If the line $y = 2x + \lambda$ is a tangent to the hyperbola $36x^2 - 25y^2 = 3600$, then $\lambda =$

$\displaystyle\lim_{x \to 0}\dfrac{(5^x - 1)^4\,\text{cosec}\,(x\log 5)}{\tan(x\log 5) \cdot \log(1 + x^2\log 25)} = \ldots\ldots$

Simplest form of the following switching circuit is

With usual notations in $\triangle$ABC, if $b\cos^2\dfrac{C}{2} + c\cos^2\dfrac{B}{2} = \dfrac{3a}{2}$ then