Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$$ Which of the following statements is (are) true?

An infinitely long thin non-conducting wire is parallel to the $$z$$-axis and carries a uniform line charge density $$\lambda .$$ It pierces a thin non-conducting spherical shell of radius $$R$$ in such a way that the arc $$PQ$$ subtends an angle $${120^ \circ }$$ at the center $$O$$ of the spherical shell, as shown in the figure. The permittivity of free space is $${ \in _0}.$$ Which of the following statement is (are) true?

In a radioactive decay chain, $${}_{90}^{232}Th$$ nucleus decays to $${}_{82}^{212}Pb$$ nucleus. Let $${N_\alpha }$$ and $${N_\beta }$$ be the number of $$\alpha $$ and $${\beta ^ - }$$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $$f,$$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)