List of top Questions asked in GATE TF

Suppose \[ u(x, t) = \frac{1}{2} \left[ g(x + ct) + g(x - ct) \right] \] is a solution of the following initial value problem of the wave equation \[ u_{tt} = 9 u_{xx}, u(x, 0) = g(x), u_t(x, 0) = 0. \] Then the value of \( c^2 \) is \(\underline{\hspace{2cm}}\) (round off to 2 decimal places).

If the numerical solution of the initial value problem \[ y' = \frac{t^2}{t + y^3}, y(0) = 1, \] is obtained by the Euler's method with step size of 0.2, then the value of \( y(0.4) \), (rounded off to two decimal places), is \(\underline{\hspace{2cm}}\).

The yarn manufacturing technology that uses perforated drums for twisting is

In roving frame, the distance between top and bottom aprons at the exit point is maintained by

Fabric structure related to weft knitting is

The smallest positive real number \( \lambda \), for which the following problem \[ y''(x) + \lambda y(x) = 0, y'(0) = 0, y(1) = 0 \] has a non-zero solution, is