If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I...
If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I with Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } \\
\hline A. & \( \int_{0}^{\infty} e^{-2 x^{2}} d x \) & p. & \( \sqrt{\pi} \) \\
\hline B. & \( \frac{d}{d t} \int_{0}^{\infty} e^{-t x^{2}} d x \) at \( t=1 \) & q. & \( \frac{3 \sqrt{\pi}}{8} \) \\
\hline C. & \( \frac{d^{2}}{d t^{2}} \int_{0}^{\infty} e^{-t x^{2}} d x \) at \( t=1 \) & r. & \( -\frac{\sqrt{\pi}}{4} \) \\
\hline D. & \( \int_{-\infty}^{\infty} e^{-x^{2}} d x \) & s. & \( \frac{\sqrt{\pi}}{2 \sqrt{2}} \) \\
\hline
\end{tabular}
(a) \( \mathrm{A}-\mathrm{s}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q} \)
(b) \( \mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{s}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q} \)
(c) \( \mathrm{A}-\mathrm{q}, \mathrm{B}-\mathrm{p}, \mathrm{C}-\mathrm{q}, \mathrm{D}-\mathrm{s} \)
(d) \( \mathrm{A}-\mathrm{s}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{q}, \mathrm{D}-\mathrm{p} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | The minimum value of the twice differentiable function \( f(x) \) \( =\int_{0}^{x} e^{x-t} f^{\p... |
| 2023-06-09 | Given that \( U_{n}=\{x(1-x)\}^{n} \) and \( n \geq 2 \) and
\[
\frac{d^{2} U_{n}}{d x^{2}}=n(n-... |
| 2023-06-09 | \( \int_{1 / 3}^{1 / 2}\left\{x\left[\frac{2}{x}\right]\right\} d x \) (where [·] is G.I.F.) and... |
| 2023-06-09 | If \( f(x)=x+\int_{0}^{1}\left(x y^{2}+x^{2} y\right)(f(y)) d y \), find \( f(x) \) |
| 2023-06-09 | Let \( f(x)=x^{3}-\frac{3 x^{2}}{2}+x+\frac{1}{4} \). Find the value of \( \left(\int_{1 / 5}^{4... |
| 2023-06-09 | If \( \lim _{n \rightarrow \infty} \frac{\left[1^{3}+2^{3}+3^{3} \ldots . .+(2 n)^{3}\right] \cd... |
| 2023-06-09 | Let \( f \) be a real-valued function defined on the interval \( (0, \infty) \) by \( f(x)=\ln x... |
| 2023-06-09 | \( I=\int_{\pi / 4}^{2 n \pi+\frac{\pi}{4}} \frac{d x}{\left(1+\pi^{\cos x}\right)\left(1+\pi^{\... |
| 2023-06-09 | Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{arr... |
| 2023-06-09 | If \( \lim _{n \rightarrow \infty}\left(\frac{{ }^{3 n} C_{n}}{{ }^{2 n} C_{n}}\right)^{1 / n}=\... |
| 2023-06-09 | If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I... |
| 2023-06-09 | Suppose that the function \( f, g, f^{\prime} \) and \( g^{\prime} \) are continuous over \( [0,... |
| 2023-06-09 | If \( U_{n}=\int_{0}^{\frac{\pi}{2}} \cos ^{n} x \cos n x d x \) then
(a) \( U_{1}, U_{2} \ldots... |
| 2023-06-09 | If \( \int_{0}^{1}\left(\sum_{k=1}^{2014} \frac{x^{2}}{x^{3}+k^{3}}\right)\left(\prod_{k=1}^{201... |
| 2023-06-09 | If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), ... |
| 2023-06-09 | \( \int_{-1}^{1}\left(e^{x^{3}}+e^{-x^{3}}\right) d x \) is less then
(a) 2
(b) \( 2 e+\frac{2}{... |
| 2023-06-09 | Let \( f:[0,1] \rightarrow[0, \infty) \) be a continuous function such that \( \int_{0}^{1} f(x)... |
| 2023-06-09 | Let \( I_{1}=\int_{0}^{\infty} \frac{x^{2} \sqrt{x}}{(1+x)^{6}} d x, I_{2}=\int_{0}^{\infty} \fr... |
| 2023-06-09 | \[
\int_{-4}^{4} \frac{\sin ^{-1}(\sin x)+\cos ^{-1}(\cos x)}{\left(1+x^{2}\right)\left(1+\left[... |
| 2023-06-09 | Let \( I(n)=\int_{2016}^{2016+\frac{1}{n}} x \cos ^{2}(x-2016) d x \)
Statement 1: \( I\left(\fr... |
| 2023-06-09 | Evaluate: \( \int_{0}^{\infty}\left(\frac{\tan ^{-1} x}{x}\right)^{3} d x \) |
0