If a hydrogen electrode is dipped in two solutions of $pH = 3$ and $pH = 6$ and a salt bridge is connected,the $emf$ of the resulting cell is .......... $V$.

If $f_n(x) = \log \log \log \ldots \log x$ (where $\log$ is repeated $n$ times),then $\int (x f_1(x) f_2(x) \ldots f_n(x))^{-1} dx$ is equal to

Read the following five statements $(1-5)$ carefully and answer the question that follows.
$(1)$ In $Equisetum$,the female gametophyte is retained on the parent sporophyte.
$(2)$ In $Ginkgo$,the male gametophyte is not independent.
$(3)$ The sporophyte of $Polytrichum$ is more developed than that of $Riccia$.
$(4)$ Sexual reproduction in $Volvox$ is isogamous.
$(5)$ Spores of slime molds lack a cell wall.
How many of the above statements are correct?

The density of gold is $19 \ g/cm^3$. If $1.9 \times 10^{-4} \ g$ of gold is dispersed in one litre of water to give a sol having spherical gold particles of radius $10 \ nm$,then the number of gold particles per $mm^3$ of the sol will be

The minimum value of $(x-\alpha)(x-\beta)$ is

Identify the incorrect statement among the following.