ISRO EC 2025 Q.73: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. The poles of $H(s)=\frac{s+1}{s^2+2s+2}$ are the roots of the denominator: $s^2+2s+2=0$.

2. The discriminant is $b^2-4ac=4-8=-4<0$, so the roots are complex, not real. This rules out options (a) and (b).

3. The roots are $s=\frac{-2\pm \sqrt{-4}}{2}=-1\pm j1$.

4. The real part is $-1$, which is nonzero, so the poles are not purely imaginary. This rules out option (d).

5. The zero at $s=-1$ is not at either pole ($-1\pm j1$), so no pole-zero cancellation occurs and the pole nature is unchanged.

6. The poles are a complex-conjugate pair with negative real parts (an underdamped, stable system with ${\omega }_n=\sqrt{2}$ and $\zeta =1/\sqrt{2}$), which is option (c).