A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong

The magnitude of pairs of displacement vectors are given. Which pair of displacement  vectors cannot be added to give a resultant vector of magnitude $13\, cm$?

$Y $ component of velocity is $20$ and $X$ component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously${\overrightarrow F _1} = - 4\hat i - 5\hat j + 5\hat k$, ${\overrightarrow F _2} = 5\hat i + 8\hat j + 6\hat k$, ${\overrightarrow F _3} = - 3\hat i + 4\hat j - 7\hat k$ and ${\overrightarrow F _4} = 2\hat i - 3\hat j - 2\hat k$ then the particle will move

The magnitude of the $X$ and $Y$ component of $\vec A$ are $7$ and $6$ respectively. Also the magnitude of $X$ and $Y$ component of $\vec A + \vec B$ are $11$ and $9$ respectively. What is the magnitude of $\vec B$  ?

A particle starting from the origin $(0,0)$ moves in a straight line in the $(x, y)$ plane. Its coordinates at a later time are $(\sqrt 3,3)$ . The path of the particle makes with the $x -$ axis an angle of  ....... $^o$