Skip to content
dronacharya.ai
← JEE Main 2026 · 6 Apr · Shift 1
MathematicsSingle correct+4 / -1Question 1 of 75

JEE Main 2026 · 6 Apr · Shift 1, Mathematics question 1

Let [⋅][\cdot] denote the greatest integer function. If the domain of the function f(x)=sin⁡−1(x+[x]3)f(x)=\sin^{-1}\left(\dfrac{x+[x]}3\right) is [α,β)[\alpha,\beta), then α2+β2\alpha^2+\beta^2 is equal to:

Choose one option
Answer and worked solution

Official answer: B

Condition. −3≤x+[x]≤3-3\le x+[x]\le3. Write x=n+fx=n+f with 0≤f<10\le f<1, so x+[x]=2n+fx+[x]=2n+f.

Each n.

  • n=−1,0,1n=-1,0,1: every f works.
  • n=2n=2: 4+f>34+f>3, so none.
  • n=−2n=-2: −4+f<−3-4+f<-3, so none.

Domain [−1,2)[-1,2): α2+β2=1+4=5\alpha^2+\beta^2=1+4=5.

(B)

Topics:Domain and rangeInverse trigonometric functions
Next question →