A shopkeeper in Rajasthan buys an article on the printed price of $₹ 50,000$ From a wholesaler in Delhi. The shopkeeper sells the article to a consumer in Rajasthan at a profit of $25\%$. On the basic cost price if the rate of GST is $18\%$, find the Amount of tax (under GST) paid by the shopkeeper to the government. 

In a right-angled $△\mathrm{ABC}$, right-angled at $\text{B}$, the perpendicular $\text{BD}$ on the hypotenuse $\text{AC}$ Is drawn.

Prove that $\mathrm{AC}\times \mathrm{CD} = (\mathrm{BC}{)}^2$

Let $\mathrm{A}(6, 4)$and $\mathrm{B}(2, 12)$ be two given points. Find the slope of a line perpendicular to $\mathrm{AB}.$

Apply step-deviation method to find the AM of the following frequency distribution.

Veena has a cumulative deposit account of ₹ $400$ per month at $10\%$ per annum simple interest. If she gets ₹ $30100$ at the time of maturity, then if the total time for which the account was held is $k$ years, then find the value of $k$.

In the given figure, $\text{A, B, C}$ and $\text{D, E, F}$ are two sets of collinear points. Prove that $\text{AD II CF.}$