The decimal number system uses the characters 0, 1, 2, ... , 8, 9, and the octal number system uses the characters 0, 1, 2, ... , 6, 7.

For example, the decimal number 12 ( = 1 × 10¹ + 2 × 10⁰) is expressed as 14 ( = 1 × 8¹ + 4 × 8⁰) in the octal number system.

The decimal number 108 in the octal number system is

A shopkeeper buys shirts from a producer and sells them at 20% profit. A customer has to pay ₹3,186.00 including 18% taxes, per shirt. At what price did the shopkeeper buy each shirt from the producer?

If, for non-zero real variables $x$, $y$, and real parameter $a > 1$,

$x : y = (a + 1) : (a - 1)$,

then, the ratio $(x^2 - y^2) : (x^2 + y^2)$ is

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll of the dice and a '4' on the second roll?