Binomial Theorem questions
776 published questions with worked solutions.
- The sum of the series ^ 4 C_0 + ^ 5 C_1x + ^ 6 C_2x^2 + ^ 7 C_3x^3 + to is
- The sum of the series ^ 2 C_0 - ^ 3 C_1x^2 + ^ 4 C_2x^4 - ^ 5 C_3x^6 + to is
- The sum of the series ^ 3 C_0 - ^ 4 C_1 12 + ^ 5 C_2 ( 12 )^2 - ^ 6 C_3 ( 12 )^3 + to is
- If |x|<1, the coefficient of x^n in the expansion of 1 x^2-3x+2 is
- If |x|< 12, the coefficient of x^4 in the expansion of 1 (1+2x)(1-x^2) is
- In the expansion of (1+x)^ -3
- If 3ax 4 + 4+ax - 2 1-ax =-x^2+bx^3+ to then
- If _e 1+x 1-x =a_0+a_1x+a_2x^2+ to then
- The coefficient of x^n, n N , in the expansion of 1+x 1+x^2 is
- Let a= x^ 2 +2x+3, x R and b= _ 0 1- ^ 2 . The value of _ r=0 ^ n a^ r b^ n-r is
- If n is a multiple of 3 then the coefficient of x^n in the expansion of _e(1 + x + x^2), |x| < 1, is
- If in the expansion of (1+x)^m (1-x)^n, the coefficients of x and x^2 are 3 and -6 respectively then
- (n+2) ^ n C_ 0 2^ n+1 - (n+1) ^ n C_ 1 2^ n + n ^ n C_ 2 2^ n-1 - is equal to
- The value of _ r=1 ^ n r( ^ n C_r + ^ r P_r) is
- The value of _ j=1 ^ n ( ^ n+1 C_j - ^ n C_j ) is equal to
- The value of _ r=0 ^ n ^ n+r C_r is equal to
- The number of integral terms in the expansion of ( 3+ [5] 5 )^ 256 is
- ^nC_ r+1 + ^nC_ r-1 +2 ^nC_r is equal to
- If ^ 2n C_6 is the greatest coefficient in the expansion of (1+x)^ 2n , n N, then n is
- The value of 30 0 30 10 - 30 1 30 11 + 30 2 30 12 - + 30 20 30 30 is, where nr= ^ n C_ r
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