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If in a positive integer such that If a number `a=p+f` whre p is an integer and `0ltflt1`. Here p is called the integral part of a and f its fractional part. Let `neplilon N and (sqrt93)+1)^(2n)=p+f`, where p is the integral part and `0ltflt1`. On the basis of bove informationi answer teh following question: The integral part p of `(sqrt(3)+1)^(2n)` is (A) an even number for al `n epsilon N` (B) an odd number for all `nepsilon N` (C) anodd or even number according as n is odd or even (D) an even or odd nuber according as n is odd or even

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Step by step text solution for If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1. Here p is called the integral part of a and f its fractional part. Let neplilon N and (sqrt93)+1)^(2n)=p+f, where p is the integral part and 0ltflt1. On the basis of bove informationi answer teh following question: The integral part p of (sqrt(3)+1)^(2n) is (A) an even number for al n epsilon N (B) an odd number for all nepsilon N (C) anodd or even number according as n is odd or even (D) an even or odd nuber according as n is odd or even by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • If n is a positive integer and (5sqrt(5)+11)^(2n+1)=I+f where I is an integer and 0 lt f lt 1 , then

    A
    I is an even integer
    B
    `(I+f)^(2)` is divisible by `2^(2n+1)`
    C
    I is divisible by 22.
    D
    None

  • Let f(x)=[x] +sqrt({x}) , where [.] denotes the integral part of x and {x} denotes the fractional part of x. Then f^(-1)(x) is

    A
    `[x] +sqrt({x})`
    B
    `[x] + {x}^(2)`
    C
    `[x]^(2)+{x}`
    D
    `{x}+sqrt({x})`

  • If (8 + 3sqrt(7))^(n) = P + F , where P is an integer and F is a proper fraction , then

    A
    P is a odd integer
    B
    P is an even integer
    C
    `F(P + F) = 1`
    D
    `(1 - F ) (P + F) = 1`

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