Limits, Continuity & Differentiability · JEE Main previous year questions

2016 2 questions

1. Q172016 · 3 Apr 2016 · Shift 1

   Let $p={\lim }_{x\to 0^{+}}{\left(1+{\tan }^2\sqrt{x}\right)}^{\frac{1}{2x}}$ then $\log p$ is equal to :

   1. A.$\frac{1}{2}$
   2. B.$\frac{1}{4}$
   3. C.$2$
   4. D.$1$
   Show answer

   Answer: A

2. Q292016 · 3 Apr 2016 · Shift 1

   ${\lim }_{n\to \infty }{\left(\frac{(n+1)(n+2)\dots 3n}{n^{2n}}\right)}^{\frac{1}{n}}$ is equal to:

   1. A.$\frac{9}{e^2}$
   2. B.$3\log 3-2$
   3. C.$\frac{18}{e^4}$
   4. D.$\frac{27}{e^2}$
   Show answer

   Answer: D