Binomial Theorem questions
776 published questions with worked solutions.
- If the coefficient of x in the expansion of (ax^2 + bx + c)(1 - 2x)^ 26 is -56 and the coefficients of x^2 and x^3 are both zero,...
- If ( 1 ^ 15 C_0 + 1 ^ 15 C_1 ) ( 1 ^ 15 C_1 + 1 ^ 15 C_2 ) ( 1 ^ 15 C_ 12 + 1 ^ 15 C_ 13 ) = ^ 13 ^ 14 C_0 ,^ 14 C_1 , ^ 14 C_ 12...
- The coefficient of x^ 48 in (1+x)+2(1+x)^2+3(1+x)^3+ +100(1+x)^ 100 is equal to:
- Let C_r denote the coefficient of x^r in the binomial expansion of (1+x)^n, n N , 0 r n. If P_n = C_0 - C_1 + 2^2 3 C_2 - 2^3 4...
- The value of ^ 100 C_ 50 51 + ^ 100 C_ 51 52 + + ^ 100 C_ 100 101 is :
- The sum of all possible values of n N, so that the coefficients of x, x^2 and x^3 in the expansion of (1+x^2)^2(1+x)^n, are in...
- Let S = 1 25! + 1 3!23! + 1 5!21! + up to 13 terms. If 13S = 2^k n! , k N, then n+k is equal to
- If _ r=0 ^ 5 ^ 11 C_ 2r+1 2r+2 = m n , gcd (m, n) = 1, then m – n is equal to _______.
- If _ r=1 ^ 30 r^2 ( ^ 30 C_r )^2 ^ 30 C_ r-1 = 2^ 29 , then is equal to _______.
- If in the expansion of (1 + x)^p (1 – x)^q, the coefficients of x and x^2 are 1 and –2, respectively, then p^2 + q^2 is equal to :
- The sum of all rational terms in the expansion of (1 + 2^ 1/3 + 3^ 1/2 )^6 is equal to _____
- For some n 10, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of (1 + x)^ n+4 be in A.P. Then the...
- Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)^ 2n-1 . If 2A = 5B,...
- Let the coefficients of three consecutive terms T_r, T_ r+1 and T_ r+2 in the binomial expansion of (a+b)^ 12 be in a G.P. and...
- The least value of n for which the number of integral terms in the Binomial expansion of ( [3] 7 + [12] 11 )^n is 183, is :
- If _ r=0 ^ 10 ( 10^ r+1 -1 10^r ) ^ 11 C_ r+1 = ^ 11 -11^ 11 10^ 10 , then is equal to :
- The sum 1 + 1+3 2! + 1+3+5 3! + 1+3+5+7 4! + upto terms, is equal to
- If _ r=1 ^ 9 ( r+3 2^r ). ^9C_r = ( 3 2 )^9 - , , N, then ( + )^2 is equal to
- The sum of all rational terms in the expansion of (2+ 3)^8 is
- In the expansion of ( [3] 2 + 1 [3] 3 )^n, n ∈ ℕ, if the ratio of 15th term from the beginning to the 15th term from the end is 1...
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