Binomial Theorem questions
776 published questions with worked solutions.
- Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)^n be the ratio 2 : 5 : 8. Then the...
- If the co-efficient of x^9 in ( x^3- 1 x )^ 11 and the coefficient of x^ -9 in ( x- 1 x^3 )^ 11 are equal, then ( )^2 is equal to...
- If the coefficient of x^ 15 in the expansion of (ax^3+ 1 bx^ 1/3 )^ 15 is equal to the coefficient of x^ -15 in the expansion of...
- If the constant term in the binomial expansion of ( x^ 5/2 2 - 4 x^1 )^9 is –84 and the coefficient of x^ -3l is 2^ , where < 0...
- The coefficient of x–6, in the expansion of ( 4x 5 + 5 2x^2 )^9, is________.
- Let > 0, be the smallest number such that the expansion of (x^ 2/3 + 2 x^3 )^ 30 has a term x^ - , N. Then is equal to________.
- The coefficients of x^p and x^q in the expansion of (1 + x)^ p+q are
- r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)^ th term and 3r^ th term in the expansion of (1 + x)^ 2n...
- If ^nC_r denotes the number of combination of n things taken r at a time, then the expression ^nC_ r+1 + ^nC_ r-1 + 2 ^nC_r equals
- If x is positive, the first negative term in the expansion of (1 + x)^ 27/5 is
- The number of integral terms in the expansion of ( 3 + 8 5)^ 256 is
- The coefficient of the middle term in the binomial expansion in powers of x of (1 + x)^4 and of (1 - x)^6 is the same if equals
- The coefficient of x^n in expansion of (1 + x)(1 - x)^n is
- If S_n = _ r=0 ^ n 1 ^nC_r and t_n = _ r=0 ^ n r ^nC_r , then t_n S_n is equal to
- If the coefficients of rth, (r+1)th and (r+2)th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy...
- If the coefficient of x^7 in [ax^2 + ( 1 bx ) ]^ 11 equals the coefficient of x^ -7 in [ax^2 - ( 1 bx ) ]^ 11 , then a and b...
- If x is so small that x^3 and higher powers of x may be neglected, then (1 + x)^ 3/2 - (1 + 12x )^3 (1 - x)^ 1/2
- If the expansion in powers of x of the function 1 (1 - ax)(1 - bx) is a_0 + a_1x + a_2x^2 + a_3x^3 + , then a_n is
- For natural numbers m, n if (1 - y)^m(1 + y)^n = 1 + a_1y + a_2y^2 + , and a_1 = a_2 = 10 then (m, n) is
- In the binomial expansion of (a - b)^n, n 5, the sum of 5^ th and 6^ th terms is zero, then a b equals
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