Limits Continuity and Differentiability Practice Questions

JEE · Mathematics · 1661 free MCQs with instant results and detailed explanations.

1661

Total

342

Easy

738

Medium

581

Hard

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Topics in Limits Continuity and Differentiability

Limits 216

Continuity 232

Differentiability 215

L'Hopital's Rule 234

Indeterminate Forms 224

Squeeze Theorem 296

Limits of Trigonometric Functions 244

Sample Questions from Limits Continuity and Differentiability

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

What is the limit of (1/x) as x approaches infinity?

A. 0

B. 1

C. Infinity

D. -Infinity

Show Answer & Explanation

Correct Answer: A

As x increases, the value of 1/x decreases towards 0.

Easy

Find the limit as x approaches 0 for (tan(x)/x).

A. 0

B. 1

C. Infinity

D. 1/2

Show Answer & Explanation

Correct Answer: B

Using the standard limit, we know that lim (x -> 0) (tan(x)/x) = 1.

Easy

Evaluate lim (x -> 0) (e^x - 1)/x.

A. 0

B. 1

C. e

D. Undefined

Show Answer & Explanation

Correct Answer: B

Using Taylor series or L'Hôpital's Rule shows that the limit equals 1.

Medium

Evaluate lim (x → 0) (e^x - 1)/x.

A. 1

B. 0

C. e

D. Undefined

Show Answer & Explanation

Correct Answer: A

Using L'Hôpital's Rule or the Taylor series expansion of e^x around 0 shows that the limit is 1.

Medium

Find the limit: lim (x → 1) (x^4 - 1)/(x - 1).

A. 4

B. 3

C. 2

D. 0

Show Answer & Explanation

Correct Answer: A

Factoring x^4 - 1 to (x - 1)(x^3 + x^2 + x + 1) allows us to cancel out the (x - 1) term, resulting in 4 when evaluated at x=1.

Medium

Compute the limit: lim (x → 0) (ln(1 + x)/x).

A. 0

B. 1

C. ∞

D. Undefined

Show Answer & Explanation

Correct Answer: B

Using L'Hôpital's rule or the Taylor expansion for ln(1+x) gives the limit as 1.

Medium

Evaluate lim (x → 0) (x^2 * sin(1/x)).

A. 0

B. 1

C. 1/2

D. Undefined

Show Answer & Explanation

Correct Answer: A

The limit of x^2 tends to 0, and since sin(1/x) is bounded between -1 and 1, the overall product approaches 0.

Hard

Find the limit: lim (x → 1) (x^3 - 1)/(x - 1).

A. 1

B. 3

C. 0

D. 2

Show Answer & Explanation

Correct Answer: B

This expression can be simplified using polynomial division or factoring the difference of cubes.

Hard

What is the limit: lim (x → 0) (x^2 sin(1/x))?

A. 1

B. 0

C. ∞

D. Undefined

Show Answer & Explanation

Correct Answer: B

As x approaches 0, x^2 approaches 0 and sin(1/x) is bounded, leading the product to also approach 0.

Q10

Hard

Evaluate the limit: lim(x → 0) (sin(5x)/x).

A. 5

B. 0

C. ∞

D. 1

Show Answer & Explanation

Correct Answer: A

Using the limit property lim(x → 0) (sin(kx)/x) = k, we have k=5.

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Limits Continuity and Differentiability — JEE Mathematics Practice Questions Online

This page contains 1661 practice MCQs for the chapter Limits Continuity and Differentiability in JEE Mathematics. The questions are organized by difficulty — 342 easy, 738 medium, 581 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 7 topics, giving you comprehensive coverage of the entire chapter.