Binomial Theorem questions
776 published questions with worked solutions.
- Consider the expansion of (1+x)^n. Let p, q, r and s be the coefficients of first, second, nth and (n+1)th terms respectively....
- For nonnegative integers s and r, let s r = cases s! r!(s-r)! & if r s, 0 & if r > s. cases For positive integers m and n, let...
- Let a and b be two nonzero real numbers. If the coefficient of x^5 in the expansion of (ax^2 + 70 27bx )^4 is equal to the...
- Let for the 9^ th term in the binomial expansion of (3 + 6x)^ n , in the increasing powers of 6x, to be the greatest for x = 3/2,...
- If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of (x^ n + 2/x^ 5 )^ 7 is 939, then the...
- If the coefficient of x^ 10 in the binomial expansion of ( x /5^ 1/4 + 5 /x^ 1/3 )^ 60 is 5^ k l, where l, k N and l is co-prime...
- Let the coefficients of the middle terms in the expansion of (1/ 6 + x)^ 4 , (1 - 3 x)^ 2 and (1 - ( /2)x)^ 6 , > 0, respectively...
- If 1 + (2 + ^ 49 C_ 1 + ^ 49 C_ 2 + … + ^ 49 C_ 49 )(^ 50 C_ 2 + ^ 50 C_ 4 + … + ^ 50 C_ 50 ) is equal to 2^ n m where m is odd,...
- The term independent of x in the expansion of (1 - x^ 2 + 3x^ 3 )((5/2)x^ 3 - 1/(5x^ 2 ))^ 11 , x 0 is :
- The number of positive integers k such that the constant term in the binomial expansion of (2x^ 3 + 3/x^ k )^ 12 , x 0 is 2^ 8 ,...
- If _ k=1 ^ 10 K^ 2 (^ 10 C_ k )^ 2 = 22000L, then L is equal to _____.
- Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of (^ 4 2 + 1/^ 4 3...
- Let the coefficients of x^ -1 and x^ -3 in the expansion of (2x^ 1/5 − 1/x^ 1/5 )^ 15 , x > 0, be m and n respectively. If r is a...
- If the constant term in the expansion of (3x^ 3 - 2x^ 2 + 5/x^ 5 )^ 10 is 2^ k I, where I is an odd integer, then the value of k...
- What is the number of terms in the expansion of [(2x-3y)^2(2x+3y)^2]^2?
- In the expansion of (1+ax)^n, the first three terms are respectively 1, 12x and 64x^2. What is n equal to?
- Let a_0, a_1, , a_ 23 be real numbers such that (1 + 2 5 x )^ 23 = _ i=0 ^ 23 a_ix^i for every real number x. Let a_r be the...
- If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ( [4] 2 + 1 [4] 3 )^n is...
- The coefficient of x^ 16 in the expansion of (x^4- 1 x^3 )^ 15 is __________
- The absolute difference of the coefficients of x^ 10 and x^7 in the expansion of (2x^2+ 1 2x )^ 11 is equal to
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