NIMCET 2017 Question Paper with solutions

Given equation of curve is
y = 2x sinx
Slope at point $\left(\frac{\mathit{\pi }}{2},\mathit{\pi }\right)$
${\left(\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}\right)}_{\left(\frac{\mathit{\pi }}{2},\mathit{\pi }\right)}$ = 2 sinx + 2x cosx
= 2 $\mathit{s}\mathit{i}\mathit{n}\frac{\mathit{x}}{2}$ 2 × 0 = 2 + 0 = 2
∴ Equation of tangent at point $\left(\frac{\mathit{\pi }}{2},\mathit{\pi }\right)$ is
y - π = ${\left(\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}\right)}_{\left(\frac{\mathit{\pi }}{2},\mathit{\pi }\right)}$ $\left(\mathit{x}-\frac{\mathit{\pi }}{2}\right)$
⇒ y - π = 2 $\left(\mathit{x}-\frac{\mathit{\pi }}{2}\right)$
⇒ y - π = 2x - π
⇒ y = 2x