Binomial Theorem questions
776 published questions with worked solutions.
- The coefficient of x^3 in the expansion of (1-x+x^2)^5 is
- If the coefficients of the 2nd, 3rd and 4th terms in the expansion of (1+x)^n, n N , are in AP then n is
- The coefficient of x^3y^4z in the expansion of (1+x+y-z)^9 is
- The coefficient of x^ 13 in the expansion of (1-x)^5(1+x+x^2+x^3)^4 is
- If the rth term is the middle term in the expansion of (x^2- 1 2x )^ 20 then the (r+3)th term is
- If the coefficient of the 5th term be the numerically greatest coefficient in the expansion of (1-x)^n then the positive integral...
- The greatest coefficient in the expansion of (1+x)^ 2n is
- The sum of the numerical coefficients in the expansion of (1+ x3+ 2y 3 )^ 12 is
- The sum of the last ten coefficients in the expansion of (1+x)^ 19 when expanded in ascending powers of x is
- The sum of the coefficients of x^ 2r , r=1,2,3, , in the expansion of (1+x)^ n is
- The sum of the coefficients in the polynomial expansion of (1+x-3x^ 2 )^ 2163 is
- The sum of the coefficients of all the integral powers of x in the expansion of (1+2 x)^ 40 is
- If (1+x-2x^ 2 )^ 8 =a_0+a_1x+a_2x^2+ +a_ 16 x^ 16 then the sum a_1+a_3+a_5+ +a_ 15 is equal to
- The sum ^ 20 C_0+ ^ 20 C_1+ ^ 20 C_2+ + ^ 20 C_ 10 is equal to
- If (1+x)^ 10 =a_0+a_1x+a_2x^2+ +a_ 10 x^ 10 then (a_0-a_2+a_4-a_6+a_8-a_ 10 )^2+(a_1-a_3+a_5-a_7+a_9)^2 is equal to
- The sum 12 , ^ 10 C_0- ^ 10 C_1+2 ^ 10 C_2-2^2 ^ 10 C_3+ +2^9 ^ 10 C_ 10 is equal to
- 1 ^ n C_1+2 ^ n C_2+3 ^ n C_3+ +n ^ n C_n is equal to
- If a_n= _ r=0 ^ n 1 ^ n C_r then _ r=0 ^ n r ^ n C_r equals
- The sum of the series _ r=1 ^ n (-1)^ r-1 ^ n C_r(a-r) is equal to
- Let (1+x)^ n = _ r=0 ^ n a_rx^ r . Then (1+ a_1 a_0 ) (1+ a_2 a_1 ) (1+ a_n a_ n-1 ) is equal to
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