If \( \frac{a}{b} + \frac{b}{a} = 1 \) and a + b = 2, then the value of a3 + b³ is:
The population of country A decreased by p% and the population of country B decreased by q% from the year 2020 to 2021. Here 'p' is greater than 'q'. Let 'x' be the ratio of the population of country A to the population of country B in the given year. What is the percentage decrease in 'x' from 2020 to 2021?
\( \frac{100(p - q)}{(100 - q)} \)
\( \frac{100(p - q)}{100 + p} \)
\( \frac{100(p - q)}{100 - p} \)
\( \frac{100(p - q)}{100 + q} \)
Piyush sold a guitar to Anuj at 16% gain and Anuj sold it to Mayank at 32% gain. If Mayank paid ₹3,828 for the guitar, what amount did Piyush pay for the same?
The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe \(\text{(Take } \pi = \frac{22}{7}\text{)}\) correct to two places of decimal.
What is the value of \( \frac{\cos 37^\circ}{\sin 53^\circ} \)?
What is the value of
\(
\cos\!\left(-\frac{17\pi}{3}\right)
\)