JEE Main 2023MathematicsInverse Trigonometric FunctionsMediumMCQ

JEE Main 2023 — Inverse Trigonometric Functions Question with Solution

JEE Main 2023 (31 Jan Shift 1)

Question

Let y=fx represent a parabola with focus -12,0 and directrix y=-12. Then S=x∈ℝ:tan-1fx+sin-1fx+1=π2:

Choose an option

Show full solutionCorrect option: A
Correct answer
Acontains exactly two elements

Step-by-step explanation

Equation of parabola with focus (-12, 0) and directrix y=-12 is:

x+122=y+14

⇒y=x2+x

Put f(x)=y=x+x2 in S,

tan-1xx+1+sin-1x2+x+1=π2

⇒0≤x2+x+1≤1

⇒x2+x≤0      …1

Also,

 x2+x≥0           …2

By 1 & 2, we have

x2+x=0⇒x=0,-1

S contains 2 element.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Inverse Trigonometric Functions 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 Inverse Trigonometric Functions 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.