The sum of the series $1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots \infty$ is

The slope of the graph as shown in the figure at points $1, 2$ and $3$ is $m_1, m_2$ and $m_3$ respectively. Then:

Given that $y = \frac{10}{\sin x + \sqrt{3} \cos x}$. The minimum value of $y$ is

The value of $\frac{d}{dx} (\cos 4x^2)$ is .......

Which of the following relation$(s)$ is/are correct?
$(A)\ \sin (90^{\circ}+\theta)=\cos (-\theta)$
$(B)\ \sin (180^{\circ}-\theta)=\cos (90^{\circ}-\theta)$
$(C)\ \sin (360^{\circ}-\theta)=\cos (360^{\circ}-\theta)$
$(D)\ \sin (180^{\circ}+\theta)=\cos (90^{\circ}-\theta)$

$\frac{d}{dx} \log(\log x) = $