In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. A binomial is a polynomial that is the sum of two terms, each of which is a monomial.  The binomial expansion formula is: (x+y) = x + nxy + n(n−1)2! xy +....... + y.  Here are some properties of binomial expansion: In binomial expansion of (x+y) number terms are (n+1) The sum of exponents of x and y is always n  The binomial expansion formula can also be written as: (a + b)n =nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + ... 1  The coefficients for varying n and b can be arranged to form... Show more

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. A binomial is a polynomial that is the sum of two terms, each of which is a monomial. 

The binomial expansion formula is: (x+y) = x + nxy + n(n−1)2! xy +....... + y. 

Here are some properties of binomial expansion:
In binomial expansion of (x+y) number terms are (n+1)
The sum of exponents of x and y is always n 
The binomial expansion formula can also be written as:
(a + b)n =nC0 an + nC1 an – 1 b1 + nC2 an – 2 b2 + ... 1 

The coefficients for varying n and b can be arranged to form Pascal's triangle. 

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Algebra Practice Test: Binomial Expansions

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25 Questions

1. The numerically greatest term in the expansion of (2 + 3x)12 when is -

none of these.

2. If (r + 1)th term in expansion of contains a and b to one and the same power, then the term is

61098

3. If n is a rational number which is not a whole number then the number of terms in the expansion of (<>1 +<> x)n<>, |x| < 1 is

nn + 1nothing can be saidinfinitely many

4. For a positive integer is equal to

2n2 - 12n2n - 12n 2

5. If x is so small that x 2 and higher powers of x can be neglected, then

6. The coefficient of 1/x in the expansion of is

2n!/[(2n - 1)!(2n + 1)!]n!/[(2n - 1)!(2n + 1)!]n!/[(n -1)!(n + 1)!]2n!/[(n - 1)!(n + 1)!]

7. In the expansion of (3x + 2)4 the coefficient of middle term is

216365481

8. If the coefficients of (2r + 4)th and (r - 2)th terms in the expansion of (1 + x) 18 are equal, then r is equal to

812106

9. If , then

10. The coefficient of y4 in the expansion of (y2 + c/y)5 is

11. If the number of terms in the expansion of (x - 2y + 3z)n are 45, then n is equal to

8679

12. If (1 + x + x2)n = C0 + C1x + C2x2 + ...... then the value of C0C1 – C1C2 + C2C3 ...... is

2n(-1)n3nnone of these

13. The co-efficient of x4 in is

504no mid term exists

14. Let Sp and Sq be the coefficients of xp and xq respectively in (1 + x)p + q then

Sp ≠ SqSp = Sq

15. Letand , then the value of k is <> ______

23

16. If the coefficient of three consecutive terms in the expansion of (1 + x)n are in the ratio 1:7:42, then the value of n is ______

60705550

17. is equal to

3n2n - 13n - 12 n

18. The coefficient of x53 in the expansion is

19. In the expansion of the term independent of Z is

TsT8T7T9

20. Sum of the series:

(1 - x)-1/2(1 - x) -1/3(1 - x) 1/3(1 + x) 1/2

21. If A and B are coefficients of xn in the expansion of (1 + x)2n and (1 + x)2n-1 respectively then

A = Bnone of these2A = BA = 2B

22. If (1 + ax + bx2) (1 – 2x)18 be expanded in ascending powers of x such that coefficients of x3 and x4 are zero, then (a, b) is equal to

none of these

23. Let (1 + x)n = and . The value of k is

2. 2 3

24. The coefficient of x17 in the expansion of (x - 1) (x - 2) (x - 3) ...... (x - 18) is –

342684171

25. is equal to

1281271297!