Explain the construction of a spherical wavefront by using Huygens' principle.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
The perpendicular distance of the plane \( r \cdot (3\hat{i} + 4\hat{j} + 12\hat{k}) = 78 \) from the origin is __________.
Derive an expression for maximum speed of a vehicle moving along a horizontal circular track.
If the mean and variance of a binomial distribution are \( 18 \) and \( 12 \) respectively, then the value of \( n \) is __________.
Predict the type of cubic lattice of a solid element having edge length of 400 pm and density of 6.25 g/ml. (Atomic mass of element = 60)
Staying in comfort at home gives one more happiness than travelling.
Match the persons given in column 'A' with opinions/characteristics given in column 'B'
Review: You have recently read a famous book/magazine. Write a Review on the same with the help of the following points: - title, front page, back page - language, features, contents - Pictures, quality, presentation - Values, vision and variety
Solve the following L.P.P. by graphical method: Maximize: \[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]
