Permutations and Combinations — NDA Mathematics PYQs

How many $7$-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?

How many sides are there in a polygon which has $20$ diagonals?

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

What is the number of positive integer solutions of $x+y+z=5$?

If the number of selections of $r$ as well as $(n+r)$ things from $5n$ different things are equal, then what is the value of $r$?

What is the number of selections of at most $3$ things from $6$ different things?

How many $4$-digit numbers that are divisible by $4$ can be formed using the digits $1,2,3$ and $4$ (repetition of digits is not allowed)?

Consider the following for the two (02) items that follow :
There are $8$ points on a plane out of which $4$ points are collinear.

How many triangles can be formed by joining these points?

Consider the following for the two (02) items that follow :
There are $8$ points on a plane out of which $4$ points are collinear.

How many quadrilaterals can be formed by joining these points?