Mathematics Part1

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 Mathematical Induction and Binomial Theorem from Chapter 8 of First Year Mathematics Part-1 with Answers

1. The term independent of $x$ in the expansion of $(a+2x)^n$ is

 2nd last term

 Middle term

 Last term

 First term

2. 4th term from the end in the expansion of $(a+b)^9$ is

 $T_4$

 $T_7$

 $T_6$

 None of these

3. The coefficient of the last term in the expansion of $(2-x)^7$ is

 7

 -1

 1

 -7

4. The general term of the binomial expansion $(a+x)^n$ is

 $\binom{n}{r}a^nx^n$

 $\binom{n}{r}a^{n-r}x^r$

 $\binom{n}{r}a^rr^{n-r}$

 $\binom{n}{r}(ax)^{n-r}$

5. The statement $4^n > 3^n + 4$ is true when

 $n$ is any positive integer

 $n=0$

 $n=1$

 $n\ge 2$

6. The sum of all binomial coefficients in the expansion of $(a+x)^n$ is

 $2^{n+1}$

 $2^n$

 $n+1$

 $2^{n-1}$

7. $\binom{2n}{0} + \binom{2n}{1} + \binom{2n}{2} + \cdots + \binom{2n}{2n}$ is equal to

 $2^{2n-1}$

 $2^{2n}$

 $2^{2n+1}$

 $2^n$

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

 $n$

 $2^n$

 $2^{n-1}$

 $n+1$

9. In the expansion $(a+x)^n$ the exponent of $x$

 Remains n every where

 Becomes 0 at the end

 Decreases from n to 0

 Increases from 0 to n

10. $\binom{n+1}{0} + \binom{n+1}{1} + \binom{n+1}{2} + \cdots + \binom{n+1}{n+1}$ is equal to

 $2^{n+1}$

 $2^n$

 $2^{n-1}$

 Cannot be determined

11. In the expansion $(a+x)^n$, the sum of exponents of $a$ and $x$ is

 2n

 n-1

 n

 n+1

12. 6th term of the expansion $(a+2x)^{13}$ is

 $\binom{13}{5}a^82^5x^5$

 $\binom{13}{8}a^52^8x^8$

 $\binom{13}{8}a^5x^8$

 $\binom{13}{5}a^8x^5$

13. The sum of even binomial coefficients in the expansion of $(a+x)^n$ is

 $2^{n+1}$

 $2^n$

 $2^{n-1}$

 $n+1$

14. The middle term(s) in the expansion of $(a-3x)^{14}$ is/are

 $T_6$ and $T_7$

 $T_8$

 $T_7$ and $T_8$

 $T_7$

15. In the expansion $(a+x)^n$ the exponent of $a$

 Remains n every where

 Increases from 0 to n

 Decreases from n to 0

 Becomes n at the end

16. The statement $3^n < n!$ is true, when $n$ is

 > 6

 4

 2

 6

17. The sum of odd binomial coefficients in the expansion of $(a+x)^n$ is

 $n+1$

 $2^n$

 $2^{n+1}$

 $2^{n-1}$

18. If $n$ is odd, the middle term(s) in $(a+x)^n$ is/are

 $\left( \frac{n}{2} +1 \right)$th and $\left( \frac{n}{2} +2 \right)$th

 $\left( \frac{n}{2} +1 \right)$th

 $\left( \frac{n+1}{2} \right)$th and $\left( \frac{n+3}{2} \right)$th

 $\left( \frac{n+1}{2} \right)$th

19. The middle term(s) in the expansion of $(a+b)^{11}$ is/are

 $T_6$ and $T_7$

 $T_5$

 $T_5$ and $T_6$

 $T_6$

20. The $(r+1)$th term in the expansion of $(a+x)^n$ is

 $\binom{n}{r+1}a^{n-r}x^r$

 $\binom{n}{r}a^{n-(r+1)}x^{r+1}$

 $\binom{n}{r}a^{n-r}x^r$

 $\binom{n}{r}a^{n-r+1}x^{r+1}$

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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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