Phototropic curvature is the result of uneven distribution of

$\sqrt{3} \operatorname{cosec} 20^{\circ} - \sec 20^{\circ}$ is equal to

The lanthanide contraction is responsible for the fact that

Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively.
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

What is the full form of $MTP$?