The coefficient of correlation of the above two data series will be equal to \(\underline{\hspace{1cm}}\)
\[\begin{array}{|c|c|} \hline X & Y \\ \hline -3 & 9 \\ -2 & 4 \\ -1 & 1 \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ 3 & 9 \\ \hline \end{array}\]
Identify the median class for the following grouped data:
\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]
Match LIST-I with LIST-II LIST-I (Differential Equation) (A) \(\frac{dy}{dx} = 2x(y-x^2+1)\) (B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\) (C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\) (D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\) LIST-II (Integrating Factor) (I) \(x^2\) (II) \(e^{-x^2}\) (III) \(x^2e^x\) (IV) \(1+x^2\) Choose the correct answer from the options given below:
If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is