A $$1 \mathrm{~kg}$$ mass is suspended from the ceiling by a rope of length $$4 \mathrm{~m}$$. A horizontal force '$$F$$' is applied at the mid point of the rope so that the rope makes an angle of $$45^{\circ}$$ with respect to the vertical axis as shown in figure. The magnitude of $$F$$ is :

(Assume that the system is in equilibrium and $$g=10 \mathrm{~m} / \mathrm{s}^2$$)

The following figure represents two biconvex lenses $$L_1$$ and $$L_2$$ having focal length $$10 \mathrm{~cm}$$ and $$15 \mathrm{~cm}$$ respectively. The distance between $$L_1$$ & $$L_2$$ is :

The resultant of two vectors $$\vec{A}$$ and $$\vec{B}$$ is perpendicular to $$\vec{A}$$ and its magnitude is half that of $$\vec{B}$$. The angle between vectors $$\vec{A}$$ and $$\vec{B}$$ is _________$$^\circ$$.

An electric field $$\vec{E}=(2 x \hat{i}) N C^{-1}$$ exists in space. A cube of side $$2 \mathrm{~m}$$ is placed in the space as per figure given below. The electric flux through the cube is ______ $$\mathrm{Nm}^2 / \mathrm{C}$$.