Previous Year Questions

C² - 42C + 437 = 0

C² - 23C - 19C + 437 = 0

C (C - 23) - 19 (C - 23) = 0

(C - 19) (C - 23) = 0

C = 19, 23

If M = 19 and N = 23

A = 17 * 19 - 23² + 1 = 323 - 529 + 1 = - 205 [ not satisfied]

If M = 23 and N = 19

A = 17 * 23 - 19² + 1 = 391 - 361 + 1 = 31 [satisfied]

Statement I.

√X² - 7² + A²/X = (A - 17) - 5²/X

X - 49 + 31²/X = (31 - 17) - 25/X

X² - 49X + 961 = 14X - 25

X² - 63X + 986 = 0

X² - 34X - 29X + 986 = 0

X (X - 34) - 29 (X - 34) = 0

(X - 29) (X - 34) = 0

X = 29, 34

Statement II.

3Y - 6² + (A - 3)²/Y = √(4Y²) + √529 - 80/Y

{3Y² - 36Y + (31 - 3)²}/Y = 2Y + 23 - 80/Y

3Y² - 36Y + 784 = 2Y² + 23Y - 80

Y² - 59Y + 864 = 0

Y² - 32Y - 27Y + 864 = 0

Y (Y - 32) - 27 (Y - 32) = 0

(Y - 27) (Y - 32) = 0

Y = 27, 32

Hence, the required product = 29 * 27 = 783