Binomial Theorem MCQs 2

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Test your understanding of Mathematical Induction and the Binomial Theorem MCQS with this quiz designed for First Year Mathematics (Punjab Board) Chapter 8. The quiz includes MCQs on induction steps, binomial expansions, and coefficients. The Binomial Theorem Quiz Test is perfect for exam prep, helping reinforce key concepts like the general term formula, induction proofs, and binomial coefficient properties. Let us start with the Binomial Theorem MCQs Test to check your knowledge.

Mathematical Induction and Binomial Theorem MCQs with Answers

Online First Year Chapter 7 Mathematical Induction and Binomial Theorem Quiz with Answers

1. If $n$ is odd number, then middle term in expansion $(a+x)^n$ is

 
 
 
 

2. The coefficient of $x^3$ in the expansion of $ is:

 
 
 
 

3. The series $(1+x)^n$ is valid if

 
 
 
 

4. The first step in mathematical induction is to prove the statement for:

 
 
 
 

5. The sum of binomial coefficients in $ is:

 
 
 
 

6. The expansion $(1-4x)^{-2}$ is valid if

 
 
 
 

7. The expansion of $(1-2x)^{-2}$ is valid if

 
 
 
 

8. The sum of exponents of $a$ and $b$ in every term of the expansion $(a+b)^n$ is

 
 
 
 

9. When $n$ is negative or fraction then general term of $(1+x)^n$ is

 
 
 
 

10. The number of terms in the expansion of $(1+x)^n$ is

 
 
 
 

11. If $n$ is even the middle terms in $(a+x)^n$ is

 
 
 
 

12. $1-x+x^2 – x^3 + \cdots$ is equal to

 
 
 
 

13. The middle term in the expansion of $(a+b)^n$ is $\left(\frac{n}{2}+1\right)$ then $n$ is

 
 
 
 

14. If $T_{r+1} = \binom{10}{r} (-2)^r (x)^{10-2r}$ the term independent of $x$ is

 
 
 
 

15. Which term of $(x+2)^8$ is independent of $x$

 
 
 
 

16. The number of terms in the expansion of $(a+b)^{20}$ is

 
 
 
 

17. $n^2 > n +3 $ is true for

 
 
 
 

18. $1+x+x^2+x^3+\cdots$ is equal to

 
 
 
 

19. Mathematical induction is a method used to prove statements related to:

 
 
 
 

20. The expansion of $ using the binomial theorem is valid when:

 
 
 
 

Online Mathematical Induction and Binomial Theorem MCQs with Answers

  • If $n$ is even the middle terms in $(a+x)^n$ is
  • Which term of $(x+2)^8$ is independent of $x$
  • The series $(1+x)^n$ is valid if
  • $1+x+x^2+x^3+\cdots$ is equal to
  • $1-x+x^2 – x^3 + \cdots$ is equal to
  • When $n$ is negative or fraction then general term of $(1+x)^n$ is
  • If $T_{r+1} = \binom{10}{r} (-2)^r (x)^{10-2r}$ the term independent of $x$ is
  • The sum of exponents of $a$ and $b$ in every term of the expansion $(a+b)^n$ is
  • The expansion of $(1-2x)^{-2}$ is valid if
  • $n^2 > n +3 $ is true for
  • If $n$ is odd number, then middle term in expansion $(a+x)^n$ is
  • The expansion $(1-4x)^{-2}$ is valid if
  • The middle term in the expansion of $(a+b)^n$ is $\left(\frac{n}{2}+1\right)$ then $n$ is
  • The number of terms in the expansion of $(1+x)^n$ is
  • The number of terms in the expansion of $(a+b)^{20}$ is
  • Mathematical induction is a method used to prove statements related to:
  • The first step in mathematical induction is to prove the statement for:
  • The expansion of $(1+x)^n$ using the binomial theorem is valid when:
  • The coefficient of $x^3$ in the expansion of $(1+x)^6$ is:
  • The sum of binomial coefficients in $(1+x)^n$ is:

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Induction Binomial Theorem Quiz 1

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The post is about “Induction Binomial Theorem Quiz”. Test your knowledge with this comprehensive MCQ Induction Binomial Theorem Quiz from Chapter 8 of First-Year Mathematics. The First Year Mathematics quiz includes 20 multiple-choice questions covering key concepts to help you prepare for exams. Perfect for students and educators! Let us start with the Induction Binomial Theorem Quiz now.

