Identify the pair(s) of physical quantities that possess identical...

Magnetizing field intensity $H$ and intensity of magnetization $I$ both have dimensions $[L^{-1} A]$.

Longitudinal strain is the ratio of change in length to original length, making it a dimensionless quantity $[M^{0} L^{0} T^{0}]$.

Magnetic susceptibility $\chi$ is defined as the ratio of intensity of magnetization to magnetizing field intensity ($\chi = \dfrac{I}{H}$). Since both $I$ and $H$ have the same dimensions, $\chi$ is also dimensionless $[M^{0} L^{0} T^{0}]$.

Magnetic field $B$ has dimensions $[M T^{-2} A^{-1}]$, which differs from $I$ and $H$.

Therefore, the pairs of physical quantities that possess identical dimensions are magnetizing field intensity and intensity of magnetization, as well as longitudinal strain and magnetic susceptibility.