EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>JEE Advanced Paper 1 - 2018>Q 26

HARD

JEE Advanced

IMPORTANT

Earn 100

Let $f : [0, \infty) \to R$ be a continuous function such that $f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t$ for all $x \in [0, \infty) .$ Then, which of the following statement(s) is (are) TRUE?

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Important Questions on Definite Integration

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 26 - Definite Integration>JEE Advanced Paper 1 - 2018>Q 27

For each positive integer

n

, let

y_{n} = {\frac{1}{n} ((n + 1) (n + 2) ... (n + n))}^{\frac{1}{n}}

. If

\lim_{n \to \infty} y_{n} = L,

then the value of

[L]

(where

[x]

is the greatest integer less than or equal to

x

) is ____