Two forces $$\overline{\mathrm{F}}_1$$ and $$\overline{\mathrm{F}}_2$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F}_1$$ and $$\vec{F}_2$$ is $$\cos ^{-1}\left(\frac{1}{n}\right)$$. The value of $$|n|$$ is _______.

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $$t(\sqrt{2}+1)$$ s. The value of t is ___________.

(use $$\mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

Four forces are acting at a point $$\mathrm{P}$$ in equilibrium as shown in figure. The ratio of force $$\mathrm{F}_{1}$$ to $$\mathrm{F}_{2}$$ is $$1: x$$ where $$x=$$ _____________.

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $${x \over 5}$$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)