If

$$ \sqrt{y-\sqrt{y-\sqrt{y-\ldots \ldots \ldots \infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \ldots \ldots \infty}}} $$

then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

If $x=\operatorname{sint}$ and $y=\sin p t$, then the value of

$$ \left(1-x^2\right) \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-x \frac{\mathrm{~d} y}{\mathrm{~d} x}+\mathrm{p}^2 y= $$

Let $\bar{a}=\hat{i}+\hat{j}-\hat{k}$ and $\bar{c}=5 \hat{i}-3 \hat{j}+2 \hat{k}$ and if $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=\overline{\mathrm{a}}$ then $|\overline{\mathrm{b}}|=$

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is