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

Using differentiation, approximate value of $f(x)=x^2-2 x+1$ at $x=2.99$ is ............

A particle moves so that $x=2+27 t-t^3$. The direction of motion reverses after moving a distance of ....... units.

Which of the following is not equal to $\mathbf{w} \cdot(\mathbf{u} \times \mathbf{v})$ ?