These Binomial Theorem MCQ and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Binomial Theorem MCQ and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Binomial Theorem MCQ and Answers

1. If the coefficients of the 6^{th} and 9^{th} terms in the expansion of (x + y)^{n }are equal, then n is ____.

(A) 15

(B) 13

(C) 6

(D) 9

**Answer:** 13

2. The ratio of the coefficient of x^{n} in the expansion of (1 + x)^{3n} to the coefficient of x^{n} in the expansion of (1 + x)^{3n-1}is ____

(A) 2

(B) 3/2

(C) 2/3

(D) 1/2

**Answer:** 3/2

3. The coefficient of xn in the expansion (1 + x + x² + …..)-n is

(A) 1

(B) (-1)n

(C) n

(D) n+1

**Answer:** (-1)n

4. In the expansion of (a + b)n, if n is even then the middle term is

(A) (n/2 + 1)th term

(B) (n/2)th term

(C) nth term

(D) (n/2 – 1)th term

**Answer:** (n/2 + 1)th term

5. If the third term in the binomial expansion of (1 + x)m is (-1/8)x² then the rational value of m is

(A) 2

(B) 1/2

(C) 3

(D) 4

**Answer:** 1/2

6. In the expansion of (a + b)n, if n is odd then the number of middle term is/are

(A) 0

(B) 1

(C) 2

(D) More than 2

**Answer:** 2

7. The general term of the expansion (a + b)n is

(A) T_{r+1} = ^{n}C_{r} × a^{r} × b^{r}

(B) T_{r+1} = ^{n}C_{r} × a^{r} × b^{n-r}

(C) T_{r+1} = ^{n}C_{r} × a^{n-r} × b^{n-r}

(D) T_{r+1} = ^{n}C_{r} × a^{n-r} × b^{r}

**Answer:** T_{r+1} = ^{n}C_{r} × a^{n-r} × b^{r}

8. The greatest coefficient in the expansion of (1 + x)10 is

(A) 10!/(5!)

(B) 10!/(5!)²

(C) 10!/(5! × 4!)²

(D) 10!/(5! × 4!)

**Answer:** 10!/(5!)²

9. The value of n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375, respectively is

(A) 2

(B) 4

(C) 6

(D) 8

**Answer:** 6

10. If n is a positive integer, then (√3+1)^{2n+1} + (√3−1)^{2n+1} is

(A) an even positive integer

(B) a rational number

(C) an odd positive integer

(D) an irrational number

**Answer:** an irrational number

11. The coefficient of xn in the expansion of (1 – 2x + 3x² – 4x³ + ……..)-n is

(A) (2n)!/n!

(B) (2n)!/(n!)²

(C) (2n)!/{2×(n!)²}

(D) None of these

**Answer:** (2n)!/(n!)²

12. The fourth term in the expansion (x – 2y)^{12} is

(A) -1670 x^{9} * y^{3}

(B) -7160 x^{9} * y^{3}

(C) -1760 x^{9} * y^{3}

(D) -1607 x^{9} * y^{3}

**Answer:** -1760 x^{9} * y^{3}

13. The smallest positive integer for which the statement 3^{n+1} < 4^{n} is true for all

(A) 4

(B) 3

(C) 1

(D) 2

**Answer:** 4

14. If the sum of the coefficients in the expansion of (a + b)n is 4096, then the greatest coefficient in the expansion is

(A) 924

(B) 792

(C) 1594

(D) None of these

**Answer:** 924

15. The greatest coefficient in the expansion of (1 + x)^{10} is

(A) 10!/(5!)

(B) 10!/(5!)^{2}

(C) 10!/(5! * 4!)^{2}

(D) 10!/(5! * 4!)

**Answer:** 10!/(5!)^{2}

16. The value of ∑(3^{r} * ^{n}_{Cr ) where 0 ≤ r ≤ 4}

(A) 2n

(B) 3n

(C) 4n

(D) 5n

**Answer:** 4n

17. The general term of the expansion (a + b)^{n} is

(A) T_{r+1} = ^{n}C_{r} * a^{r} * b^{r}

(B) T_{r+1} = ^{n}C_{r} * a^{r} * b^{n-r}

(C) T_{r+1} = ^{n}C_{r} * a^{n-r} * b^{n-r}

(D) T_{r+1} = ^{n}C_{r} * a^{n-r} * b^{r}

**Answer:** T_{r+1} = ^{n}C_{r} * a^{n-r} * b^{r}

18. The value of 1/81^{n} – (10/81^{n} ) * ^{2n}C_{1} + (10^{2} /81^{n} ) * ^{2n}C_{2} – (10^{3} /81^{n} ) * ^{2n}C_{3} + ……. + 10^{2n} /81^{n} is

(A) 2

(B) 0

(C) 1/2

(D) 1

**Answer:** 1

19. If n is positive integer, then (√3+1)^{2n}−(√3−1)^{2n} is

(A) an irrational number

(B) an odd positive integer

(C) none of these

(D) a rational number

**Answer:** an irrational number

20. If the fourth term in the expansion (ax + 1/x)^{n} is 5/2, then the value of x is

(A) 4

(B) 6

(C) 8

(D) 5

**Answer:** 6