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CUET UG Continuity, Differentiability & Derivatives — practice questions

Explore 36 free Continuity, Differentiability & Derivatives questions in CUET UG Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Continuity, Differentiability & Derivatives questions and exercises with answers

Showing questions 1–30 of 36.

A function whose graph can be drawn without lifting the pen is:Read the answer and worked solution →If f is not continuous at c, then c is called a point of:Read the answer and worked solution →If a function is differentiable at a point, it is also:Read the answer and worked solution →The rule for differentiating a composite function is the:Read the answer and worked solution →f(x) = x squared at x = 0 is:Read the answer and worked solution →Functions written with y not isolated are called:Read the answer and worked solution →Continuity of f at c requires the limit at c to equal:Read the answer and worked solution →Theorem 1 concerns two functions that are both:Read the answer and worked solution →Theorem 2 deals with which kind of function?Read the answer and worked solution →Theorem 3 says differentiability at a point implies:Read the answer and worked solution →Does continuity at a point guarantee differentiability?Read the answer and worked solution →The chain rule can be extended to composites of:Read the answer and worked solution →An alternative to repeated product rule for many factors is:Read the answer and worked solution →For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:Read the answer and worked solution →The function f(x) = |x| at x = 0 is continuous but not:Read the answer and worked solution →To differentiate an implicit relation you use the:Read the answer and worked solution →A function that fails the limit test at a point is:Read the answer and worked solution →Composites of continuous functions, by Theorem 2, are:Read the answer and worked solution →An alternative to repeated product rule for many factors is:Read the answer and worked solution →The rule for differentiating a composite function is the:Read the answer and worked solution →If a function is differentiable at a point, it is also:Read the answer and worked solution →Functions written with y not isolated are called:Read the answer and worked solution →Continuity of f at c requires the limit at c to equal:Read the answer and worked solution →Theorem 1 concerns two functions that are both:Read the answer and worked solution →Theorem 3 says differentiability at a point implies:Read the answer and worked solution →To differentiate an implicit relation you use the:Read the answer and worked solution →A function that fails the limit test at a point is:Read the answer and worked solution →Theorem 2 deals with which kind of function?Read the answer and worked solution →A function whose graph can be drawn without lifting the pen is:Read the answer and worked solution →Does continuity at a point guarantee differentiability?Read the answer and worked solution →

Worked practice questions

A function whose graph can be drawn without lifting the pen is:

  1. Continuous
  2. Discontinuo
  3. Undefined a
  4. Increasing a
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Correct answer: A. Continuous

1. Continuity is about the graph having no break. 2. A break forces the pen off the paper. 3. So an unbroken graph means the function is continuous. 4. The answer is continuous. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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If f is not continuous at c, then c is called a point of:

  1. Convergence a
  2. Discontinuity
  3. Differentiabil
  4. Integrability a
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Correct answer: B. Discontinuity

1. Continuity can fail at a particular point. 2. That point gets its own name. 3. It is called a point of discontinuity. 4. So the answer is discontinuity. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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If a function is differentiable at a point, it is also:

  1. Constant there
  2. Increasing there
  3. Undefined there
  4. Continuous there
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Correct answer: D. Continuous there

1. Differentiability is the stronger condition. 2. It cannot hold where the graph breaks. 3. So a differentiable function is continuous at that point. 4. The answer is continuous there. _Source: syllabus Mathematics, Ch 5 'Continuity and Differentiability'_

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