The value of $$\int\limits_0^{2\pi } {\left[ {\sin 2x\left( {1 + \cos 3x} \right)} \right]} dx$$,
where [t] denotes the greatest integer function is :

If the coefficients of x² and x³ are both zero, in the expansion of the expression (1 + ax + bx² ) (1 – 3x)¹⁵ in powers of x, then the ordered pair (a,b) is equal to :

If Q(0, –1, –3) is the image of the point P in the plane 3x – y + 4z = 2 and R is the point (3, –1, –2), then the area (in sq. units) of $$\Delta $$PQR is :

The line x = y touches a circle at the point (1,1). If the circle also passes through the point (1, – 3), then its radius is :