Careers360 Logo
Engineering and Architecture
Search Colleges, Exams, Schools & more
JEE Main Chemistry High Weightage Chapters and Topics 2025
  1. Home
  2. JEE Main
  3. Study Material
  4. Series Involving Binomial Coefficients - Practice Questions & MCQ

Series Involving Binomial Coefficients - Practice Questions & MCQ

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

Quick Facts

  • Series Involving Binomial Coefficients is considered one of the most asked concept.

  • 123 Questions around this concept.

Solve by difficulty

QuestionEASY

In the expansion of (1+x)^5 the sum of the coefficient of the terms is

View Solution

In the expansion of (1+x)^n  the sum of coefficients of odd powers of x is

View Solution

If \\(1+x)^n=C_0+C_1 x+C_2 x^2+\ldots+C_n x^nso, then the value of C_0+C_2+C_4+C_6+\ldots

View Solution

In the expansion of (1+x)^{50}, the sum of the coefficient of odd powers of x is

View Solution

In the expansion of (1+x)^5, the sum of the coefficient of the terms is.

View Solution

Concepts Covered - 1

Series Involving Binomial Coefficients

1. Sum of Binomial Coefficients 

\\C_{0}+\mathrm{C}_{1}+C_{2}+C_{3}+\ldots \ldots+C_{n}=2^{n}\\\text{or}\;\;\;\sum_{r=0}^{n} {^n} C_{r}=2^{n}
 

2. Sum of Binomial coefficients with alternate sign

\\C_{0}-\mathrm{C}_{1}+C_{2}-C_{3}+\ldots \ldots .+(-1)^{n} C_{n}=0\\\text{or}\;\;\;\sum_{r=0}^{n}(-1)^{r}\ ^{n} C_{r}=0

 

3. Sum of the Binomial coefficients of the odd terms & Sum of the Binomial coefficients of the even terms 

Adding the above two series we get,

\\2\cdot{(\mathrm{C}_{0}+\mathrm{C}_{2}+\mathrm{C}_{4}+\ldots \ldots)}=2^n\\\mathrm{C}_{0}+\mathrm{C}_{2}+\mathrm{C}_{4}+\ldots \ldots=2^{n-1}

Similarly, on subtracting we get,

\mathrm{C_{1}+C_{3}+C_5\ldots \ldots .}=2^{n-1}

Hence, the sum of the binomial coefficients of the odd terms = Sum of the binomial coefficients of the even terms 

I.e. \mathrm{C_{1}+C_{3}+C_5\ldots \ldots .=C_{0}+C_{2}+C_4+\ldots \ldots=2^{n-1}}

Study it with Videos

Series Involving Binomial Coefficients

Study other Related Concepts

Series Involving Binomial Coefficients Current Topic

Binomial Theorem - Formula, Expansion, Problems and Applications
Some Standard Expansions
General and Middle Terms
Greatest Term (numerically)
An Important Theorem
Problems on Divisibility
Finding last digits
Important Result (Comparison)
Multinomial Theorem
Series Involving Binomial Coefficients

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

Get Answer to all your questions

JEE Main Articles

JEE Main Eligibility Criteria 2025- Marks in 12th, Age Limit, Number of Attempts
Oct 17, 2024
JEE Main Syllabus 2025 PDF (Physics, Chemistry, Maths)
Oct 17, 2024
JEE Main Exam Date 2025 - NTA JEE Mains Session 1 & 2 Exam Schedule
Oct 17, 2024
JEE Main Registration 2025 Session 1, 2 - IIT Application Form Date, Fees, Documents Required
Oct 17, 2024
JEE Main Exam Pattern 2025 (Revised) - Total Marks in JEE Mains, Paper Pattern, Marking Scheme
Oct 17, 2024
JEE Main 2025 - Exam Pattern (Revised), Dates, Registration, Preparation Tips, Previous Year Papers
Oct 17, 2024
How to Prepare for JEE Main 2025?- Study Plan
Oct 17, 2024
JCECE Application Form 2024, Registration (Closed) - Apply Online here
Oct 17, 2024

B.Tech/B.Arch Admissions OPEN

UPES B.Tech Admissions 2025
UPES B.Tech Admissions 2025
Apply

Ranked #46 among universities in India by NIRF | Highest CTC 50 LPA | 100% Placements

Amity University, Noida B.Tech Admissions 2024
Amity University, Noida B.Tech Admissions 2024
Apply

Asia's Only University with the Highest US & UK Accreditation

JSS University Noida Admissions 2024
JSS University Noida Admissions 2024
Apply

170+ Recruiters Including Samsung, Zomato, LG, Adobe and many more | Highest CTC 47 LPA

Atlas SkillTech University | B.Tech Admissions
Atlas SkillTech University | B.Tech Admissions
Apply

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

Parul University B.Tech Admissions 2025
Parul University B.Tech Admissions 2025
Apply

India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package

Vidyashilp University B.Tech Admissions 2025
Vidyashilp University B.Tech Admissions 2025
Apply

Avail upto 100% Scholarships

View All Application Forms
News and Notifications
JEE Main 2025 Live: Exam date, registration soon; eligibility, syllabus, latest updates
October 18, 2024 - 07:53 AM IST
JEE Main 2025: NTA scraps optional questions in section B introduced during COVID pandemic
October 17, 2024 - 10:33 PM IST
How to prepare for JEE Main 2025 in 3 months? Study plan, important topics
October 17, 2024 - 05:18 PM IST
NTA Exam Calendar 2025 Live: JEE Main, NEET, CUET schedule to be announced soon; download at nta.ac.in
October 15, 2024 - 10:25 PM IST
NTA Exam Calendar 2025: JEE Main, NEET, CUET exam dates soon
October 15, 2024 - 07:24 AM IST
JEE Main, NEET, CUET 2025 Dates Live: NTA to announce exam calendar soon on nta.ac.in; latest updates
October 14, 2024 - 07:26 AM IST
NTA Exam Calendar 2025 Live: JEE Main, NEET, CUET, tentative schedule soon at nta.ac.in; how to download
October 12, 2024 - 09:40 PM IST

Download Careers360 App's

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

  • student
    300M+

    Students

  • colleges
    36,000+

    Colleges

  • exams
    550+

    Exams

  • ebook
    1500+

    E-Books

  • certification
    16000+

    Certifications

student
Mobile Screen

We Appeared in

Joint Entrance Examination (Main)      
JEE Main 2025 Sample Papers
Back to top