Question

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

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

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

If $\stackrel{\wedge}{\mathrm{a}}$, $\stackrel{\wedge}{\mathrm{b}}$ and $\stackrel{\wedge}{\mathrm{c}}$ are mutually perpendicular unit vectors, then find value of $|2\stackrel{\wedge}{\mathrm{a}}$ + $\stackrel{\wedge}{\mathrm{b}}$ + $\stackrel{\wedge}{\mathrm{c}}|$.

If Δ = $\begin{vmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{vmatrix}$ , write the minor of the element $a_{23}.$

Evaluate : $\textstyle\int$ cos⁻¹(sin x) dx.

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