These Binomial Theorem Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Binomial Theorem Questions 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 Questions and Answers

1. If α and β are the roots of the equation x² – x + 1 = 0 then the value of α^{2009} + β^{2009} is

(A) 0

(B) 1

(C) -1

(D) 10

**Answer:** 1

2. If n is a positive integer, then (√5+1)^{2n} + 1 − (√5−1)^{2n} + 1 is

(A) an odd positive integer

(B) not an integer

(C) none of these

(D) an even positive integer

**Answer:** not an integer

3. If the coefficient of x^{3}y^{8} and x^{8}y^{3} in the expansion of (x + y)^{n} is the same, then the value of n is ____.

(A) 10

(B) 11

(C) 5

(D) 13

**Answer:** 11

4. The number of terms in the expansion of (x+y)^{6} + (x-y)^{6}is ____

(A) 14

(B) 7

(C) 4

(D) 3

**Answer:** 4

5. If the expansion of (x + a)^{n},n ε N has 22 terms, then, n is equal to ____

(A) 22

(B) 24

(C) 21

(D) 23

**Answer:** 21

6. 8^{n} – 7n – 1 is always divisible by ____.

(A) 64

(B) 7

(C) 49

(D) 8

**Answer:** 49

7. The sum of the coefficients ^{n}c_{1 }+ ^{n}c_{2 }+ ^{n}c_{3} + …^{n}c_{n} is equal to ____

(A) 2^{n}

(B) 2^{n+ 1}

(C) 2^{n + 1}

(D) 2^{n – 1}

**Answer:** 2^{n – 1}

8. The middle term in the expansion of [x^{3 }/3 – 2/x^{2 }]^{11}is ____.

(A) 5th term

(B) 6th term

(C) 5th and 6th terms

(D) 6th and 7th terms

**Answer:** 6th and 7th terms

9. (2 + 5)^{2} – (2 – 5)^{2}= ____.

(A) 820

(B) 1455

(C) 410

(D) 2905

**Answer:** 2905

10. The 6^{th} term from the end, in the expansion of (x + a)^{14} is ____

(A) 10th term from the beginning

(B) 9th term from the beginning

(C) 6th term from the beginning

(D) 8th term from the beginning

**Answer:** 10th term from the beginning

11. The expression ^{7}c_{0} + ^{7}c_{1} + ^{7}c_{2} + ^{7}c_{3} + … + ^{7}c_{7}is equal to ____

(A) 64

(B) 128

(C) 63

(D) 127

**Answer:** 128

12. Number of terms in the expansion of (y^{2} + 2xy + x^{2}) ^{30}is ____

(A) 31

(B) 43

(C) 61

(D) 91

**Answer:** 61

13. If in the expansion of (1- x)^{2n – 1}, the coefficient of x_{γ} is A_{γ}, then A_{γ }– 1 + A_{2n} – γ is ____.

(A) 1

(B) 5

(C) 0

(D) 3

**Answer:** 0

14. The coefficient of x^{6} in the expansion (1 + x^{2} + x) (2 + x^{2})^{6}is ____.

(A) 420

(B) 300

(C) 200

(D) 400

**Answer:** 400

15. The coefficient of x^{5} in the expansion [1+X+X^{2}+x^{3}]^{13} is—

(A) 300

(B) 1000

(C) 2000

(D) 2728

**Answer:** 2728

16. If the integers r > 1, n > 2 and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)^{2n} are equal, then

(A) n = 2r

(B) n = 3r

(C) n = 2r + 1

(D) none of these

**Answer:** n = 2r

17. The two successive terms in the expansion of (1 + x)^{24} whose coefficients are in the ratio 1 : 4 are

(A) 3rd and 4th

(B) 4th and 5th

(C) 5th and 6th

(D) 6th and 7th

**Answer:** 5th and 6th

18. The coefficients of x^{n} in the expansion of (1 + x)^{2n} and (1 + x)^{2n ~1} are in the ratio

(A) 1 : 2

(B) 1 : 3

(C) 3 : 1

(D) 2:1

**Answer:** 2:1

19. If the coefficients of 2nd, 3rd and the 4th terms in the expansion of (1 + x)^{n} are in A.P., then the value of n is

(A) 2

(B) 7

(C) 11

(D) 14

**Answer:** 7

20. If A and B are coefficients of x^{n }in the expansions of (1 + x)^{2n} and (1 + x)^{2n}–^{1 }respectively, then A/B equals to

(A) 1

(B) 2

(C) 1/2

(D) 1/n

**Answer:** 2