A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is
(1) $8 : 1$
(2) $9 : 7$
(3) $4 : 3$
(4) $5 : 3$

A machine gun fires a bullet of mass 40 g with a velocity $1200 \mathrm {~ms} ^ { - 1 }$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
(1) one
(2) four
(3) two
(4) three

Two masses $M _ { 1 }$ and $M _ { 2 }$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _ { 2 }$ is twice that of $M _ { 1 }$, the acceleration of the system is $a _ { 1 }$. When the mass $M _ { 2 }$ is thrice that of $M _ { 1 }$, the acceleration of the system is $a _ { 2 }$. The ratio $\frac { a _ { 1 } } { a _ { 2 } }$ will be
(1) $\frac { 1 } { 3 }$
(2) $\frac { 2 } { 3 }$
(3) $\frac { 3 } { 2 }$
(4) $\frac { 1 } { 2 }$

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m _ { 1 }$ and $m _ { 2 }$. If the acceleration of the system is $\frac { g } { 8 }$, then the ratio of the masses $\frac { m _ { 2 } } { m _ { 1 } }$ is :
(1) $8 : 1$
(2) $5 : 3$
(3) $4 : 3$
(4) $9 : 7$

Let $a \in \{-6, -4, -2, 2, 4, 6\}$ be the leading coefficient of a real-coefficient cubic polynomial $f(x)$. If the graph of the function $y = f(x)$ intersects the $x$-axis at three points whose $x$-coordinates form an arithmetic sequence with first term $-7$ and common difference $a$, how many values of $a$ satisfy $f(0) > 0$?
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5