KVPY SX SB Exam 20141 Question Paper

Question : 19 of 120

Marks: +1, -0

For a real number r let [r] denote the largest integer less than or equal to r . Let a > 1 be a real number which is not an integer, and let k be the smallest positive integer such that

[a ^k ] > [a]^k

. Then which of the following statements is always true?

$k≤ 2 ([a ] +1)^2$
$k ≤ ([a ] + 1) ^4$
$k≤ 2 ^{ [a ] +1}$
$k≤ 1/ {a-[a ] }+1$

Validate

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