Private sector activities prioritize profit generation, focusing on customer satisfaction and innovation. Companies like Tata and Infosys invest in quality services to stay competitive. However, this profit motive often leads to cost-cutting measures, such as outsourcing, which affects job security. Despite this, private enterprises significantly contribute to GDP and employment. For instance, IT companies in India provide high-paying jobs and export earnings, driving economic growth.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD. 
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$. 
आपका घनिष्ठ मित्र दूसरे मुसीबत को, आपके घर में उसका स्वागत किस प्रकार करता है? विस्तार से लिखिए।