Find the amount of bill for the following inter-state transaction of goods/services :

$MRP(\text{ in }₹)$	$950$	$1,200$	$1,500$	$1,800$
Discount $\%$	$32$	$30$	$28$	$40$
GST $\%$	$28$	$12$	$18$	$5$

 

The maturity value of a cumulative deposit account is $₹31,800$ in $2$years. If the rate of interest is $10\%$ per annum, find the monthly installment of this deposit.

In the given figure, $\mathrm{AB}$ is a diameter and $\mathrm{DC}$ is tangent which meets $\mathrm{AB}$produced at point $\mathrm{C}.$If angle $\angle \mathrm{DAC}=\mathrm{x}°,$ find  $\angle \mathrm{DCB}$ and $\angle \mathrm{DBC}$ in terms of $\mathrm{x}°.$

If $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are sides of a right triangle where $\mathrm{c}$ is the hypotenuse, prove that the radius of the circle which touches the sides of the triangle is $\mathrm{r}=\frac{\mathrm{a}+\mathrm{b}-\mathrm{c}}{2}$.