Which of the following hydroxides is acidic?

$\cos \left[\cos ^{-1}\left(-\frac{1}{7}\right)+\sin ^{-1}\left(-\frac{1}{7}\right)\right]$ is equal to

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \, \Omega$ resistor. The galvanometer shows a null point when the tapping-key is at the $52 \, cm$ mark. The end corrections are $1 \, cm$ and $2 \, cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is $.......... \Omega$.

$_6 C^{12}$ and $_1 T^3$ are formed in nature due to the nuclear reaction of a neutron with:

The molecular formula of diphenylmethane is $C_{13}H_{12}$. How many structural isomers are possible when one of the hydrogen atoms is replaced by a chlorine atom?

The figure below shows two paths that may be taken by a gas to go from a state $A$ to a state $C$. In process $AB$,$400 \, J$ of heat is added to the system and in process $BC$,$100 \, J$ of heat is added to the system. The heat absorbed by the system in the process $AC$ will be ............. $J$.