$\displaystyle \text{Find the value of } a \text{ from the following:} \\ \sqrt{(9)}^{-5} \times \sqrt{(3)}^{-7} = \sqrt{(3)}^{-a}$

The ratio of two numbers are $\displaystyle 3:4$. The difference of their squares is $\displaystyle 28$ greater is:

The price of scooter and moped are in the ratio $\displaystyle 7:9$. The price of moped is $\displaystyle ₹1,600$ more than that of scooter. Then the price of moped is:

If $\displaystyle A:B=3:7$, then $\displaystyle 3a+2b:4a+5b=?$

The ratio of number of boys and the number of girls in a school is found to be $\displaystyle 15:32$. How many boys and equal number of girls should be added to bring the ratio to $\displaystyle 1:2$?

In a certain business A and B received profit in certain ratio B and C received profits in the same ratio. If A gets $\displaystyle ₹1600$ and C gets $\displaystyle ₹2500$ then how much does B get?

The ratio of two quantities is $\displaystyle 15:17$. If the consequent of its inverse ratio is $\displaystyle 15$, then the antecedent is: