Binomial Theorem questions
776 published questions with worked solutions.
- What is the value of C(51, 21)-C(51, 22)+C(51, 23)-C(51, 24)+C(51, 25)-C(51, 26)+C(51, 27)-C(51, 28)+C(51, 29)-C(51, 30)?
- In the expansion of (x+ 1 x )^ 2n , what is the (n+1)th term from the end (when arranged in descending powers of x)?
- What is _ r=0 ^ n 2^rC(n, r) equal to?
- If the sixth term in the binomial expansion of (x^ - 8 3 +x^2 _ 10 x )^8 is 5600, then what is the value of x?
- How many terms are there in the expansion of (3x-y)^4(x+3y)^4?
- Consider the following statements for a fixed natural number n : 1. C(n, r) is greatest if n=2r 2. C(n, r) is greatest if n=2r-1...
- What is the coefficient of x^ 10 in the expansion of (1-x^2)^ 20 (2-x^2- 1 x^2 )^ -5 ?
- If the 4th term in the expansion of (mx+ 1 x )^n is 5 2 , then what is the value of mn?
- In a binomial expansion of (x+y)^ 2n+1 (x-y)^ 2n+1 , the sum of middle terms is zero. What is the value of ( x^2 y^2 )?
- In the expansion of (1+x)^p(1+x)^q, if the coefficient of x^3 is 35, then what is the value of (p+q)?
- What is the number of rational terms in the expansion of (3^ 12 +5^ 14 )^ 12 ?
- If the sum of binomial coefficients in the expansion of (x+y)^n is 256, then the greatest binomial coefficient occurs in which...
- Which one of the following is the greatest coefficient in the expansion of (1+x)^ 100 ?
- What is the coefficient of x^ 2n in the expansion of the following? (1+x)^ 2n (1+ 1 x )^ 2n
- Consider the following statements in respect of the expansion of (x^2+x^ -2 +2)^4 : I. The number of terms in the expansion is 5....
- If C_0, C_1, C_2, , C_n are the coefficients in the expansion of (1+x)^n, then what is the value of C_1+C_2+C_3+ +C_n?
- What is the coefficient of the middle term in the expansion of (1+4x+4x^2)^5?
- What is C(n, 1)+C(n, 2)+ +C(n, n) equal to?
- What is the sum of the coefficients of first and last terms in the expansion of (1+x)^ 2n , where n is a natural number?
- How many terms are there in the expansion of ( a^2 b^2 + b^2 a^2 +2 )^ 21 where a 0, b 0?
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