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Physics

A wooden stick of length L, radius R and density

has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value for the mass m (in terms of given parameters) that would make the stick float vertically in equilibrium in liquid of density

(>p).

Chemistry

An acid type indicator, HIn differs in colour from its conjugate base (In^-). The human eye is sensitive to colour differences only when the ratio[In^-]/[HIn] is greater than 10 or smaller than 0.1. What should be the minimum change in the pH of the solution to observe a complete colour change (K_a = 1.0 x 10^-5)?

Mathematics

X and Y are two sets and f : X

Y. If {f(c) = y; c

X, y

Y} and {f^-1(d) = x; d

Y, x

X}, then the true statement is

(a)	f(f^-1(b)) = b	(b)	f(f ^-1(a)) = a
(c)	f(f ^-1(b)) = b, b Y	(d)	f(f ^-1(a)) = a, a X

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