Question
  In the word ‘SYSTEMATIC’, first all the letters
are written in an alphabetical order form, then remove all the vowels from the arrangement then how many such pair/pairs of letters are there, each of which have as many letters between them in the word (forward direction) as they have between them in the English alphabetical series?Solution
there is only one pair ST.Â
The word -
S Y S T E M A T I C
  A C E I M S S T T Y
  C M S S T T YÂ
- For what value of a does the quadratic equation x² + ax + 81 = 0 have real and identical roots?
I. 88x² - 13 x – 56 = 0
II. 15 y² + 41 y + 28 = 0
If a and b are the roots of x² + x – 2 = 0, then the quadratic equation in x whose roots are 1/a + 1/b and ab is
I. 6x2 – 7x - 20 = 0
II. 3y2Â - y - 14 = 0
I. 2y2 + 13y + 15 = 0
II. 2x2 + 11 x + 12 = 0
I. 7x² + 27x + 18 = 0
II. 19y² - 27y + 8 = 0
I. x² + 11x + 24 = 0
II. y² + 17y + 72 = 0
I. 24x² - 58x + 23 = 0
II. 20y² + 24y – 65 = 0
 If x satisfies x² – 14x + 40 = 0, find x.
I. 2x2 – 5x – 12 = 0
II. 2y2 + 13y + 20 = 0