The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

For retting of jute,the fermenting microbe used is:

$A$ sonometer wire resonates with a given tuning fork,forming standing waves with five antinodes between the two bridges when a mass of $9 \, kg$ is suspended from the wire. When this mass is replaced by a mass $M$,the wire resonates with the same tuning fork,forming three antinodes for the same positions of the bridges. The value of $M$ is .... $kg$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

The normal freezing point $(f.p.)$ of nitrobenzene is $278.82\, K$. If a non-volatile solute is dissolved in it and a solution of $0.25\, m$ (molality) is prepared,the observed $f.p.$ of the solution is $276.82\, K$. Evaluate $K_f$ of nitrobenzene in $K\, kg\, mol^{-1}$.

The specific rotation of the equilibrium mixture of $\alpha-D$-glucose and $\beta-D$-glucose is ....... $^\circ$.