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

The number of ways in which 5 boys and 5 girls can be seated for a photograph so that no two girls sit next to each other is

2³ⁿ - 7n - 1 is divisible by

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

, then r is

If the r^th term in the expansion of contains x⁴ , then r is equal to

The number of positive odd divisors of 216 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 x^-7 in the expansion of  will be