$A$ 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 $m_1 : m_2$ (assuming $m_1 > m_2$) is:

The Earth $E$ moves in an elliptical orbit with the Sun $S$ at one of the foci as shown in the figure. Its speed of motion will be maximum at the point:

The $\Delta H_f^o$ for $CO_{2(g)}$,$CO_{(g)}$ and $H_2O_{(g)}$ are $-393.5$,$-110.5$ and $-241.8 \ kJ \ mol^{-1}$ respectively. The standard enthalpy change (in $kJ$) for the reaction $CO_{2(g)} + H_{2(g)} \to CO_{(g)} + H_2O_{(g)}$ is

The structure of a mixed oxide is cubic close packed $(ccp)$. The cubic unit cell of the mixed oxide is composed of oxide ions. One-fourth of the tetrahedral voids are occupied by divalent metal $A$,and the octahedral voids are occupied by a monovalent metal $B$. The formula of the oxide is:

The shortest distance of the point $(a, b, c)$ from the $x$-axis is

Which fungus has proven to be an effective biological control agent?