WBCS Mains 2020 Official Paper-VI

In a circle touching the side $BC$ of $\Delta ABC$ at $P$ and sides $AB$ and $AC$ produced at $Q$ and $R$ respectively. If $AQ=10\text{cm}$, then the perimeter of $\Delta ABC$ is:

If the semi perimeter of a right-angled triangle be $s\text{cm}$ and hypotenuse be $c\text{cm}$, then the area of the triangle is:

The income of Priya is $40\%$ higher than that of Liza and the income of Disha is $20\%$ less than that of Liza. Income of Priya is higher than income of Disha by:

Three solid spheres of gold whose radii are $1\text{cm}$, $6\text{cm}$ and $8\text{cm}$ respectively are melted into a single solid sphere. Then the radius of the sphere is:

Present ages of Ram and Laxman are in the ratio of $5:4$ respectively. Three years hence, the ratio of their ages will become $11:9$ respectively. What is Laxman's present age?