Cascaded two-ports multiply their T (ABCD) matrices in order, so the work is to write each T-section's matrix and then multiply.

Step 1 — the standard T-section matrix. For a section with series arm Z₁, shunt arm Z₂ and series arm Z₃:

\(A=1+\dfrac{Z_{1}}{Z_{2}},\quad B=Z_{1}+Z_{3}+\dfrac{Z_{1}Z_{3}}{Z_{2}},\quad C=\dfrac{1}{Z_{2}},\quad D=1+\dfrac{Z_{3}}{Z_{2}}\)

Step 2 — the first section (2 Ω, 10 Ω, 4 Ω):

\(A_{1}=1+\dfrac{2}{10}=1.2,\qquad B_{1}=2+4+\dfrac{8}{10}=6.8\)

\(C_{1}=\dfrac{1}{10}=0.1,\qquad D_{1}=1+\dfrac{4}{10}=1.4\)

Step 3 — the second section (4 Ω, 20 Ω, 8 Ω):

\(A_{2}=1+\dfrac{4}{20}=1.2,\qquad B_{2}=4+8+\dfrac{32}{20}=13.6\)

\(C_{2}=\dfrac{1}{20}=0.05,\qquad D_{2}=1+\dfrac{8}{20}=1.4\)

Step 4 — multiply.

\(A=A_{1}A_{2}+B_{1}C_{2}=(1.2)(1.2)+(6.8)(0.05)=1.44+0.34=1.78\)

\(B=A_{1}B_{2}+B_{1}D_{2}=(1.2)(13.6)+(6.8)(1.4)=16.32+9.52=25.84\ \Omega\)

\(C=C_{1}A_{2}+D_{1}C_{2}=(0.1)(1.2)+(1.4)(0.05)=0.12+0.07=0.19\ \text{S}\)

\(D=C_{1}B_{2}+D_{1}D_{2}=(0.1)(13.6)+(1.4)(1.4)=1.36+1.96=3.32\)

Three of the four entries match option 1 exactly, and the fourth is 0.19 against the printed 0.195 — a rounding in the paper. No other option comes close, so option 1 is the answer.

Two checks worth making. First, the order of multiplication matters: matrix products do not commute, and the section nearest the input must be written first. Second, a passive reciprocal network must satisfy

\(AD-BC=1\)

Here \(1.78\times3.32-25.84\times0.19=5.909-4.910=0.999\) — unity to within the rounding, confirming the arithmetic.

Why ABCD parameters suit cascades is exactly this multiplication property: they relate input voltage and current to output voltage and current, so one section's output variables are the next section's input variables and the matrices chain directly. Z or Y parameters have no such property.

Hence, the T-parameters are those of option 1.