JEE Main 2017 — Functions Question with Solution
From: JEE Main 2017 (Offline)
Question
Let , b, c . If (x) = ax2 + bx + c is such that
+ b + c = 3 and (x + y) = (x) + (y) + xy,
then is equal to
+ b + c = 3 and (x + y) = (x) + (y) + xy,
then is equal to
Choose an option
Show full solutionCorrect option: D
Correct answer
D330
Step-by-step explanation
f(x) = ax2 + bx + c
f(1) = a + b + c = 3 f (1) = 3
Now f(x + y) = f(x) + f(y) + xy ...(1)
Put x = y = 1 in eqn (1)
f(2) = f(1) + f(1) + 1
= 2f(1) + 1
f(2) = 7
Similarly f(3) = 12
f(4) = 18
= 3 + 7 + 12 + 18 + 25 + 33 + 42 + 52 + 63 + 75 = 330
f(1) = a + b + c = 3 f (1) = 3
Now f(x + y) = f(x) + f(y) + xy ...(1)
Put x = y = 1 in eqn (1)
f(2) = f(1) + f(1) + 1
= 2f(1) + 1
f(2) = 7
Similarly f(3) = 12
f(4) = 18
= 3 + 7 + 12 + 18 + 25 + 33 + 42 + 52 + 63 + 75 = 330
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This is a previous-year question from JEE Main 2017, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.