The variance of $50$ observations is $7$. If each observation is multiplied by $6$ and then $5$ is subtracted from it,then the variance of the new data is

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

Consider the following reaction: $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$. The rate of this reaction in terms of $N_2$ at $T \ K$ is $-\frac{d[N_2]}{dt} = 0.02 \ mol \ L^{-1} \ s^{-1}$. What is the value of $-\frac{d[H_2]}{dt}$ (in units of $mol \ L^{-1} \ s^{-1}$) at the same temperature?

$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is

Which of the following ethers is a liquid at room temperature?

$A$ plane is parallel to two lines whose direction ratios are $(1, 0, -1)$ and $(-1, 1, 0)$ and it contains the point $(1, 1, 1)$. If it cuts the coordinate axes at $A$,$B$,and $C$,then the volume of the tetrahedron $OABC$ is (in cubic units):