← Back to practice

JEE Advance 2025 Paper 1

JEE Advance · 2025

94 questions · One at a time

Answers and solutions are AI-generated — please cross-check with your study materials.

View question paper
49
MCQ3 marks

Let R\mathbb{R}   denote the set of all real numbers. Define the function f:RRf: \mathbb{R} \to \mathbb{R}   by f(x)={22x2x2sin1xif x02if x=0f(x) = \begin{cases} 2 - 2x^{2} - x^{2} \sin \frac{1}{x} & \text{if } x \neq 0 \\ 2 & \text{if } x = 0 \end{cases}  . Then which one of the following statements is TRUE?

  • A.The function f is NOT differentiable at x = 0
  • B.There is a positive real number δ\delta  , such that f is a decreasing function on the interval (0, δ\delta  )
  • C.For any positive real number δ\delta  , the function f is NOT an increasing function on the interval (δ-\delta  , 0)Correct
  • D.x = 0 is a point of local minima of f
49 of 94