According to Hooke's law of elasticity,if stress is increased,the ratio of stress to strain

The condition that $f(x)=a x^3+b x^2+c x+d$ has no extreme value,is

When glucose reacts with bromine water,the main product is

$A$ block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope,the force exerted by the rope on the block is-

Which sample contains a greater number of nuclei: a $5.00 \, \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \, y$) or a $4.45 \, \mu Ci$ sample of $^{243}Am$ (half-life $7370 \, y$)?

If the pressure at half the depth of a lake is equal to $2/3$ of the pressure at the bottom of the lake,then what is the depth of the lake in $m$? (Assume atmospheric pressure $P_0 = 10^5 \ Pa$,density of water $\rho = 10^3 \ kg/m^3$,and $g = 10 \ m/s^2$)