Question
 In the word ‘OCCUPATION’ all consonants are
written as their preceding letter and all vowels are written as their following letters. Now all letters are arranged in alphabetical order from left to right and all the repeated letters are eliminated. Then, how many such 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
The word - O C C U P A T I O N
    P B B V O B S J P M
    B B B J M O P P S V
    B J M O P S V
Only OP is there for the forward arrangement. Â
- 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