How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

If in a regular polygon the number of diagonals is $54$,then the number of sides of this polygon is

There are $10$ points in a plane of which no three points are collinear except $4$ points. The number of distinct triangles that can be formed by joining these points such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is:

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

Six '$X$'s have to be placed in the squares of the figure such that each row contains at least one '$X$'. In how many different ways can this be done?

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. The probability that no two of them are consecutive is -