Question

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\hat{i}-3\hat{k},$ ${\vec{b}}=2{\hat{j}}-{\hat{k}},$ $\stackrel{\rightarrow}{c}=2\hat{i}-3\hat{j}+2\hat{k}.$

Write the sum of the order and degree of the differential equation. $\begin{array}{r l}{\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}+\left({\frac{d y}{d x}}\right)^{3}+x^{4}\,}&{{}=0.}\end{array}$

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

Find : $\int{\frac{3\,x}{3\,x-1}}\,d x$

Evaluate $\textstyle\int$ sec² (7 – 4x) dx.

Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.