Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Partial Differential Equations Laplace Equation, Heat and Wave Equations
Let u be the unique solution of
\(\left.\begin{array}{c} \frac{\partial^2 u}{\partial t^2}-\frac{\partial^2 u}{\partial x^2}=0, x \in \mathbb{R}, t>0 \\ u(x, 0)=f(x), \frac{\partial u}{\partial t}(x, 0)=0, x \in \mathbb{R} \end{array}\right\}\)
where f : ℝ → ℝ satisfies the relations f(x) = x(1 - x) ∀ x ∈[0, 1] and f(x + 1) = f(x) ∀ x ∈ ℝ.
Then \(u\left(\frac{1}{2}, \frac{5}{4}\right)\) is
1
\(\frac{1}{8}\)
2
\(\frac{1}{16}\)
3
\(\frac{3}{16}\)
4
\(\frac{5}{16}\)
5
Question Not Attempted