How many ways are there to arrange the nine letters in the word ALLAHABAD?
The number of diagonals which can be drawn by joining the angular points of a heptagon is
At certain college the housing office has decided to appoint, for each floor, one male and one female residental advisor. The pairs of advisors can be selected for a seven story building from 12 male and 15 female candidates are
Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences B and C are there such that (i) each is sorted in ascending order (ii) B has 5 and c has 3 elements and (iii) the result of merging B ans C given A?
A person deposiits Rs 300 in a saving account of SBI at an interest rate of 5% per annum compounded annually. The obatin amount in his account at the end of r yeras is
The generating function for thr sequence 2, 2, 2, 2, 2, 2 is
The generating function for the sequence 0, 1, 2, 4, 8, ...... is
Solution of recurrence relation
ar - 5ar-1 + 8ar-2 - 4ar-3 = 0 is
The solution of the recurrence relation
ar + 6ar-1 + 12ar-2 - 8ar-3 = 0 is
The sum of the series
12 + 22 + 32 + ...+r2 is