111^(n)C_(1)^(n+2)C_(1)^(n+4)C_(1)^(n)C_(2)^(n+2)C_(2)^(n+4)C_(2)| is

If 3^n is a factor of the determinant |{:(1,1,1),(.^nC_1,.^(n+3)C_1,.^(n+6)C_1),(.^nC_2, .^(n+3)C_2, .^(n+6)C_2):}| then the maximum value of n is ……..

Knowledge Check

  • The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(2))/(2n)

    A
    `underset(0)overset(1)intx^(n-1)(1-x)^(n)dx`
    B
    `underset(1)overset(2)intx^(n)(x-1)^(n-1)dx`
    C
    `underset(1)overset(2)int(1+x)^(n)dx`
    D
    `underset(0)overset(1)int(1-x)^(n)x^(n-1)dx`

  • The value of (n+2).^(n)C_(0).2^(n+1)-(n+1).^(n)C_(1).2^(n)+(n).^(n)C_(2).2^(n-1)-….." to " (n+1) terms is equal to

    A
    4
    B
    4n
    C
    `4(n+1)`
    D
    `2(n+2)`

  • If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

    A
    `7`
    B
    `8`
    C
    `9`
    D
    `11`

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