Three blocks $$\mathrm{M_1, M_2, M_3}$$ having masses $$4 \mathrm{~kg}, 6 \mathrm{~kg}$$ and $$10 \mathrm{~kg}$$ respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope $$\mathrm{1, T_1}$$ when they are moving upward with acceleration of $$2 \mathrm{~ms}^{-2}$$ is __________ $$\mathrm{N}$$ (if $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

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 _______.

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)