For each positive integer n, let yn = (1/n)((n+1)(n+2)⋅s(n+n))(1/n) For x ∈ ℝ let [L] be the greatest integer less than or equal to x. If displaystyle limn → ∞ yn = L, then the value of [L] is .

Questions from JEE Advanced 2018

1. Let and be two planes. Then, which of the following statement(s) is (are) TRUE?

2. For every twice differentiable function with which of the following statement(s) is (are) TRUE?

3. Let and be two non-constant differentiable functions.If
for all ,
and , then which of the following statement(s) is (are) TRUE?

4. Let be a continuous function such that for all . Then, which of the following statement(s) is (are) TRUE?

5. PARAGRAPH X
Let be the circle in the -plane defined by the equation .
Question: Let and be the chords of passing through the point and parallel to the x-axis and the y-axis, respectively. Let be the chord of passing through and having slope -1. Let the tangents to at and meet at , the tangents to at and meet at , and the tangents to at and meet at . Then, the points , and lie on the curve

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