How many words can be formed with the letter of the word ‘NUMBER’ when alll vowels are never together?
Vowels in the word NUMBER = U, E, rest are 4 consonants Number of ways having vowel together =(1+4)! × 2!= 5! × 2! = 120 × 2 = 240 Total number of words using all letters = 6! = 720 Number of words having vowels are never together = 720 – 240 = 480
I. x2 + 91 = 20x
II. 10y2 - 29y + 21 = 0
I. 63x² + 146x + 80 = 0
II. 42y² + 109y + 70 = 0
I. 5x2 – 7x – 6 =0
II. 2y2 – 5y – 7 =0
I. x² + 11x + 24 = 0
II. y² + 17y + 72 = 0
I. 8x² + 2x – 3 = 0
II. 6y² + 11y + 4 = 0
I. 2x2 - 9 x + 9 = 0
II. 2y2 - 7 y + 3 = 0
I. 195x² - 46x - 21 = 0
II. 209y² + 7y - 12 = 0
I. 27(p + 2) = 2p(24 – p)
II. 2q2 – 25q + 78 = 0
I. 2x2– 25x + 33 = 0
II. 3y2+ 40y + 48 = 0
I. x2 + 16x + 63 = 0
II. y2 + 2y - 15 = 0
