Question

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

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

Write the degree of the differential equation : $\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-2{\frac{d^{2}y}{d x^{2}}}-{\frac{d y}{d x}}+1=0.$

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

If A is a square matrix such that A² = I, then find the simplified value of (A – I)³ + (A + I)³ – 7A.

Write the value of : $\textstyle\int{\frac{\sec^{2}x}{\operatorname{cosec}^{2}x}}d x.$

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