$a, b, c$ are real numbers. The quadratic equation $a x^2-b x+c=0$ has equal roots, which is $\beta$, then

The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis. Which one of the following sequences shows the correct precedence as per the given passage?

The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is

A circle with center $O$ is shown in the figure. A rectangle $P Q R S$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area of shaded portion is $\_\_\_\_$ .