Binomial Theorem questions
776 published questions with worked solutions.
- If the constant term in the expansion of ger, then the value of k is equal to
- _ i j; i,j=0 ^n ^nC_i , ^nC_j is equal to
- If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ( [4]2+ 1 [4]3 )^n is 6:1,...
- If the coefficients of three consecutive terms in the expansion of (1+x)^n are in the ratio 1:5:20, then the coefficient of the...
- The absolute difference of the coefficients of x^ 10 and x^7 in the expansion of (2x^2+ 1 2x )^ 11 is equal to
- The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)^ n+2 , which are in the ratio 1:3:5, is...
- The coefficient of x^5 in the expansion of (2x^3- 1 3x^2 )^5 is
- Let (a+bx+cx^2)^ 10 = _ i=0 ^ 20 p_ix^i, a,b,c N. If p_1=20 and p_2=210, then 2(a+b+c) is equal to
- Let K be the sum of the coefficients of the odd powers of x in the expansion of (1+x)^ 99 . Let a be the middle term in the...
- If the 1011^ th term from the end in the binomial expansion of ( 4x 5- 5 2x )^ 2022 is 1024 times 1011^ th term from the...
- If the coefficient of x^7 in (ax- 1 bx^2 )^ 13 and the coefficient of x^ -5 in (ax+ 1 bx^2 )^ 13 are equal, then a^4b^4 is equal...
- _ k=0 ^6 ^ 51-k C_3 is equal to
- If ( ^ 30 C_1 )^2+2 ( ^ 30 C_2 )^2+3 ( ^ 30 C_3 )^2+ +30 ( ^ 30 C_ 30 )^2= ,60! (30!)^2 , then is equal to
- If the sum of the coefficients of all even powers of x in the product (1+x+x^2+ +x^ 2n ) (1-x+x^2-x^3+ +x^ 2n ) is 61, then n is...
- If C_r= ^ 25 C_r and C_0+5 C_1+9 C_2+ +(101) C_ 25 =2^ 25 k, then k is equal to
- For a positive integer n, (1+ 1x )^n is expanded in increasing powers of x. If three consecutive coefficients in this expansion...
- Let (2x^2+3x+4 )^ 10 = _ r=0 ^ 20 a_rx^r. Then a_7 a_ 13 is equal to
- The natural number m, for which the coefficient of x in the binomial expansion of (x^m+ 1 x^2 )^ 22 is 1540, is
- The coefficient of x^4 in the expansion of (1+x+x^2+x^3 )^6 in powers of x, is
- For integers n and r, let nr= cases ^nC_r,& if n r 0 0,& otherwise cases . The maximum value of k for which the sum _ i=0 ^k 10 i...
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