To solve this problem, we need to analyze the statements given in the context of Young's double slit experiment.$\\$In Young's double slit experiment, the angular separation $\theta$ of the fringes is given by:$\\ \theta = \frac{\lambda}{d} \\$where $\lambda$ is the wavelength of the light used and $d$ is the distance between the slits.$\\$Let's analyze each statement:$\\$• Statement I: If the screen is moved away from the plane of slits, angular separation of the fringes remains constant.$\\$The angular separation $\theta$ depends only on the wavelength $\lambda$ and the slit separation $d. \\$It does not depend on the distance between the slits and the screen.$\\$Therefore, Statement I is true.$\\$• Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength,$\\$the angular separation of fringes decreases.$\\$From the formula $\theta = \frac{\lambda}{d},$ if $\lambda$ increases, then $\theta$ increases as well.$\\$Therefore, Statement II is false.$\\$Based on the analysis, the correct option is:$\\$Statement I is true but Statement II is false.$\\$Thus, the correct answer is Option 3.