Question

Write the value of the determinant : $\begin{vmatrix}102 & 18 & 36 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{vmatrix}$

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

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

Write the integrating factor of the differential equations ${\sqrt{x}}{\frac{d y}{d x}}+y=e^{-2{\sqrt{x}}}\,.$

Let R={(a,a³): a is a prime number less than 5} be a relation. Find the range of R.

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.

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