Online First Year Mathematical Induction Binomial Theorem Quiz with Answers
Please go to Induction Binomial Theorem Quiz 1 to view the test

Online Induction Binomial Theorem Quiz First Year Mathematics

  • The statement $4^n > 3^n + 4$ is true when
  • The statement $3^n < n!$ is true, when $n$ is
  • The general term of the binomial expansion $(a+x)^n$ is
  • The number of terms in the expansion of $(a+b)^n$ is
  • In the expansion $(a+x)^n$, the sum of exponents of $a$ and $x$ is
  • The $(r+1)$th term in the expansion of $(a+x)^n$ is
  • In the expansion $(a+x)^n$ the exponent of $a$
  • In the expansion $(a+x)^n$ the exponent of $x$
  • The middle term(s) in the expansion of $(a+b)^{11}$ is/are
  • The middle term(s) in the expansion of $(a-3x)^{14}$ is/are
  • 6th term of the expansion $(a+2x)^{13}$ is
  • 4th term from the end in the expansion of $(a+b)^9$ is
  • The term independent of $x$ in the expansion of $(a+2x)^n$ is
  • The coefficient of the last term in the expansion of $(2-x)^7$ is
  • The sum of all binomial coefficients in the expansion of $(a+x)^n$ is
  • The sum of odd binomial coefficients in the expansion of $(a+x)^n$ is
  • The sum of even binomial coefficients in the expansion of $(a+x)^n$ is
  • $\binom{n+1}{0} + \binom{n+1}{1} + \binom{n+1}{2} + \cdots + \binom{n+1}{n+1}$ is equal to
  • $\binom{2n}{0} + \binom{2n}{1} + \binom{2n}{2} + \cdots + \binom{2n}{2n}$ is equal to
  • If $n$ is odd, the middle term(s) in $(a+x)^n$ is/are

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IPFP Test School and Classroom Management 3

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Prepare for the HEC IPFP Test School and Classroom Management with this comprehensive Quiz. The Higher Education Commission (HEC) IPFP (Indigenous PhD Fellowship Program) test assesses educators’ understanding of key teaching concepts, including classroom discipline, student engagement, lesson planning, and effective learning environments. This IPFP Test School and Classroom Management Quiz covers essential topics such as behavior management, instructional strategies, teacher-student communication, and educational psychology, helping aspiring and current teachers refine their skills for a successful teaching career. Test your knowledge and boost your confidence for the HEC IPFP exam! Let us start with the IPFP Test School and Classroom Management Quiz now.

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Created by 25f0d9fdcd0763332da999662046f137e4f48fed77307ac0d7385f4cffd81e72?s=32&d=mm&r=gMuhammad Imdad Ullah

IPFP Test School and Classroom Management 3

Test your knowledge of school and classroom management with this HEC IPFP quiz! Assess key concepts, strategies, and best practices for effective teaching and learning environments. Perfect for educators and aspiring teachers!

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1 / 20

The authoritarian model is more suitable for

2 / 20

The individual in the group given the task of directing and coordinating is

3 / 20

The process of directing others towards the accomplishment of some objectives is

4 / 20

What do the E and D rules mean

5 / 20

The process of making a judgment is called

6 / 20

The cash book is maintained by

7 / 20

Teacher salaries and allowances are collectively written in

8 / 20

Motivating others to achieve certain goals is

9 / 20

All financial transactions of the school occurring from day to day are entered in

10 / 20

Directing must be consistent with

11 / 20

The power delegated throughout an organization is

12 / 20

Micro planning is done in

13 / 20

The characteristics of a good planner are:

14 / 20

Which pension is granted to a civil servant who retires at the age of sixty

15 / 20

A person who possesses qualities of leadership is

16 / 20

ADP is an abbreviation of

17 / 20

A program of activities that is designed to attain educational ends is

18 / 20

The ACR cannot be initiated for a period of less than

19 / 20

In case of new recruitment, the probation period is

20 / 20

The smallest interacting parts of systems are

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Online IPFP Test School and Classroom Management Quiz qith Answers

Online IPFP Test School and Classroom Management 3

  • The process of directing others towards the accomplishment of some objectives is
  • The characteristics of a good planner are:
  • The power delegated throughout an organization is
  • Motivating others to achieve certain goals is
  • Teacher salaries and allowances are collectively written in
  • A program of activities that is designed to attain educational ends is
  • The cash book is maintained by
  • All financial transactions of the school occurring from day to day are entered in
  • The smallest interacting parts of systems are
  • ADP is an abbreviation of
  • Which pension is granted to a civil servant who retires at the age of sixty
  • In case of new recruitment, the probation period is
  • The authoritarian model is more suitable for
  • Directing must be consistent with
  • What do the E and D rules mean
  • The process of making a judgment is called
  • The ACR cannot be initiated for a period of less than
  • Micro planning is done in
  • The individual in the group given the task of directing and coordinating is
  • A person who possesses qualities of leadership is

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