Which one of the following is correctly matched?

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to

Which of the following plants are used as green manure in crop fields and in sandy soils?

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

If $x \sqrt{1+y}+y \sqrt{1+x}=0$, then $\frac{d y}{d x}$ is equal to

The surface of water in a water tank of cross-sectional area $750 \, cm^2$ on the top of a house is $h \, m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \, mm^2$ is $30 \, cm/s$. At that instant,$\frac{dh}{dt}$ is $x \times 10^{-3} \, m/s$. The value of $x$ will be $.............$.