$A$ polygon has $44$ diagonals. The number of its sides is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

If $x$ is the number of ways in which six women and six men can be arranged to sit in a row such that no two women are together and if $y$ is the number of ways they are seated around a table in the same manner,then $x: y=$ (in $: 1$)

$10$ distinct points are taken on a circle. Then using these points:
Statement $I$: The number of triangles that can be formed is $100$
Statement $II$: The number of chords that can be formed is $45$
Which of the following is correct?

There are $n$ distinct points on the circumference of a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then what is the value of $n$?