JEE Advanced 2021 Paper 2 Mathematics Q16

Mathematics

Problem

Let ψ₁,ψ₂,f,g:[0,∞) → ℝ with f(0)=g(0)=0, ψ₁(x)=e⁻ˣ+x, ψ₂(x)=x²−2x−2e⁻ˣ+2, f(x)=∫₋ₓˣ(|t|−t²)e⁻ᵗ² dt and g(x)=∫₀ˣ²√t e⁻ᵗ dt for x>0. Which statement is true?

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