The ninth term of the expansion is

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

The sum of the rational terms in the expansion of is

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

How many 10 digit numbers can be written by suing digits 9 and 2

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

2³ⁿ - 7n - 1 is divisible by

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