Embibe Experts Solutions for Chapter: Properties of Triangles, Exercise 1: MHT-CET 2017

In $∆ABC$ with usual notations $a=4, b=3$, $\angle A={60}^{°}$, then $c$ is a root of the equation

If two angles of $∆ABC$ are $\frac{\pi }{4}$ and $\frac{\pi }{3}$, then the ratio of the smallest and the greatest side is

With usual notations in $∆ABC$, if $a=2,b=3,c=5$ and $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{k+7}{30}$, then $k=$

In $\mathrm{\Delta }ABC$, if ${\sin }^{2}A+{\sin }^{2}B={\sin }^{2}C$ and $l\left(AB\right)=10$, then the maximum value of the area of $\mathrm{\Delta }ABC$ is

With usual notations, in $∆ABC$, if  $b{\cos }^2\frac{C}{2}+c{\cos }^2\frac{B}{2}=\frac{3a}{2}$, then