Start learning →

JEE Main Continuity and Differentiability — practice questions

Explore 16 free Continuity and Differentiability questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Continuity and Differentiability with Quill →

Continuity and Differentiability questions and exercises with answers

Showing questions 1–16 of 16.

A function $f$ is continuous at a point $c$ if:Read the answer and worked solution →The derivative of $e^x$ with respect to $x$ is:Read the answer and worked solution →The derivative of $\log_e x$ with respect to $x$ is:Read the answer and worked solution →By the chain rule, $\dfrac{d}{dx} f(g(x))$ equals:Read the answer and worked solution →The function $f(x) = |x|$ is continuous everywhere but is NOT differentiable at:Read the answer and worked solution →Every differentiable function is necessarily:Read the answer and worked solution →The derivative of $e^{2x}$ with respect to $x$ is:Read the answer and worked solution →The derivative of $\log_e(x^2)$ with respect to $x$ is:Read the answer and worked solution →A function $f$ is continuous at $c$ only if the left-hand limit, right-hand limit and $f(c)$ are:Read the answer and worked solution →The derivative of $x e^x$ with respect to $x$ is:Read the answer and worked solution →Rolle's theorem requires that $f$ be continuous on $[a,b]$, differentiable on $(a,b)$ and:Read the answer and worked solution →The derivative of $\tan x$ with respect to $x$ is:Read the answer and worked solution →The derivative of $\sqrt{x}$ with respect to $x$ is:Read the answer and worked solution →Match the rule name to its statementRead the answer and worked solution →Spot the wrong step in the derivativeRead the answer and worked solution →Continuity — true or false?Read the answer and worked solution →

Worked practice questions

A function $f$ is continuous at a point $c$ if:

  1. $\displaystyle\lim_{x\to c} f(x) = 0$
  2. $\displaystyle\lim_{x\to c} f(x) = f(c)$
  3. $f(c) = 0$
  4. $f$ is differentiable at $c$ only
Show answer and solution

Correct answer: B. $\displaystyle\lim_{x\to c} f(x) = f(c)$

f is continuous at c when lim_{x→c} f(x) exists and equals f(c).

Open this question →

The derivative of $e^x$ with respect to $x$ is:

  1. $e^x \ln x$
  2. $\dfrac{1}{x}$
  3. $x e^{x-1}$
  4. $e^x$
Show answer and solution

Correct answer: D. $e^x$

d/dx(eˣ) = eˣ — the exponential is its own derivative.

Open this question →

The derivative of $\log_e x$ with respect to $x$ is:

  1. $e^x$
  2. $x$
  3. $\dfrac{1}{x}$
  4. $\ln x$
Show answer and solution

Correct answer: C. $\dfrac{1}{x}$

d/dx(ln x) = 1/x.

Open this question →

How to practise

  1. Choose a Continuity and Differentiability question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Continuity and Differentiability practice for JEE Main. Read explanations as you go. No signup form needed to start.

Practise Continuity and Differentiability →

More Mathematics topics

Statistics and ProbabilityDeterminantsVector Algebra and 3D GeometryContinuity, Differentiability & DerivativesDifferential EquationsIntegrals and ApplicationsMatrices and DeterminantsRelations, Functions & Inverse Trigonometry