There are 5 people - A, B, C, D, E, standing in a queue. How many ways are available to form the queue such that D is not ahead of E ?

The two series a₁, a₂, ……… and b₁, b₂, ……. are two arithmetic progressions, where a₁+ b₁= 100 and a₂₄– a21= b₉₇– b₁₀₀.  Find the sum of the 100 terms  (a₁+ b₁₀₀), (a₂+ b₉₉),…………. (a₁₀₀+ b₁).

How is Venkat’s brother’s father’s brother’s father’s daughter’s sister’s daughter’s brother related to Venkat?