Mathematical Induction and Binomial Theorem

Chapter 8 Mathematical Induction and Binomial Theorem, First Year Mathematics Books, Part 1 MCQs math, Intermediate mathematics Quiz with Answers

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. The sum of binomial coefficients in $ is:

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

16. $1+x+x^2+x^3+\cdots$ is equal to

 
 
 
 

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

 
 
 
 

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

 
 
 
 

19. $1-x+x^2 – x^3 + \cdots$ is equal to

 
 
 
 

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

 
 
 
 

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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