TOP 100+ Binomial Theorem Questions and Answers

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 α2009 + β2009 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 x3y8 and x8y3 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)6is ____

(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. 8n – 7n – 1 is always divisible by ____.

(A) 64

(B) 7

(C) 49

(D) 8

Answer: 49


7. The sum of the coefficients ncncnc3 + …ncn is equal to ____

(A) 2n

(B) 2n+ 1

(C) 2n + 1

(D) 2n – 1

Answer: 2n – 1


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

(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 6th 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 7c0 + 7c1 + 7c2 + 7c3 + … + 7c7is equal to ____

(A) 64

(B) 128

(C) 63

(D) 127

Answer: 128


12. Number of terms in the expansion of (y2 + 2xy + x230is ____

(A) 31

(B) 43

(C) 61

(D) 91

Answer: 61


13. If in the expansion of (1- x)2n – 1, the coefficient of xγ is Aγ, then Aγ – 1 + A2n – γ is ____.

(A) 1

(B) 5

(C) 0

(D) 3

Answer: 0


14. The coefficient of x6 in the expansion (1 + x2 + x) (2 + x2)6is ____.

(A) 420

(B) 300

(C) 200

(D) 400

Answer: 400


15. The coefficient of x5 in the expansion [1+X+X2+x3]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 xn 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  xn   in the expansions of (1 + x)2n and (1 + x)2n1  respectively, then A/B  equals to

(A) 1

(B) 2

(C) 1/2

(D) 1/n

Answer: 2


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