Which one of the following pairs of hormones can easily pass through the cell membrane of a target cell and bind to a receptor inside it (mostly in the nucleus)?

$A$ particle of mass $1 \times 10^{-26} \ kg$ and charge $1.6 \times 10^{-19} \ C$ travelling with a velocity $1.28 \times 10^6 \ ms^{-1}$ along the positive $X$-axis enters a region in which a uniform electric field $E$ and a uniform magnetic field of induction $B$ are present. If $E = -102.4 \times 10^3 \ \hat{k} \ NC^{-1}$ and $B = 8 \times 10^{-2} \ \hat{j} \ Wbm^{-2}$,the direction of motion of the particle is:

The maximum value of the function $f(x)=3x^3-18x^2+27x-40$ on the set $S=\{x \in R : x^2+30 \leq 11x\}$ is

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

All wires have the same resistance $r$. The equivalent resistance between $A$ and $B$ is $R$ when the keys $K_1$ and $K_2$ are open. Now,if the keys are closed,what will be the new equivalent resistance?

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is