JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q11

MathematicsSingle correct+4 / -1Question 11 of 90

$\displaystyle\lim_{n\to\infty}\sum_{r=1}^n\frac r{2r^2-7rn+6n^2}$ is equal to :

\log_e\left(\dfrac{\sqrt3}2\right)

\log_e\left(\dfrac{3\sqrt3}4\right)

\log_e\left(\dfrac{27}4\right)

\log_e\left(\dfrac43\right)

Answer and worked solution

Official answer: B

Riemann sum. $\displaystyle\int_0^1\frac{x\,dx}{2x^2-7x+6}=\int_0^1\left(\frac2{x-2}-\frac{3/2}{x-\frac32}\right)dx=\ln\frac{3\sqrt3}4$ .

(B)

Topics:Limit of a sum Partial fractions

JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 11