JEE Main 2022MathematicsLimitsMediumMCQ

JEE Main 2022 — Limits Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let fx be a polynomial function such that fx+f'x+f''x=x5+64. Then, the value of limx→1fxx-1 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A-15

Step-by-step explanation

Let fx=x-1x4+ax3+bx2+cx+d

fx+f'x+f''x=x5+a+4x4+b+3a+16x3+

9a+2b+c-12x2+d+c+4b-6ax+c-2b

∵  fx+f'x+f''x=x5+64

⇒  a+4=0, b+3a+16=0, 9a+2b+c-12=0, d+c+4b-6a=0

⇒  a=-4, b=-4, c=56, d=-64

So limx→1fxx−1=limx→1x4−4x3−4x2+56x−64

=1-4-4+56-64=-15

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About this question

This is a previous-year question from JEE Main 2022, covering the Limits 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.