The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is

The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is

Consider a car moving on a straight road with a speed of $100\, m/s$. The distance at which the car can be stopped is ........ $m$. (Take $g = 10\, m/s^2$ and $\mu_k = 0.5$)

$A$ body weighs $700 \, gm \, wt$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth?

$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed is:

If $f$ is a differentiable function such that $f(2x+1) = f(1-2x)$ for all $x \in R$,then what is the minimum number of roots of the equation $f'(x) = 0$ in the interval $x \in (-5, 10)$,given that $f(2) = f(5) = f(10)$?