The logarithm of $32\sqrt[5]{4}$ to the base $2\sqrt{2}$ is:

An insulated container contains $4 \, \text{moles}$ of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to this gas, due to which $2 \, \text{moles}$ of gas are dissociated into atoms, but the temperature of the gas remains constant. Then:

On addition of $1 \ mL$ solution of $10 \% \ NaCl$ to $10 \ mL$ gold sol in the presence of $0.025 \ g$ of starch,the coagulation is just prevented. What is the gold number of starch?

$e^{\log (\cosh^{-1} 2)}$ is equal to :

At a certain place,a magnet makes $30$ oscillations per minute. At another place where the magnetic field is double,its time period will be:

$A$ bag contains $5$ black balls,$4$ white balls,and $3$ red balls. If a ball is selected at random,the probability that it is a black or red ball is