Previous Year Questions

II: 3Ny² - (5N + 1)y + 4 = 0

Sum of the roots of equation II is 11.

5N + 1 = 11

N = 2

6y² - 11y + 4 = 0

6y² - 8y - 3y + 4 = 0

(2y - 1)(3y - 4) = 0

y = ½, 4/3

Larger root of equation I = 1 + 4/3 = 7/3

I: (Mx)² - 36x + 2.5(5M - 1) = 0

49M²/9 - 252/3 + 12.5M - 2.5 = 0

49M² + 112.5M - 778.5 = 0

49M² + 259.5M - 147M - 778.5 = 0

(49M + 259.5)(M - 3) = 0

M = 3, -259.5/49 (not possible)

9x² - 36x + 35 = 0

9x² - 15x - 21x + 35 = 0

(3x - 5)(3x - 7) = 0

x = 5/3, 7/3

Sum of smaller roots of equation I and II together = ½ + 5/3 = 13/6

2Np² - (4M + 2.5)p + 1.5(M + N) = 0

2*2p² - (4*3 + 2.5)p + 1.5(3 + 2) = 0

4p² - 14.5p + 7.5 = 0

4p² - 12p - 2.5p + 7.5 = 0

(4p - 2.5)(p - 3) = 0

p = 2.5/4, 3

Required product = 13/6 * 3 = 13/2 = 6.5