JEE Class main Answered

p(x) = x + a x + b

p(10 ) = 10 + 10 a + b  = 10 + 5 = 15  , because it is given that 10a + b = 5

p(11) = 11 + 11 a + b = 10 + 10a +b + a + 1 = 16 + a

p(10)p(11) = 15 ( 16 + a )  = 240 + 15 a  ...........................(1)

if  p(10) p(11) = p(n) = n + a n + b =  n + a n + 5 - 10 a

p(10)p(11) = a ( n - 10) + ( n + 5 ) .........................(2)

if we compare (1) and (2)

we get from coefficient a , n -10 = 15  or n = 25

we get from constant term ,  n+5 = 240  or  n = 235

value of n got from coefficient of a and value of n got from constant term are not consistent.

Hence the formulation of probelm is wrong .