Question

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).

If m and n are the order and degree, respectively of the differential equation $\textstyle y\left({\frac{d y}{d x}}\right)^{3}+x^{3}\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-x y$= sin x, then write the value of m + n.

Write the value of : $\textstyle\int{\frac{x+\cos6.x}{3\,x^{2}\,+\,\sin6.x}}\,d x\,.$

Write the projection of $\stackrel{\rightarrow}{b}\$ +$\stackrel{\rightarrow}{c}\$ on $\stackrel{\rightarrow}{a}\$,where $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$, $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{c}\$ = $2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$

If ${\left[\begin{array}{l l}{a+4}&{3b}\\ {8}&{-6}\end{array}\right]}={\left[\begin{array}{l l}{2a+2}&{b+2}\\ {8}&{a-8b}\end{array}\right]},$ write the value of a – 2b.

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.

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