Limits, Continuity & Differentiability · JEE Main previous year questions

2002 4 questions

1. Q452002 · 27 Apr 2002 · Shift 1

   ${\lim }_{x\to \infty }{\left(\frac{x^2+5x+3}{x^2+x+2}\right)}^x$

   1. A.$e^4$
   2. B.$e^2$
   3. C.$e^3$
   4. D.$1$
   Show answer

   Answer: A

2. Q462002 · 27 Apr 2002 · Shift 1

   Let $f(2)=4$ and $f^{\prime }(x)=4$. Then ${\lim }_{x\to 2}\frac{xf(2)-2f(x)}{x-2}$ is given by

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

3. Q472002 · 27 Apr 2002 · Shift 1

   ${\lim }_{x\to 0}\frac{\log x^n-[x]}{[x]},n\in N$, ( [x] denotes the greatest integer less than or equal to x )

   1. A.has value $-1$
   2. B.has value $0$
   3. C.has value $1$
   4. D.does not exist
   Show answer

   Answer: D

4. Q482002 · 27 Apr 2002 · Shift 1

   If $f(1)=1,f^{\prime }(1)=2$, then ${\lim }_{x\to 1}\frac{\sqrt{f(x)}-1}{\sqrt{x}-1}$ is

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

   Answer: A