Binomial Theorem questions
776 published questions with worked solutions.
- The coefficient of x^4 in the expansion of (1+x+x^2+x^3 )^ 11 , is
- The number of terms in the expansion of (x^2+1+ 1 x^2 )^n, n N, is
- The number of terms whose values depend on x in the expansion of (x^2-2+ 1 x^2 )^n, is
- If n is an odd natural number and ^nC_0< ^nC_1< ^nC_2< < ^nC_r> ^nC_ r+1 > ^nC_ r+2 > > ^nC_n, then r=
- The coefficient of x^8y^6z^4 in the expansion of (x+y+z)^ 18 , is not equal to
- _ 0 i<j 10 ^ 10 C_j , ^jC_i is equal to
- The greatest coefficient in the expansion of (1+x)^ 10 , is
- If the coefficients of second, third and fourth terms in the expansion of (1+x)^ 2n are in A.P., then
- The coefficient of x^5 in the expansion of (2-x+3x^2 )^6, is
- If the sum of the coefficients in the expansion of ( x^2-2x+1 )^ 35 is equal to the sum of the coefficient in the expansion of...
- The coefficient of x^5 in the expansion of (x+3)^6 is
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n, then for n odd, C_1^2+C_3^2+C_5^2+ +C_n^2 is equal to
- The term independent of x in the expansion of (1+x)^n (1+ 1x )^n, is
- Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2+(1+x)^3+ +(1+x)^ 49 +(1+mx)^...
- The coefficients of three consecutive terms of (1+x)^ n+5 are in the ratio 5:10:14. Then n is equal to
- The value of ( ^ 21 C_1- ^ 10 C_1 )+ ( ^ 21 C_2- ^ 10 C_2 )+ ( ^ 21 C_3- ^ 10 C_3 )+ ( ^ 21 C_4- ^ 10 C_4 )+ + ( ^ 21 C_ 10 - ^...
- If the number of terms in the expansion of (1- 2x+ 4 x^2 )^n, x 0, is 28, then the sum of the coefficients of all the terms in...
- The sum of coefficients of integral powers of x in the binomial expansion of (1-2 x )^ 50 is
- Coefficient of x^ 11 in the expansion of (1+x^2 )^4 (1+x^3 )^7 (1+x^4 )^ 12 is
- If the coefficients of x^3 and x^4 in the expansion of (1+ax+bx^2 )(1-2x)^ 18 in powers of x are both zero, then (a,b) is equal to
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