A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that it forms a $$\triangle \mathrm{OPQ}$$, where $$\mathrm{O}$$ is the origin. If the area of $$\triangle \mathrm{OPQ}$$ is least, then the slope of the line $$\mathrm{PQ}$$ is
If feasible region is as shown in the figure, then related inequalities are
![MHT CET 2023 13th May Morning Shift Mathematics - Linear Programming Question 12 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lqrusle4/569409e6-15d5-4b76-a9c9-f190bc4587ca/d46628c0-a6f4-11ee-be1d-bfea558b36de/file-6y3zli1lqrusle5.png?format=png)
The general solution of the equation $$3 \sec ^2 \theta=2 \operatorname{cosec} \theta$$ is
A right circular cone has height $$9 \mathrm{~cm}$$ and radius of base $$5 \mathrm{~cm}$$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $$\frac{\pi}{\mathrm{A}} \mathrm{cm} / \mathrm{sec}$$. where $$\mathrm{A}$$ is area of the water surface at that instant, then cone is completely filled in