Binomial Theorem questions
776 published questions with worked solutions.
- For 2 r n, nr+2 n r-1 + n r-2 is equal to
- Find the coefficient of x^4 in the expansion of (1-9x+20x^2 )^ -1 .
- Find the largest value of n among all possible natural numbers n, such that the coefficient of x in the expansion of (x^3+ 1 x^4...
- The coefficients of the (r-1)^ th , r^ th and (r+1)^ th terms in the expansion of (1+x)^n are in the ratio 1:3:5. Find the...
- For n N, in the expansion of ( [4] x^ -3 +a [4] x^5 )^n, the sum of all binomial coefficients lies between 200 and 400 and the...
- Find the number of integral terms in the expansion of (5^ 12 +7^ 18 )^ 1024 .
- If the coefficient of the 3^ rd term from the end in the expansion of (y^ 1/2 +x^ 1/3 )^n is 45, then find the value of n.
- Find the total number of irrational terms in the binomial expansion of ( [4]5+ [5]4 )^ 100 .
- If the middle term in the binomial expansion of ( 1x+x x )^ 10 is 63 8, then find the value of 6 ^2x+ x-2.
- Find the term independent of x in the binomial expansion of (1- 1x+3x^5 ) (2x^2- 1x )^8.
- Find the total number of terms in the expansion of ( 1+x^2 + 1-x^2 )^4+ ( 2x^2 1+x^2 + 1-x^2 )^4.
- If the coefficients of 2^ nd , 3^ rd and 4^ th terms in the expansion of (1+x)^ 2n are in A.P., then find the value of 2n^2-9n+8.
- Find the sum of the coefficients of even powers of x in the expansion of (1+x+x^2+x^3 )^5.
- If the sum of the coefficients of 1^ st , 2^ nd and 3^ rd terms in the expansion of (x- 3 x^2 )^n, x 0, n N, is 559, then find...
- Find the coefficient of x^6 in the expansion of 1 (1-x+x^2 )^3 , |x|<1.
- If the coefficients of the (r-1)^ th , r^ th and (r+1)^ th terms in the expansion of (x+1)^n are in the ratio 2:15:70, then find...
- Find the sum of the coefficients of all even degree terms in x in the expansion of (x+ x^2-1 )^6+ (x- x^2-1 )^6, x R-(-1,1).
- Find the sum of the digits of the coefficient of the middle term in the expansion of (1+3x+3x^2+x^3 )^6.
- In the expansion ( [4]2+ 1 [4]3 )^n, if the ratio of the 5^ th term from the beginning to the 5^ th term from the end is 6:1,...
- If n is a positive integer, then ( 3+1 )^ 2n - ( 3-1 )^ 2n is
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