What is the sum of the coefficients of first and last terms in the expansion of (1 + x)²ⁿ, where n is a natural number?

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

Consider the following statements:

1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.

2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.

Which of the above statements is/are correct?

How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?