Binomial Theorem questions
776 published questions with worked solutions.
- Let a and b be the coefficient of x^3 in (1+x+2x^2+3x^3 )^4 and (1+x+2x^2+3x^3+4x^4 )^4 respectively. Then the value of 4a/b is
- Given (1-2x+5x^2-10x^3 )(1+x)^n=1+a_1x+a_2x^2+ and that a_1^2=2a_2 then the value of n is
- If the coefficients of the r^ th , (r+1)^ th , (r+2)^ th terms in the expansion of (1+x)^ 14 are in AP, then the largest value of...
- The value of 1 n! + 1 2! ,(n-2)! + 1 4! ,(n-4)! + is
- If x= 13, then the greatest term in the expansion of (1+4x)^8 is the
- If the fourth term in the expansion of x^ ( 1 x+1 ) +x^ 1/12 ^6 is equal to 200 and x>1, then x is equal to
- The sum ^ 40 C_0+ ^ 40 C_1+ ^ 40 C_2+ + ^ 40 C_ 20 is equal to
- The coefficient of x^5 in the expansion of 1+x^2 1+x , |x|<1, is
- Coefficient of x^ -4 in ( 32- 3 x^2 )^ 10 is
- The number of rational terms in the expansion of ( [3]4+ 1 [4]6 )^ 20 , is
- If the binomial expansion of (a+bx)^ -2 is 14-3x+ , then (a,b)=
- The number of terms in the expansion of (1+2x+x^2 )^ 20 , when expanded in descending powers of x, is
- If the ninth term in the expansion of 3^ _3 25^ x-1 +7 +3^ - 18 _3 (5^ x-1 +1 ) ^ 10 is equal to 180 and x>1, then x equals
- If the coefficient of (r+1)^ th term in the expansion of (1+x)^ 2n be equal to that of (r+3)^ th , then
- The coefficient of the middle term in the expansion of (1+x)^ 2n , is
- The sum of the rational terms in the expansion of (2^ 1/5 + 3 )^ 20 , is
- If the third term in the binomial expansion of (1+x)^m is - 18x^2, then the rational value of m, is
- If _ r=0 ^ 2n a_r(x-100)^r= _ r=0 ^ 2n b_r(x-101)^r and a_k= 2^k ^kC_n for all k n, then b_n equals
- The coefficient of x^n in the expansion of (1+x)^2 (1-x)^3 , is
- The coefficient of x^m in (1+x)^p+(1+x)^ p+1 + +(1+x)^n, p m n is
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