If, $\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _{\mathrm{e}}|\mathrm{f}(\theta)|+\mathrm{c}$ (where c is a constant of integration), then the ordered pair $(\lambda,|f(\theta)|)$ is equal to

The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is

If $\cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y \sin x=6 x, 0

Equation of the plane, through the points $(-1,2,-2)$ and $(-1,3,2)$ and perpendicular to $y \mathrm{z}$ - plane, is