The product of the lengths of the perpendiculars drawn from the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ to the tangent at any point on the ellipse is

If the coordinate axes are the bisectors of the angles between the pair of lines $ax^2 + 2hxy + by^2 = 0$ where $h^2 > ab$ and $a \neq b$,then

Consider the following reactions:
$C_2H_2 \xrightarrow[500^{\circ}C]{\text{red hot iron tube}} A$
$A \xrightarrow[70^{\circ}C]{\text{conc. } HNO_3, \text{conc. } H_2SO_4} B$
$B \xrightarrow{LiAlH_4} C_6H_5-N=N-C_6H_5$
$A$ and $B$ are:

In the photoelectric effect,if the work functions of $Li$,$Na$,and $Rb$ are $2.41 \ eV$,$2.30 \ eV$,and $2.09 \ eV$ respectively,what could be the approximate work function of $K$ in $eV$?

Let $ABC$ be a triangle such that $\angle ACB = \frac{\pi}{6}$ and let $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively. The value$(s)$ of $x$ for which $a = x^2+x+1, b = x^2-1$ and $c = 2x+1$ is (are):

Which of the following is concerned with eubacteria?
$(1)$ Methanogens $(2)$ Anabaena $(3)$ $N_2$ fixation $(4)$ Thermoacidophiles $(5)$ Eukaryotes $(6)$ Diatoms $(7)$ Gelatinous sheath $(8)$ Heterocyst