Mathematics Part1

Online MCQs about First Year Mathematics Part1 and Part2, Intermediate Mathematics Part1 multiple choice questions 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. If $n$ is even the middle terms in $(a+x)^n$ is

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

9. The sum of binomial coefficients in $ is:

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

15. $1-x+x^2 – x^3 + \cdots$ is equal to

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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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Permutation Combination Math MCQs 4

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With this quick Quiz Permutation Combination Math MCQs, test your understanding of Chapter 7 (Permutation, Combination, and Probability) from First Year Intermediate Mathematics. The Permutation Combination Math MCQs covers key concepts like (i) Arrangements (Permutations), (ii) Selections (Combinations), (iii) Probability rules, (iv) Factorial notation, and (v) Real-world applications (e.g., dice, cards, committees). Let us start with Permutation Combination Math MCQs now.

Please go to Permutation Combination Math MCQs 4 to view the test
Online Permutation Combination Math MCQs from First Year Mathematics

Permutation Combination Math MCQs with Answers

  • If two events do not affect the occurrence or non-occurrence of each other, then these are called
  • If two events affect the occurrence or nonoccurrence of each other, then these are called
  • If $A, B$, and $C$ are independent events, then $P(A\cap B \cap C)$ is equal to
  • If $A, B$, and $C$ are disjoint events then $P(A\cup B\cup C)$ is equal to
  • If $P(A) = \frac{5}{7}, P(B) = \frac{7}{9}$, $P(A \cap B)$ is equal to
  • If $A$ and $B$ are two independent events, $P(A \cap B) = \frac{1}{169}$, $P(A) = \frac{1}{13}$, $P(B)=$
  • The number of ways to sit 4 persons in a train on a straight sofa is
  • Four people want to sit on a circular sofa; the total ways is
  • A card is drawn from a deck of 52 playing cards. The probability of a card being drawn is an ace is
  • If ${}^nC_6 = {}^C_{12}$ then $n$ equals
  • For independent events $P(A \cap B)$ =
  • If $\binom{n}{12} = \binom{n}{8}$, then the value of $n$ =
  • If $A$ and $B$ are disjoint event then $P(A\cup B)$ =
  • With usual notation ${}^nP_n$ equals:
  • If ${}^nC_6 ={}^nC_8$ then $n$ equals
  • The sample space for tossing a coin is
  • The probability of the non-occurrence of an event $E$ is equal to
  • How many 3-digit numbers can be formed from 1, 2, 3, 4 without repetition?
  • If ${}^nC_5={}^nC_9$​, then $n$=?
  • If $P(A) = 0.3$ and $P(B) = 0.4$, and $A$ and $B$ are independent, then $P(A ∪ B)$ is:

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