The function f(x, y) satisfies the Laplace equation

$$\Delta$$²f(x, y) = 0

on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) is :

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

$$\int {\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 3} - {{{x^4}} \over 4} + ....} \right)dx} $$ is equal to :

An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are $$\omega$$ rad/s and T s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are