The diagram shows the islands of Mumbai. We have the central node labeled "Islands of Mumbai," and surrounding nodes labeled as Mumbai, Wadala, and Mazgaon.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Explain the construction of a spherical wavefront by using Huygens' principle.
The perpendicular distance of the plane \( r \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78 \) from the origin is __________.