For the differential equation given below, which one of the following options is correct?

$$ \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=0,0 \leq x \leq 1,0 \leq y \leq 1 $$

The divergence of the curl of a vector field is

If two unbiased coins are tossed, then what is the probability of having at least one head?

$$ \text { The values of a function } f \text { obtained for different values of } x \text { are shown in the table below. } $$

$$ \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 0.25 & 0.5 & 0.75 & 1.0 \\ \hline f(x) & 0.9 & 2.0 & 1.5 & 1.8 & 0.4 \\ \hline \end{array} $$

$$ \text { Using Simpson's one-third rule, } $$

$$ \int_0^1 f(x) d x \approx $$__________[Rounded off to 2 decimal places]