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Mathematics - Continuity and Differentiability

Practise 10 KVPY previous year questions on Continuity and Differentiability, compiled from papers spanning 2010 to 2019. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KVPY tests.

  1. 1Let f : R R be a function defined by f x = sin x 2 x if x 0 0 if x = 0 Then, at x = 0 , f is2019 (SB/SX)
  2. 2Let f : - 1 , 1 R be a differentiable function satisfying f x 4 = 16 f x 2 for all x - 1 , 1 f 0 = 0 The number of such functions is2019 (SB/SX)
  3. 3Let f x = x |sin x| , x R . Then,2018 (SB/SX)
  4. 4f : - 1 , 1 R be a function defined by f x = x 2 cos x for x 0 0 for x = 0 The set of points where f is not differentiable is2018 (SB/SX)
  5. 5Define , for all real , where Then05 Nov, 2017 (SB/SX)
  6. 6For a real number let denote the largest number less than or equal to . for let . Then:2014 (SB/SX)
  7. 7Let be defined as The number of points in at which the function is continuous is :2014 (SB/SX)
  8. 8Consider the function Then is discontinuous2014 (SB/SX)
  9. 9For real with define , where for a real number we denote by the largest integer less than or equal to r. The number of points of discontinut2013 (SB/SX)
  10. 10Let be a continuous function satisfying , for all . Then the number of elements in the set is-2010 (SB/SX)

Frequently Asked Questions

1.How many questions are available for Continuity and Differentiability?

This chapter includes 10 questions compiled from KVPY papers spanning 2010 to 2019.

2.Are these questions only from KVPY, or from other exams too?

These are KVPY questions specifically for the Continuity and Differentiability chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Continuity and Differentiability an important chapter for KVPY Mathematics?

Continuity and Differentiability has appeared in 6 of the 11 years of KVPY papers covered here, with 10 questions across 6 papers - about 2 per paper it appears in.