Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
(a) $\overrightarrow{a}+\overrightarrow{b}$
(b) $3a_x+2b_y$
(c) $(\overrightarrow{a}+\overrightarrow{b}-\overrightarrow{c})$

A vehicle is moving on a road with an acceleration a $=20 \mathrm{m} {\mathrm{s}}^{-2}$ as shown in figure. The frictional coefficient between the block of mass $\left(m\right)$ and the vehicle so that block is does not fall downward is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In the given arrangement all surfaces are smooth. What acceleration should be given to the system, for which the block $m_2$ doesn't slide down?

A trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $\left(\alpha \right)$ equal to

A block of mass $m$ is kept on horizontal turn table at $x$ distance from the centre. If coefficient of friction between block and surface of turn table is $\mu$, then maximum angular speed of the table so that block does not slip is

If trolley accelerates horizontally with acceleration a then bob is displaced backward from its initial vertical position. The angular deflection of the bob in equilibrium is