JEE Main 2017MathematicsDifferential EquationsHardMCQ

JEE Main 2017 — Differential Equations Question with Solution

JEE Main 2017 (09 Apr Online)

Question

Let f be a polynomial function such that f3x=f′x. f′′x, for all x∈R. Then :

Choose an option

Show full solutionCorrect option: B
Correct answer
Bf′′2-f′2=0

Step-by-step explanation

Degree of fx will be 3

f(x)=ax3+bx2+cx+d

f3x=27ax3+9bx2+3cx+d

f'(x)=3ax2+2bx+c

f′′x=6ax+2b

f3x=f′x f′′x

Comparing the coefficient, we get

27a=18a2 ⇒a= 3 2

Also b=0, c=0, d=0

fx=32x3, f( 2 )=12

⇒ f′x=92x2, f′′x=9x

Hence, f'(2)=18, f''(2)=18

Hence, f''2−f'(2)=0

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About this question

This is a previous-year question from JEE Main 2017, covering the Differential Equations 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.