The specific heats, C _ p and C _ v of a gas of diatomic molecules,...

For $A$ :
$R = {C}_{p} - {C}_{v} = 29 - 22 = 7$
${C}_{v} = \dfrac{fR}{2}$
$⇒ 22 = \dfrac{f \times 7}{2}$
$⇒ f = \dfrac{44}{7} = 6.3$
$⇒ f \approx 6$

(5 rotational + translational, 1 vibrational)

For $B$ :
$R = {C}_{p} - {C}_{V} = 30 - 21 = 9$
${C}_{v} = \dfrac{fR}{2} = 21$
$⇒ f = \dfrac{21 \times 2}{9} = \dfrac{42}{9} = 4.66 ≃ 5$
$∴ f ≃ 5$

(5 rotational + transitional, 0 vibrational)