Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by

$A = \{x_1, x_2, x_3, x_4\}$; $B = \{y_1, y_2, y_3, y_4\}$. $A$ function $f: A \to B$ is defined. The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

Forelimbs of cat,lizard used in walking; forelimbs of whale used in swimming and forelimbs of bats used in flying are an example of

$A$ concave mirror of focal length $f$ (in air) is immersed in water $(\mu = 4/3)$. The focal length of the mirror in water will be

$A$ man of mass $m$ starts falling towards a planet of mass $M$ and radius $R$. As he reaches near to the surface,he realizes that he will pass through a small hole in the planet. As he enters the hole,he sees that the planet is really made of two pieces: a spherical shell of negligible thickness of mass $2M/3$ and a point mass $M/3$ at the centre. What is the change in the force of gravity experienced by the man?

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-y^2=8$ to its asymptotes is