2³ⁿ - 7n - 1 is divisible by

From 12 books, the difference between number of ways a selection of 5 books when one specified book is always excluded and one specified book is always included, is

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

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

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

The sum of the rational terms in the expansion of is

The coefficient of x^-7 in the expansion of  will be

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