Let f : [$$-$$3, 1] $$ \to $$ R be given as

$$f(x) = \left\{ \matrix{ \min \,\{ (x + 6),{x^2}\}, - 3 \le x \le 0 \hfill \cr \max \,\{ \sqrt x ,{x^2}\} ,\,0 \le x \le 1. \hfill \cr} \right.$$

If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to ___________.

A sound wave of frequency 245 Hz travels with the speed of 300 ms^$$-$$1 along the positive x-axis. Each point of the wave moves to and from through a total distance of 6 cm. What will be the mathematical expression of this travelling wave?

Which one of the following will be the output of the given circuit?

Match List - I with List - II

	List - I		List - II
(a)	Phase difference between current and voltage in a purely resistive AC circuit	(i)	$${\pi \over 2}$$; current leads voltage
(b)	Phase difference between current and voltage in a pure inductive AC circuit	(ii)	zero
(c)	Phase difference between current and voltage in a pure capacitive AC circuit	(iii)	$${\pi \over 2}$$; current lags voltage
(d)	Phase difference between current and voltage in an LCR series circuit	(iv)	$${\tan ^{ - 1}}\left( {{{{X_C} - {X_L}} \over R}} \right)$$

Choose the most appropriate answer from the options given below :