We calculate growth rate for each category:
Primary:
Initial = $42137$, Final = $68718$
Growth = $\frac{68718 - 42137}{42137} \times 100 \approx 63.08%$
Secondary:
Initial = $8820$, Final = $20177$
Growth = $\frac{20177 - 8820}{8820} \times 100 \approx 128.74%$
Higher Secondary:
Initial = $65303$, Final = $82175$
Growth = $\frac{82175 - 65303}{65303} \times 100 \approx 25.87%$
Graduate:
Initial = $25343$, Final = $36697$
Growth = $\frac{36697 - 25343}{25343} \times 100 \approx 44.85%$
Clearly, the smallest growth is $25.87%$ for Higher Secondary.
Checking incorrect options:
(A) Primary — $63.08%$, higher than $25.87%$.
(B) Secondary — $128.74%$, the highest growth rate, so incorrect.
(D) Graduate — $44.85%$, larger than $25.87%$.
\(\boxed{\text{Correct Answer: (C) Higher secondary}}\)