JEE Main 2016MathematicsContinuity and DifferentiabilityEasyMCQ

JEE Main 2016 — Continuity and Differentiability Question with Solution

JEE Main 2016 (10 Apr Online)

Question

Let a,b∈R,a≠0. If the function f, defined as

fx=2x2a, 0≤x<1a, 1≤x<22b2-4bx3, 2≤x<8,is continuous in the interval 0, ∞, then an ordered pair a,b can be 

Choose an option

Show full solutionCorrect option: C
Correct answer
C2,1-3

Step-by-step explanation


Here, fx is continuous at x=1   ⇒limx→1-fx=limx→1+fx
⇒2a=a  ⇒a= ±  2

Since, f(x) is continuous at x=2

⇒limx→2-fx=limx→2+fx

⇒a=2b2-4b22

Put a= 2

⇒2=b2-2b  ⇒b2-2b-2=0

⇒b=2± 4+4.22=1± 3

Hence, a,b≡2,1±3

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About this question

This is a previous-year question from JEE Main 2016, covering the Continuity and Differentiability 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.