The angle $\theta$, at which the curves $y=3^x$ and $y=7^x$ intersect, is given by

The function $\mathrm{f}(x)=x^3-6 x^2+\mathrm{ax}+\mathrm{b}$ satisfies the conditions of Rolle's theorem in $[1,3]$. Then the values of $a$ and $b$ are respectively

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

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