Question

If f : R → R is defined by f(x) = $(3-x^{3})^{1/3},$ then find fof(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.

Write the sum of the order and degree of the differential equation $1+\left(\frac{d y}{d x}\right)^{4}=7\left(\frac{d^{2}y}{d x^{2}}\right)^{3}\,.$

If R = {(x, y) : x + 2y = 8} is a relation on N, writethe range of R.

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.

Find : $\textstyle\int{\frac{\sin^{2}\!x-\cos^{2}\!x}{\sin^{2}\!x\cos^{2}\!x}}\,d x$

Write value of $\textstyle\int$ sec x(sec x + tan x) dx