Which one of the following pairs is incorrectly matched?

Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0$,where $a \neq -1$ is a real number. Then,a root of this equation,among the following,is

How many organisms in the list given below show autotrophic nutrition method? Lactobacillus,Nostoc,Chara,Wolffia,Nitrosomonas,Nitrobacter,Porphyra,Streptococcus,Saccharomyces,Trypanosoma.

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after the collision with a velocity equal to $\frac{1}{10}$th of its original velocity. Then the mass of the second body is (in $kg$)

Plants deficient in the element zinc show effects on the biosynthesis of which plant growth hormone?

Which of the following is $NOT$ a mode of nutrition?