TOP 100+ Binomial Expansion Questions and Answers

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

1. The sum of the coefficient of the polynomial (1 + x – 3x2 )2143 is

(A) -1

(B) 1

(C) 0

(D) None of these

Answer: -1


2. Which one the following is the common factor of (4743 + 4343 ) and (4747 + 4347 )

(A) 47 – 43

(B) 47 + 43

(C) (4743 + 4343 )

(D) (4747 + 4347 )

Answer: 47 + 43


3. If n is a positive integer, then (3 + √i)n+(3 -√i)n is

(A) a nonreal number

(B) a positive real number

(C) a real number

(D) none of these

Answer: a nonreal number


4. The coefficient of y in the expansion of (y2 + c/y)5 is

(A) 29c

(B) 10c

(C) 10c3

(D) 20c2

Answer: 10c3


5. The number 111111…………..1 (91 times) is

(A) not an odd number

(B) none of these

(C) not a prime

(D) an even number

Answer: not a prime


6. The remainder when (17)200 is divided by 18 is

(A) 0

(B) 1

(C) 2

(D) 17

Answer: 1


7. The value of 1/81n – (10/81n ) * 2nC1 + (102 /81n ) * 2nC2 – (103 /81n ) * 2nC3 + ……. +  102n /81n is 

(A) 2

(B) 0

(C) 1/2

(D) 1

Answer: 4


8. The coefficient of a-6 b4 in the expansion (1/a – 2b/3)10 is

(A) 1102/27

(B) 1120/72

(C) 1120/27

(D) 1120/37

Answer: 1120/27


9. The term independent of x in (√x – 2/x)18 is

(A) 18C4 * 24

(B) 18C5 * 25

(C) 18C6 * 26

(D) None of these

Answer: 18C6 * 26


10. The number (101)100 – 1 is divisible by

(A) 100

(B) 1000

(C) 10000

(D) All the above

Answer: All the above


11. The coefficient of a4 * b5 in the expansion of (a + b)9 is

(A) 9C4

(B) 9C3

(C) 8C4

(D) 8C3

Answer: 9C4


12. In the binomial expansion of (71/2 + 51/3)37, the number of integers are

(A) 2

(B) 4

(C) 6

(D) 8

Answer: 6


13. In the binomial expansion of (a + b)n, the coefficient of fourth and thirteenth terms are equal to each other, then the value of n is

(A) 10

(B) 15

(C) 20

(D) 25

Answer: 15


14. The fourth term in the expansion (x – 2y)12 is

(A) -1670 x9 × y³

(B) -7160 x9 × y³

(C) -1760 x9 × y³

(D) -1607 x9 × y³

Answer: -1760 x9 × y³


15. 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


16. The number of ordered triplets of positive integers which are solution of the equation x + y + z = 100 is

(A) 4815

(B) 4851

(C) 8451

(D) 8415

Answer: 4851


17. The coefficient of y in the expansion of (y² + c/y)5 is

(A) 10c

(B) 10c²

(C) 10c³

(D) None of these

Answer: 10c³


18. 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


19. if n is a positive ineger then 23nn – 7n – 1 is divisible by

(A) 7

(B) 9

(C) 49

(D) 81

Answer: 49


20. (1.1)10000 is _____ 1000

(A) greater than

(B) less than

(C) equal to

(D) None of these

Answer: greater than


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