The coefficient of xⁿ in the expansion of (1+2x+3x² +...) is

How many words can be formed from the letters of the word DOGMATIC, if all the vowels remain together?

The sum of the rational terms in the expansion of is

The number of different permutations of the word 'BANANA' is

The total number of terms in the expansion of  (x+y)¹⁰⁰ +(x-y)¹⁰⁰ after simplification is

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

The number of ways of distributing 8 identical balls in 3 distinct boxes, so that move of the boxes is empty, is

The coefficient of x in the expansion of (1+x)(1+2x)(1+3x)...(1+100x) is

The ninth term of the expansion is

The sum of the digits in the unit place of all numbers formed with the help of 3,4,5,6 taken all at a time is