The maximum value of $Z=x+y$,subjected to $x+y \leq 10$,$5x+3y \geq 15$,$x \leq 6$,$x, y \geq 0$.

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be .............. $Joule$.

An engine is supposed to operate between two reservoirs at temperatures $727^{\circ}C$ and $227^{\circ}C$. The maximum possible efficiency of such an engine is:

Current is flowing through a conducting hollow pipe whose cross-section is shown in the figure. The value of magnetic induction will be zero at

According to our convention,when do we focus on the defining features of a living organism?