JEE Main 2023MathematicsContinuity and DifferentiabilityMediumNumerical

JEE Main 2023 — Continuity and Differentiability Question with Solution

JEE Main 2023 (06 Apr Shift 1)

Question

Let a∈ℤ and t be the greatest integer ≤t, then the number of points, where the function fx=a+13 sinx, x∈0,π is not differentiable, is ____________

Enter your answer

Show full solutionCorrect answer: 25
Correct answer
25

Step-by-step explanation

Given,

fx=a+13 sinx, x∈0,π

⇒f(x)=[13 sinx]+a, as a∈Integer

Now let g(x)=13 sinx, now plotting the diagram of y=13sinx we get,

Now from above diagram we can see that,

f(x)=13 sinx is not differentiable at intersection points of y=k, k∈[1,13] & k∈Z

⇒Points of non-differentiability=12×2+1=25

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Continuity and Differentiability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, 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.