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

$A$ radioactive nucleus $A$ with a half-life $T$ decays into a nucleus $B$. At $t = 0$,there is no nucleus $B$. At some time $t$,the ratio of the number of $B$ to that of $A$ is $0.3$. Then,$t$ is given by:

The equation of the circle passing through the point $(1,2)$ and through the points of intersection of $x^2+y^2-4x-6y-21=0$ and $3x+4y+5=0$ is given by

$A$ black body has a maximum wavelength ${\lambda _m}$ at a temperature of $2000 \; K$. Its corresponding wavelength at a temperature of $3000 \; K$ will be:

Assertion : In humans,the gamete contributed by the male determines whether the child produced will be male or female.
Reason : Sex in humans is a polygenic trait depending upon a cumulative effect of some genes on $X-$ chromosome and some on $Y-$ chromosome.

$A$ ball is dropped from a height $h$ on a floor of coefficient of restitution $e$. The total distance covered by the ball just before the second hit is