The length of rod is measured by meter scale having least count $0.1$ cm and diameter is measured by vernier callipers having least count $0.01$ cm. Length of rod is $5.0$ cm and radius $2.0$ cm. The percentage error in the calculated value of the volume is

A vector $\vec{A}$ when added to the sum of the vectors $(\hat{i} - 2\hat{j} + 2\hat{k})$ and $(-2\hat{i} + \hat{j} - \hat{k})$ gives a unit vector along Y axis. The magnitude of vector $\vec{A}$ is

A stone falls from the top of a tower of height $100$ m and at the same time another stone is projected vertically upwards from the ground with a velocity $25$ m/s. The two stones meet after

A particle performing U.C.M. of radius $\dfrac{\pi}{2}$ m makes 'x' revolutions in time t. Its tangential velocity is