Previous Year Questions

Let the largest positive odd number and smallest positive even number be 'a' and 'b' respectively.

C² - 6C + M = 0

The sum of roots of equation = β + α = 6

The products of roots of the equation = β. α

If the product of the roots of the equation is a prime number, then the sum of the equation is 1 more than the products of the equation.

So, M = 5

X² + 3MX - 184 = 0

X² + 3 * 5X - 184 = 0

X² + 15X - 184 = 0

X² + 23X - 8X - 184 = 0

X (X + 23) - 8 (X + 23) = 0

(X - 8) (X + 23) = 0

X = 8, -23

If X = 8

The average of five consecutive positive odd numbers = 2^X - 5

= 2⁸ - 5

= 251

If X = - 23

The average of five consecutive positive odd numbers = 2^X - 5

= 2^-23 - 5

= 1/2²³ - 5 [not satisfied]

A/Q

b + b + 2 + b + 4 + b + 6 + b + 8 = 5 (M³ + 1)

5b + 20 = 5 (5³ + 1)

b + 4 = 126

b = 122

a + a - 2 + a - 4 + a - 6 + a - 8 = 5 * 251

5a - 20 = 5 * 251

a - 4 = 251

a = 255

Hence, the required difference = 255 - 122 = 133