List of top Engineering Mathematics Questions on Differential Equations asked in TS PGECET

If \( A \) and \( B \) are independent events and \( P\left((A - B) \cup (B - A)\right) = k - P(A)P(B) \), then \( k = \) 

The maximum value of \(x^2 y z^3\), subject to \(x + y + z = 42\) exist at \((x, y, z) = (\alpha, \beta, \gamma)\), then \(\alpha\beta\gamma =\)
Given below are pair of functions \(f(x)\) and \(g(x)\). Which pair is not linearly independent?
The solution of \(\frac{\partial^2 u}{\partial t^2} = 4\frac{\partial^2 u}{\partial x^2}\), \(t > 0\), \(-\infty < x < \infty\) satisfying the conditions \(u(x,0) = x\) and \(\frac{\partial u}{\partial t}(x,0) = 0\) is