Question
If in the word "BALLOON", all the consonants are changed
to the 3rd preceding letter and all the vowels are changed to the immediately preceding letter as per the English alphabetical series from left to right, and all the letters are then arranged as per the English alphabetical series from right to left, then the position of how many letters remains unchanged?Solution
B A L L O O N Consonants: B, L, L, N Vowels: A, O, O Applying the rule: B -> Y (3 preceding) L -> I (3 preceding) L -> I (3 preceding) N -> K (3 preceding) A -> Z (preceding) O -> N (preceding) O -> N (preceding) Result: Y Z I I N N K Reverse alphabetical order: Z Y N N K I I The original order is B A L L O O N. Comparing positions: B is in position 1, Z in position 1. No change. In the original order, A is in 2nd position. In the transformed order, Y is in 2nd position and so on. Therefore, none of the letter maintains its position.
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
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 45x + 450 = 0
Equation 2: y² - 48y + 540 = 0�...
I. 14p² + 9p - 8 = 0
II. 4q² - 19q + 12 = 0
I. 35x² + 83x + 36 = 0
II. 42y² + 53y + 15 = 0
I. x² - (16)2 = 0
II. 2y - 14 = 0
I. 5q = 7p + 21
II. 11q + 4p + 109 = 0
I. 2x² - 9x + 10 = 0
II. 3y² + 11y + 6 = 0
I. 2p2 - 3p – 2 = 0 II. 2q2 - 11q + 15 = 0
Solve the quadratic equation:
5x² − 13x + 6 = 0
I. 2y² - 35y + 132 = 0
II. 2x² - 31x + 110 = 0