If $\frac{x^2+x+1}{x^2+2x+1} = A + \frac{B}{x+1} + \frac{C}{(x+1)^2}$,then $A-B$ is equal to

The mechanism of the reaction $2NO_2 + F_2 \to 2NO_2F$ is given by:
$(i)$ $NO_2 \xrightarrow{slow} NO_2^*$
$(ii)$ $NO_2^* + F_2 \xrightarrow{fast} NO_2F + F$
$(iii)$ $F + NO_2 \xrightarrow{fast} NO_2F$
Select the correct statement regarding this reaction.

Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$

The maximum possible number of real roots of the equation $x^5 - 6x^2 - 4x + 5 = 0$ is

$A$ concave mirror gives an image three times as large as the object placed at a distance of $20 \ cm$ from it. For the image to be real,the focal length should be ...... $cm$.

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$,where $[y]$ denotes the greatest integer not exceeding $y$,then $\{f(x) : |x| < 71\}$ is equal to