The total number of permutations of the letters of the word "$BANANA$" is

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals

The value of $r$ for which $^{20}C_r \cdot ^{20}C_0 + ^{20}C_{r-1} \cdot ^{20}C_1 + ^{20}C_{r-2} \cdot ^{20}C_2 + \dots + ^{20}C_0 \cdot ^{20}C_r$ is maximum is:

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is

Eleven books consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is

The number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is