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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Match the following columns: Column-I Column-II (A) _ n → ∞ 4 [...

Match the following columns:

Column-I

Column-II

(A) \displaystyle \lim_{n \to

\infty} 4 \left[ \frac{1}{n^2}

e^{\frac{1}{n}} +

\frac{2}{n^2}

e^{\frac{2}{n}} +

\frac{3}{n^2}

e^{\frac{3}{n}} + \dots +

\frac{1}{n}

e^{\frac{n}{n}} \right] =

(P) \displaystyle 0

(B) \displaystyle \int_0^1 \ln \left( \frac{1}{x} -

1 \right) dx =</td><td>(Q) \displaystyle 1</td></tr><tr><td>(C) \displaystyle \int_0^{10\pi}

\left( \lim_{x \to y} \left(

\frac{\sin x - \sin y}{x - y} \right) \right)dy =</td><td>(R) \displaystyle 2</td></tr><tr><td>(D) \displaystyle \int_0^\infty \frac{\ln(x + \frac{1}{x}) dx}{(1 + x²)} = \frac{\pi}{2} \lna ,then \displaystyle a =</td><td>(S) \displaystyle 4</td></tr><tr><td></td><td>(T) \displaystyle 5</td></tr></table>

Correct answer

0

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