A beam of alpha particles projected along +x axis, experience a force due to magnitic field along the +y axis. What is the direction of the magnetic field?

According to Right-hand rule, the direction of force ($\overrightarrow{F}$) on positively charged particle will be perpendicular to the plane of paper upward and on negatively charged particle will be perpendicular to the plane of paper downwards. As, $\overrightarrow{F}=q \left(\overrightarrow{v}\times \overrightarrow{B}\right) or, \left|\overrightarrow{F}\right| =q \left|\overrightarrow{v}\times \overrightarrow{B}\right| = q v B \sin \theta$
If $v=1, q=1 and \sin \theta =1 or \theta ={90}^o$, then
$F=1\times 1\times B\times 1=B$
Thus the magnetic field induction at a point in the field is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.
The direction of $\overrightarrow{F}$ is the direction of cross-product of velocity $\overrightarrow{v}$ and magnetic field $\overrightarrow{B}$, which is perpendicular to the plane containing  $\overrightarrow{v}$ and  $\overrightarrow{B}$.
Thus, from the cross product rule and Right-hand rule, the direction of magnetic field is along + Z-axis.