Question

Write the value of $\textstyle\int\!{\frac{1-\sin x}{\cos^{2}x}}\,d x\,.$

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

Find the differential equation representing the family of curves $V={\frac{A}{r}}+B,$ where A and B are arbitrary constants.

If A is square matrix of order 3 such that $|a d j A|=$ 64, find $|A|.$

If A is a square matrix of order 3 such that $|a d j\,A|$ = 225, find $|A^{\prime}|.$

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

If matrix A = $\left(\begin{array}{l l }3 & -3 \\ -3 & 3\end{array}\right)$ and A² = λA, then write the value of λ.