Question

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\stackrel{\wedge}{j},$ $\vec{b}=2\hat{i}-3\hat{j},$ $\vec{c}=2\hat{i}+3\hat{k},$

Evaluate x if : $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$

Evaluate: $\textstyle\int\cot{x}(cosec x-1)e^{x}d x$ .

If ${\left[\begin{array}{l l}{a+4}&{3b}\\ {8}&{-6}\end{array}\right]}={\left[\begin{array}{l l}{2a+2}&{b+2}\\ {8}&{a-8b}\end{array}\right]},$ write the value of a – 2b.

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

If f : R→ R defined by f(x) = $\textstyle{\frac{3x+5}{2}}$ is an invertible function, then find $f^{-1}(x).$

If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)