When a charged particle enters a uniform magnetic field its kinetic energy

Two identical charged particles enter a uniform magnetic field with same speed but at angles $30^o$ and $60^o$ with field. Let $a, b$ and $c$ be the ratio of their time periods, radii and pitches of the helical paths than

Two particles $x$ and $y$ have equal charges and possessing equal kinetic energy enter in a uniform magnetic field and describe circular path of radius of curvature $r_1$ and $r_2$ respectively. The ratio of their masses is

A proton and an electron both moving with the same velocity $v$ enter into a region of magnetic field directed perpendicular to the velocity of the particles. They will now move in circular orbits such that

A particle of charge $q$ and mass $m$ is moving along the $x$ -axis with a velocity $v$ and enters a region of electric field $E$ and magnetic field $B$ as shown in figure below for which figure the net force on the charge may be zero

A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is