If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is ..........

The negation of " $\forall, n \in N, n+7>6$ " is .............

If the vectors $x \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+y \hat{\mathbf{j}}-z \hat{\mathbf{k}}$ are collinear then the value of $\frac{x y^2}{z}$ is equal

$$\begin{aligned} & \text { If } \int \tan (x-\alpha) \tan (x+\alpha) \cdot \tan 2 x d x \\ & =p \log |\sec 2 x|+q \log |\sec (x+\alpha)| \\ & +r \log |\sec (x-\alpha)|+c \text { then } p+q+r=\ldots \ldots \ldots \end{aligned}$$