The sum of the rational terms in the expansion of is

, then r is

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

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

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

The number of permutations of the letters of the word 'CONSEQUENCE' in which all the three E's are together is

The ninth term of the expansion is

2³ⁿ - 7n - 1 is divisible by

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

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