Question

Find the position vector of a point which divides the join of points with position vectors $\;\stackrel{\rightarrow}{(a}-2\stackrel{\rightarrow}{b})$ and $\;\stackrel{\rightarrow}{(2a}+\stackrel{\rightarrow}{b})$ externally in the ratio 2 : 1.

Write the differential equation formed from the equation y = mx + c, where m and c are arbitrary constants.

Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).

Evaluate $\textstyle\int\!{\frac{(1+\log x)^{2}}{x}}\,d x\,.$

If 3A – B = $\left(\begin{array}{l l }5 & 0 \\ 1 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l }4 & 3 \\ 2 & 5\end{array}\right)$ , then find the matrix A.

Evaluate $\textstyle\int{\frac{2}{1+\cos2x}}\,d x$

Evaluate: $\textstyle\int(1-x){\sqrt{x}}\,d x~.$