Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integral $$\,\,\int\limits_{ - 1}^{ + 1} {\left| x \right|dx\,\,} $$ is

The argument of the complex number $${{1 + i} \over {1 - i}},$$ where $$i = \sqrt { - 1} ,$$ is

A block weighing 200N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in newton) P=10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after 10 seconds is _______

A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coeficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is