JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q69

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MathematicsSingle correct+4 / -1Question 69 of 90

If $f:\mathbf R\to\mathbf R$ is a function defined by $f(x)=[x-1]\cos\left(\dfrac{2x-1}2\right)\pi$ , where [·] denotes the greatest integer function, then f is :

discontinuous only at x = 1

discontinuous at all integral values of x except at x = 1

continuous only at x = 1

continuous for every real x

Answer and worked solution

Official answer: D

Jumps cancel. $[x-1]$ jumps only at integers, where $\cos\frac{(2x-1)\pi}2=\cos\left(\text{odd}\cdot\frac\pi2\right)=0$ . So f is continuous everywhere.

(D)

Topics:Continuity

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 69