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Limit quiz pdf test cbse, Cheat Sheet of Mathematics

National Institutes of Technology (NITs)Mathematics

This document contains detailed and conceptually strong notes on the Chapter “Limits of Functions”, prepared for undergraduate, postgraduate, and competitive examination preparation. Subject / Course: Mathematics – Limits of Functions Level: BSc / BSc (Honours) / MSc / Engineering Mathematics CSIR-NET / GATE / JAM / University Exams Syllabus Coverage: As per UGC–NET / CSIR–NET / GATE and standard university syllabus Author / Prepared by: MSc Mathematics (NIT)

Typology: Cheat Sheet

2025/2026

Available from 02/03/2026

raj-kumar-sharma-1
raj-kumar-sharma-1 🇮🇳

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Advanced MCQ Quiz on Limits
Instructions
Each question has one correct option. Calculators are not allowed.
1. lim
x→0
sin x−x+x3
6
x5
A. 0
B. −1
120
C. 1
120
D. Does not exist
2. lim
x→0
ex−cos x−x
x2
A. 0
B. 1
2
C. 1
D. Does not exist
3. lim
x→0sin x
x1/x2
A. 0
B. 1
C. e−1/6
D. e−1/2
4. lim
x→0
ln(1 + x)−sin x
x3
A. −1
3
B. 1
3
C. −1
6
D. Does not exist
1
pf3
pf4
pf5

Partial preview of the text

Download Limit quiz pdf test cbse and more Cheat Sheet Mathematics in PDF only on Docsity!

Advanced MCQ Quiz on Limits

Instructions

Each question has one correct option. Calculators are not allowed.

  1. lim x→ 0 sin^ x^ −^ x^ +^

x 63 x^5 A. 0 B. − 1201 C. 1201 D. Does not exist

  1. lim x→ 0 e

x (^) − cos x − x x^2 A. 0 B. (^12) C. 1 D. Does not exist

  1. lim x→ 0

sin x x

 1 /x 2

A. 0

B. 1

C. e−^1 /^6 D. e−^1 /^2

  1. lim x→ 0 ln(1 +^ xx) 3 −^ sin^ x

A. −^13 B. (^13) C. −^16 D. Does not exist

  1. (^) xlim→ 0 + xsin^ x A. 0 B. 1 C. ∞ D. Does not exist
  2. lim x→ 0 tan^ x^ x− 3 sin^ x

A. (^13) B. −^13 C. (^12) D. 0

  1. (^) xlim→∞ x

ln

1 +^1 x

− (^) x^1

A. 0

B. −^12

C. 12

D. − 1

  1. lim x→ 01 −^ cos^ x^ −^

x 22 x^4 A. − 241 B. 241 C. 0 D. Does not exist

  1. (^) xlim→ 0 +(sin x)ln^ x A. 0 B. 1 C. ∞ D. Does not exist
  2. lim x→ 0 e

tan x (^) − ex x^3 A. 0 B. (^13) C. 1

B. −^16

C. 13

D. 0

  1. lim x→ 0 arctan^ xx 3 −^ sin^ x

A. 0 B. (^13) C. −^13 D. −^16

  1. (^) xlim→ 0 +

x

x

A. 0

B. 1

C. ∞

D. Does not exist

  1. lim x→ 0 x

3 sin x − x + x 63 A. 1 B. − 1 C. ∞ D. Does not exist

  1. lim x→ 0 (1 + x + x^2 )^1 /x

A. e B. e^2 C. 1 D. ∞

  1. lim x→ 0 e

x^2 − cos x x^2 A. 0 B. 1 C. (^12) D. Does not exist

  1. (^) xlim→∞

x^2 + x + 1 −

x^2 + x

A. 0

B. 12

C. 1

D. ∞

  1. lim x→ (^0) ln(1 + x^ x) − tan x

A. 0 B. ∞ C. Finite nonzero D. Does not exist

  1. lim x→ 0 (cos x + x sin x)^1 /x^2

A. 1 B. e−^1 /^2 C. e−^1 D. 0

  1. lim x→ 0 sin^ x^ −x^ arctan 5 x

A. 0 B. (^13) C. (^15) D. Does not exist

  1. (^) xlim→ 0 +(ln x)x

A. 0 B. 1 C. ∞ D. Does not exist

  1. lim x→ 0 e

x (^) − 1 − sin x x^3 A. (^16) B. −^16 C. 0 D. Does not exist