Binomial Theorem questions
776 published questions with worked solutions.
- If (1+x+x^2 )^n= _ r=0 ^ 2n a_rx^r then, a_1-2a_2+3a_3- -2na_ 2n is equal to
- The number of terms in the expansion of (a+b+c)^ 10 is
- The coefficient of x^3y^4z^5 in the expansion of (xy+yz+xz)^6 is
- If (1+2x+3x^2 )^ 10 =a_0+a_1x+a_2x^2+ +a_ 20 x^ 20 , then a_1 equals
- If a_k is the coefficient of x^k in the expansion of (1+x+x^2 )^n for k=0,1,2, ,2n then a_1+2a_2+3a_3+ +2na_ 2n is equal to
- The number of dissimilar terms in the expansion of (a+b)^n is n+1 therefore number of dissimilar terms of the expansion (a+b+c)^...
- In the expansion of (1+3x+2x^2 )^6 the coefficient of x^ 11 is
- The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to
- If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^n, then the value of the expression ( b b+c )^2-...
- The coefficient of the term independent of x in the expansion of (1+x+2x^3 ) ( 32x^2- 1 3x )^9 is
- If T_0,T_1,T_2, ,T_n represents the terms in the expansion of (x+a)^n, then (T_0-T_2+T_4- )^2+ (T_1-T_3+T_5- )^2 is equal to
- The coefficients of x^2y^2, yzt^2 and xyzt in the expansion of (x+y+z+t)^4 are in the ratio
- If (1+x)^n= _ r=0 ^na_rx^r and b_r=1+ a_r a_ r-1 and _ r=1 ^nb_r= (101)^ 100 100! , then n is
- 1 1! ,(n-1)! + 1 3! ,(n-3)! + 1 5! ,(n-5)! + is equal to
- If (1+x)^ 15 =C_0+C_1x+C_2x^2+ +C_ 15 x^ 15 , then C_2+2C_3+3C_4+ +14C_ 15 is equal to
- If a,b,c are in AP, then the sum of the coefficients of 1+ (ax^2-2bx+c ) ^ 1973 is
- The coefficient of x^n in the polynomial (x+ ^nC_0 ) (x+3 , ^nC_1 ) (x+5 , ^nC_2 ) [x+(2n+1) , ^nC_n ]
- If (1+x)^n=C_0+C_1x+C_2x^2+ C_nx^n, then C_0^2+C_1^2+C_2^2+C_3^2+ +C_n^2 is equal to
- If n is even, then the middle term in the expansion of (x^2+ 1x )^n is 924x^6, then n is equal to
- If the coefficient of 7^ th and 13^ th term in the expansion of (1+x)^n are equal, then n is equal to
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