Q . 23⁵²⁴ is divided by 24 the reminder is-

By formula -

a² - b² = (a+b) (a-b)

When n is even (xⁿ - aⁿ) is completely divisible by (x+a)

so (23⁵²⁴ - 1⁵²⁴) is completely divisible by (23+1 ) i.e. 24

=> (23⁵²⁴ - 1) is completely divisible by 24

=> On dividing(23⁵²⁴) by 24 we get 1 as reminder.

So the reminder is 1