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TIFR Mathematics 2022 | Part A | Question: 19

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The value of
\[\lim _{n \rightarrow \infty} \int_{0}^{1} \frac{n e^{x}}{1+n^{2} x^{2}} d x\]
is

  1. $\pi e$
  2. $\frac{\pi}{2}$
  3. $\frac{\pi}{2} e$
  4. $\pi$
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TIFR Mathematics 2022 | Part A | Question: 3
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]?$ $0$ $1$ $2$ $\infty$
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]?$ $0$$1$$2$$\infty$
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