A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $$4 m$$, then the time period of small oscillations will be __________ s. [take $$g=\pi^2 m s^{-2}$$]

In an experiment to measure the focal length $$(f)$$ of a convex lens, the magnitude of object distance $$(x)$$ and the image distance $$(y)$$ are measured with reference to the focal point of the lens. The $$y$$-$$x$$ plot is shown in figure.

The focal length of the lens is ________ $$\mathrm{cm}$$.

A vector has magnitude same as that of $$\vec{A}=3 \hat{i}+4 \hat{j}$$ and is parallel to $$\vec{B}=4 \hat{i}+3 \hat{j}$$. The $$x$$ and $$y$$ components of this vector in first quadrant are $$x$$ and 3 respectively where $$x=$$ _________.