Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

Consider the following statements regarding Werner's theory of coordination compounds:
$(1)$ Ligands are connected to the metal ions by coordinate bonds (dative bonds).
$(2)$ Secondary valencies have directional properties.
$(3)$ Secondary valencies are non-ionisable.
Which of these statements are correct?

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at temperature $T \ K$. The piston of cylinder $A$ is free to move,while that of cylinder $B$ is held fixed. The same amount of heat $dQ$ is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in $B$ is (where $\gamma = \frac{C_{p}}{C_{v}}$):

Identify the correct statement among the following options:

$I$. Two non-zero,non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

Which of the following is not considered as an organometallic compound?