Picking r people out of n people sitting in a circle such that no two are adjacent = (n-r+1)Cr - (n-r-1)C(r-2)Picking r people out of n people sitting in a row such that no two are adjacent = (n - r + 1)Cr @hemant_malhotra

Mass point Geometry lecture - @gaurav_sharma

Kaprekar's constant 6174 is known as Kaprekar's constant. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2 and repeat.The above process will always yield 6174, in at most 7 iterations. The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration.

A quadratic function f (x ) = ax^2 + bx + c, can be expressed in the standard form : a(x-h)^2 + kby completing the square. The graph of f(x) is a parabola with vertex (h,k); the parabola opens upward if a > 0 or downward if a < 0. Maximum or Minimum Value of a Quadratic Function Let f be a quadratic function with standard form f (x) = a( x − h )^2 + k.The maximum or minimum value of f occurs at x = hIf a > 0, then the minimum value of f is f(h) = k.If a < 0, then the maximum value of is f (h) = k We now derive a formula for the maximum or minimum of the quadratic functionF(x) = ax^2 + bx + c.For either of the two cases (the quadratic having a maxima or a minima), the maxima or the minima,as the case may be, will occur when x = - b/2athe maximum or minimum value is f(-b/2a) = c - b^2/4aremember that - b/2a = sum of roots/2

Multiplication factor This is a very important understanding of percentages from calculations point of view. What this basically does is: it converts a percentage question to a ratio question. And dealing with ratios are always easier than to deal with percentages, as ratios are easier to calculate. So, if a value increases by 20%, which is 1/5th: the multiplication factor must be (1+1/5) = 6/5, as the value is increasingIf the value reduces by 30%, which is 3/10: the multiplication factor must be (1 - 3/10) = 7/10, as the value is reducing Try to use multiplication factors in the basic questions to ease up your calculations