Radius of gyration of a body depends on

The $P-V$ diagram of a system undergoing thermodynamic transformation is shown in the figure. The work done on the system in going from $A$ $\rightarrow B$ $\rightarrow C$ is $50 \ J$ and $20 \ cal$ of heat is given to the system. The change in internal energy between $A$ and $C$ is ...... $J$.

The $Ka$ of $H_2O_2$ is of the order of:

Arrange the following compounds in decreasing order of reactivity towards nucleophilic addition reactions:
$(I) HCHO$
$(II) CH_3CHO$
$(III) CH_3COCH_3$
$(IV) CH_3CH_2COCH_2CH_3$

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

If $\bar{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\bar{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$,then the value of $(2 \bar{a}-\bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a}+2 \bar{b})) = $