Binomial Theorem questions
776 published questions with worked solutions.
- Let n k denotes ^nC_k and [ n k ]= cases n k , & if 0 k n 0, & otherwise cases If A_k= _ i=0 ^9 9 i [ 12 12-k+i ]+ _ i=0 ^8 8 i [...
- If ^ 20 C_r is the co-efficient of x^r in the expansion of (1+x)^ 20 , the value of _ r=0 ^ 20 r^2 ,^ 20 C_r is equal to
- The maximum value of the term independent of 't' in the expansion of (tx^ 1/5 + (1-x)^ 1/10 t )^ 10 where x (0,1) is
- Let m, n N and gcd(2, n) = 1. If 30 30 0 +29 30 1 + .+2 30 28 +1 30 29 =n.2^m, then n + m is equal to (Here n k = ^nC_k)
- If the maximum value of the term independent of t in the expansion of (t^ 2 x^ 1/5 + (1 - x)^ 1/10 /t)^ 15 , x 0, is K, then 8K...
- If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of (2x^ 3 + 3/x)^ 10 is 5^ 10 - 3^...
- Let C_ r denote the binomial coefficient of x^ r in the expansion of (1 + x)^ 10 . If for , ℝ, C_ 1 + 3 2C_ 2 + 5 3C_ 3 + .......
- _ i,j=0, i j ^ n ^nC_i , ^nC_j is equal to
- If the coefficients of x and x^ 2 in the expansion of (1 + x)^p(1 − x)^q, p, q 15, are −3 and −5 respectively, then the...
- If ^ 40 C_ 0 + ^ 41 C_ 1 + ^ 42 C_ 2 + …. + ^ 60 C_ 20 = (m/n) ^ 60 C_ 20 , m and n are coprime, then m + n is equal to _____.
- If the coefficient of a^7b^8 in the expansion of (a+2b+4ab)^ 10 is K.2^ 16 , then K is equal to _____ .
- If the term without x in the expansion of (x^ 2/3 + x^3 )^ 22 is 7315, then | | is equal to __________.
- Let the sixth term in the binomial expansion of ( 2^ _2(10-3^x) + [5] 2^ (x-2) _23 )^m, in the increasing powers of 2^ (x-2) _23...
- The value of 1 1!50! + 1 3!48! + 1 5!46! + + 1 49!2! + 1 51! is :
- If the coefficients of x^7 in (ax^2+ 1 2bx )^ 11 and x^ -7 in (ax- 1 3bx^2 )^ 11 are equal, then
- For r = 0, 1, , 10, let A_r, B_r and C_r denote, respectively, the coefficient of x^r in the expansions of (1+x)^ 10 , (1+x)^ 20...
- The coefficients of three consecutive terms of (1 + x)^ n+5 are in the ratio 5 : 10 : 14. Then n =
- Coefficient of x^ 11 in the expansion of (1 + x^2)^4(1 + x^3)^7(1 + x^4)^ 12 is
- Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2+(1+x)^3+ +(1+x)^ 49 +(1+mx)^...
- Let X= ( ^ 10 C_1 )^2+2 ( ^ 10 C_2 )^2+3 ( ^ 10 C_3 )^2+ +10 ( ^ 10 C_ 10 )^2, where ^ 10 C_r, r 1,2, ,10 denote binomial...
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