Binomial Theorem questions
776 published questions with worked solutions.
- If in the expansion of (1+x)^ 20 , the coefficients of r^ th and (r+4)^ th terms are equal, then the value of r, is
- If n is a positive integer and C_k= ^nC_k, then _ k=1 ^nk^3 ( C_k C_ k-1 )^2 equals
- The coefficient of x^3 in ( x^5 + 3 x^3 )^6, is
- If n is even positive integer, then the condition that the greatest term in the expansion of (1+x)^n may have the greatest...
- If m,n,r are positive integers such that r<m,n, then ^mC_r+ ^mC_ r-1 , ^nC_1+ ^mC_ r-2 , ^nC_2+ + ^mC_1 , ^nC_ r-1 + ^nC_r equals
- The expression 1 4x+1 ( 1+ 4x+1 2 )^7- ( 1- 4x+1 2 )^7 is a polynomial in x of degree
- The number of non-zero terms in the expansion of (1+3 2x )^9+ (1-3 2x )^9, is
- The coefficient of x^7 in the expansion of (x-2x^2 )^ -3 , is
- The sum of the magnitudes of the coefficients in the expansion of (1-x+x^2-x^3 )^n, is
- The coefficient of x^n in the expansion of 1 (1-x)(3-x) , is
- If n>3, then xyz ,C_0-(x-1)(y-1)(z-1)C_1+(x-2)(y-2)(z-2)C_2-(x-3)(y-3)(z-3)C_3+ +(-1)^n(x-n)(y-n)(z-n)C_n equals
- The coefficient of x^ 10 in the expansion of (1+x^2-x^3 )^8, is
- In the expansion of (x^4- 1 x^3 )^ 15 , the coefficient of x^ 39 , is
- If n>1, then (1+x)^n-nx-1 is divisible by
- If C_0,C_1,C_2, ,C_n denote the binomial coefficient in the expansion of (1+x)^n, then the value of a ,C_0+(a+b)C_1+(a+2b)C_2+...
- The sum of the coefficients of the polynomial (1+x-3x^2 )^ 2143 is
- The value of C_0+3C_1+5C_2+7C_3+ +(2n+1)C_n is equal to
- The value of C_0^2+3 C_1^2+5 C_2^2+ to (n+1) terms, is
- If the coefficient of the middle term in the expansion of (1+x)^ 2n+2 is p and the coefficients of middle terms in the expansion...
- The ratio of the coefficient of x^ 15 to the term independent of x in (x^2+ 2x )^ 15 , is
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