• 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
JEE Main Rank vs College 2025: Admission Chances in Top Engineering Colleges
  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

JEE Main 2026: January Question Paper with Solutions

JEE Main 2026 Tools: College Predictor

JEE Main 2026: Important Formulas | Foreign Universities in India

Comprehensive Guide: IIT's | NIT's | IIIT's

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
GNA University B.Tech Admissions 2026

100% Placement Assistance | Avail Merit Scholarships | Highest CTC 43 LPA

Apply
Amity University-Noida B.Tech Admissions 2026

Among top 100 Universities Globally in the Times Higher Education (THE) Interdisciplinary Science Rankings 2026

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 College Predictor
Discover your college admission chances with the JEE Main 2026 College Predictor. Explore NITs, IIITs, CFTIs and other institutes based on your percentile, rank, and details.
Try Now

\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

Get Answer to all your questions

B.Tech/B.Arch Admissions OPEN

Amity University-Noida B.Tech Admissions 2026
Apply

Among top 100 Universities Globally in the Times Higher Education (THE) Interdisciplinary Science Rankings 2026

Amrita University B.Tech 2026
Apply

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

MAHE, Manipal - B.Tech Admissions 2026
Apply

Last Date to Apply: 15th March | NAAC A++ Accredited | Accorded institution of Eminence by Govt. of India | NIRF Rank #3

Vignan's Deemed to be University B.Tech Admissions 2026
Apply

70th University Ranked by NIRF | 80th Engineering Rank by NIRF | Accredited by NBA and NAAC A+

UPES B.Tech Admissions 2026
Apply

Last Date to Apply: 26th March | Ranked #43 among Engineering colleges in India by NIRF | Highest Package 1.3 CR , 100% Placements

MIT World Peace University B.Tech Admissions 2026
Apply

Highest CTC 44.14 LPA | UGC Approved | 1600+ Recruiters | 100% Placement

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

College Predictor