$$\int \log x \cdot[\log (e x)]^{-2} d x=\ldots$$

If $y=\log \left[\frac{x+\sqrt{x^2+25}}{\sqrt{x^2+25}-x}\right]$ then $\frac{d y}{d x}=\ldots \ldots$

If the scalar triple product of the vectors $-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ is 272 then $\lambda=\ldots \ldots$

- The edge of a cube is decreasing at the rate of $0.04 \mathrm{~cm} / \mathrm{sec}$. If the edge of the cube is 10 cms , then rate of decrease of surface area of the cube is...