$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from both holes are the same. Then,$R$ is equal to

Let $f(x) = \begin{cases} \frac{x^4 - 5x^2 + 4}{|(x - 1)(x - 2)|}, & x \ne 1, 2 \\ 6, & x = 1 \\ 12, & x = 2 \end{cases}$. Then $f(x)$ is continuous on the set

When a certain circuit consisting of a constant $emf$ $E$,an inductance $L$,and a resistance $R$ is closed,the current in it increases with time according to curve $1$. After one parameter ($E$,$L$,or $R$) is changed,the increase in current follows curve $2$,when the circuit is closed a second time. Which parameter was changed and in what direction?

The excess pressure inside a spherical soap bubble of radius $1 ~cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 ~mm$ high. The surface tension of the bubble is: (in $~N/m$)

Chromatophores take part in