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 – 3x^{2} )^{2143} is

(A) -1

(B) 1

(C) 0

(D) None of these

**Answer:** -1

2. Which one the following is the common factor of (47^{43} + 43^{43} ) and (47^{47} + 43^{47} )

(A) 47 – 43

(B) 47 + 43

(C) (47^{43} + 43^{43} )

(D) (47^{47} + 43^{47} )

**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 (y^{2} + c/y)^{5} is

(A) 29c

(B) 10c

(C) 10c^{3}

(D) 20c^{2}

**Answer:** 10c^{3}

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 1/81^{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:** 4

8. The coefficient of a^{-6} b^{4} 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) ^{18}C_{4} * 2^{4}

(B) ^{18}C_{5} * 2^{5}

(C) ^{18}C_{6} * 2^{6}

(D) None of these

**Answer:** ^{18}C_{6} * 2^{6}

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 a^{4} * b^{5} in the expansion of (a + b)^{9} is

(A) ^{9}C_{4}

(B) ^{9}C_{3}

(C) ^{8}C_{4}

(D) ^{8}C_{3}

**Answer:** ^{9}C_{4}

12. In the binomial expansion of (7^{1/2} + 5^{1/3})^{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 x^{9} × y³

(B) -7160 x^{9} × y³

(C) -1760 x^{9} × y³

(D) -1607 x^{9} × 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