Number of ways of selecting 3 consecutive objects out of 15 objects (distinct) placed around a circle is

If , then 

The number of ways in which 6 gentlemen and 3 ladies be seated round a table so that every gentleman may have a lady by his side is

If 
then the values of a and b are

A circle having radius 7 touches both the axes and lies in 1^st quadrant. If the circle is rolled along the positive x-axis and completes on rotation. Then equation of circle in final position is

If 

For such questions, we should know different formulas.

Let α and β be the distinct roots of   

For such questions, we should know the different formulas of limits.

For such questions, we should know different formulae of limit.

The number of n-digit numbers,no two consecutive digits being the same is

A reserve of 12 railway station masters is to be divided into two groups of 6 each one for day duty and the other for night duty. The number of ways in which this can be done if two specified persons A,B should not be included in the same group is