Limits, Continuity & Differentiability · JEE Main previous year questions

2004 3 questions

1. Q462004 · 24 Apr 2004 · Shift 1

   If ${\lim }_{x\to \infty }{\left(1+\frac{a}{x}+\frac{b}{x^2}\right)}^{2x}=e^2$, then the value of $a$ and $b$, are

   1. A.$a=1$ and $b=2$
   2. B.$a=1$ and $b\in R$
   3. C.$a\in R$ and $b=2$
   4. D.$a\in R$ and $b\in R$
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   Answer: B

2. Q472004 · 24 Apr 2004 · Shift 1

   Let $f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[0,\frac{\pi }{2}\right]$. If $f(x)$ is continuous in $\left[0,\frac{\pi }{2}\right]$, then $f\left(\frac{\pi }{4}\right)$ is

   1. A.$-1$
   2. B.$\frac{1}{2}$
   3. C.$-\frac{1}{2}$
   4. D.$1$
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   Answer: C

3. Q632004 · 24 Apr 2004 · Shift 1

   ${\lim }_{n\to \infty }{\sum }_{r=1}^n\frac{1}{n}{e}^{\frac{r}{n}}$ is

   1. A.$e+1$
   2. B.$e-1$
   3. C.$1-e$
   4. D.$e$
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   Answer: B