• Engineering and Architecture
  • Management and Business Administration
  • Medicine and Allied Sciences
  • Law
  • Animation and Design
  • Media, Mass Communication and Journalism
  • Finance & Accounts
  • Computer Application and IT
  • Pharmacy
  • Hospitality and Tourism
  • Competition
  • School
  • Study Abroad
  • Arts, Commerce & Sciences
  • Learn
  • Online Courses and Certifications
Best Coaching for JEE Main in India with Fees Structure - Preparation Institutes
  1. Home
  2. JEE Main
  3. Study Material
  4. Sandwich Theorem - Practice Questions & MCQ

Sandwich Theorem - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • 68 Questions around this concept.

Solve by difficulty

QuestionMEDIUM

For each $t \epsilon R$, let $[t]$ be the greatest integer less than or equal to $t$. Then

$
\lim _{x \rightarrow 0} x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\ldots .+\left[\frac{15}{x}\right]\right)
$
 

View Solution

\text { If } \lim _{x \rightarrow 0} \frac{a e^x+b \cos x+c e}{e^{2 x}-2 e^x+1}=4 \text {, then }:

View Solution

\text { Evaluate: } \lim _{x \rightarrow 0}\left(\frac{1^x+2^x+3^x+\ldots+n^x}{n}\right)^{a / x}:

View Solution

Which of the following is true for the real valued functions f(x),h(x),g(x) 

\lim _{x \rightarrow a} f(x)=L, \lim _{x \rightarrow-a} g(x)=L, \lim _{x \rightarrow-a} f(x)=N, \lim _{x \rightarrow a} g(x)=N?

View Solution

The integer \mathrm{n} for which \mathrm{\lim _{x \rightarrow 0}\left\{\frac{(\cos x-1)\left(\cos x-e^2\right)}{x^n}\right\}} is a finite, non-zero real number, is

 

View Solution

\mathrm{\lim _{n \rightarrow \infty}\left[\sqrt{\left(n^2+n+1\right)}-\left[\sqrt{\left(n^2+n+1\right)}\right]\right)}
where [ ] denotes the greatest integer function:

View Solution

\mathrm{\lim _{n \rightarrow \infty} \sum_{r=1}^n \frac{r}{\left(n^2+n+r\right)} \text { equals : }}

View Solution
Amrita University B.Tech 2026

Recognized as Institute of Eminence by Govt. of India | NAAC ‘A++’ Grade | Upto 75% Scholarships

Apply
UPES B.Tech Admissions 2026

Ranked #43 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements

Apply

\mathrm{ Assume\, \, that \lim _{\theta \rightarrow-1} f(\theta) exists and \frac{\theta^2+\theta-2}{\theta+3} \leq \frac{f(\theta)}{\theta^2} \leq \frac{\theta^2+2 \theta-1}{\theta+3} }
\mathrm{ holds\, \, for \, \, certain\, \, interval\, \, containing\, \, the \, \, point \, \, \theta=-1 then \lim _{\theta \rightarrow-1} f(\theta) : }

View Solution

\text{ Evaluate :}\mathrm{\lim _{n \rightarrow \infty} \frac{1}{1+n^2}+\frac{2}{2+n^2}+\ldots .+\frac{n}{n+n^2}}.

View Solution
JEE Main 2026: Preparation Tips & Study Plan
Download the JEE Main 2026 Preparation Tips PDF to boost your exam strategy. Get expert insights on managing study material, focusing on key topics and high-weightage chapters.
Download EBook

\text{ Evaluate :}\mathrm{\lim _{x \rightarrow \infty} \frac{x+7 \sin x}{-2 x+13}}  using Sandwich Theorem.

View Solution

Concepts Covered - 1

Sandwich Theorem

Sandwich Theorem

Sandwich theorem is also known as the squeeze play theorem. It is typically used to find the limit of a function via comparison with two other functions whose limits are known or are easily calculated.

Sandwich Theorem 

Let $f(x), g(x)$ and $h(x)$ be real functions such that $f(x) \leq g(x) \leq h(x)$ for all $x$ in the neighbourhood of $x=a$. If $\lim _{x \rightarrow a} f(x)=l=\lim _{x \rightarrow a} h(x)$, then $\lim _{x \rightarrow a} g(x)=l$.

 

Study it with Videos

Sandwich Theorem

Study other Related Concepts

Sandwich Theorem Current Topic

Limit
Left-Hand Limits and Right-Hand Limits
Algebra of Limits
Limit of Indeterminate Form and Algebraic limit
Limit of Algebraic function
Limit Using Expansion
Sandwich Theorem
Limits of Trigonometric Functions
Exponential and Logarithmic Limits
Limits of the form (1 power infinity)

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Sandwich Theorem

Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus

Page No. : 2.7

Line : 6

Clear your Basics with NCERT

E-books & Sample Papers

JEE Main 2026 Paper 2 (B.Arch) Syllabus

2009+ Downloads

Get Answer to all your questions

Study Resources, Applications and Opportunities

Amity University Noida B.Tech Admissions 2026
Apply

Among Top 30 National Universities for Engineering (NIRF 2024) | 30+ Specializations | AI Powered Learning & State-of-the-Art Facilities

Amrita University B.Tech 2026
Apply

Recognized as Institute of Eminence by Govt. of India | NAAC ‘A++’ Grade | Upto 75% Scholarships

UPES B.Tech Admissions 2026
Apply

Ranked #43 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements

Lovely Professional University B.Tech Admissions 2026
Apply

India's Largest University | NAAC A++ | 100% Placements Record | Highest CTC 2.5 Cr PA | 150 + Programmes across Multiple Disciplines

New Horizon College of Engineering B.E. Admissions 2025
Apply

AICTE ‘Platinum’ institute | NIRF 2024 Rank Band 151-200 under the engineering category | Tier-1 accreditation by NBA | Merit & Sports Scholarships

IITs- A Complete Guide
Get now

Dive into everything you need to know about IITs—from eligibility and cutoffs to fees and placements.

View all Application Forms

Student Community: Where Questions Find Answers

Ask and get expert answers on exams, counselling, admissions, careers, and study options.
Download Careers360 App
All this at the convenience of your phone

  • Regular Exam Updates

  • Best College Recommendations

  • College & Rank predictors

  • Detailed Books and Sample Papers

  • Question and Answers

Scan and download the app

OR

Mock Test Series