Each statement in the key is called

If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3},$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

The mean of the numbers obtained on throwing a die having $1$ on three faces,$2$ on two faces,and $5$ on one face is

$A$ wire elongates by $l \, mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$):

The cell reaction $Mn + 2Ag_{(C_1)}^{+} (aq) \to Mn_{(C_2)}^{+2} (aq) + 2Ag$ is represented by

In a resonance tube experiment,a tuning fork resonates with an air column of length $12 ~cm$ and again resonates when the air column is $38 ~cm$ long. The end correction will be: (in $~cm$)