jee-main 2012 Q73

jee-main · India · offline Indefinite & Definite Integrals Piecewise/Periodic Function Integration

If the integral $\displaystyle\int_{0}^{10} \frac{\lfloor x \rfloor e^{x}}{e^{\lfloor x \rfloor}} dx = \alpha(e-1)$, then $\alpha$ is equal to (where $\lfloor x \rfloor$ denotes the greatest integer function)
(1) $\frac{1}{e-1}$
(2) $\frac{10}{e-1}$
(3) $\frac{e}{e-1}$
(4) $\frac{e^{10}-1}{e-1}$

If the integral $\displaystyle\int_{0}^{10} \frac{\lfloor x \rfloor e^{x}}{e^{\lfloor x \rfloor}} dx = \alpha(e-1)$, then $\alpha$ is equal to (where $\lfloor x \rfloor$ denotes the greatest integer function)\\
(1) $\frac{1}{e-1}$\\
(2) $\frac{10}{e-1}$\\
(3) $\frac{e}{e-1}$\\
(4) $\frac{e^{10}-1}{e-1}$

Paper Questions

Q2 Q3 Q4 Q5 Q6 Q12 Q25 Q26 Q30 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90