Binomial Theorem questions
776 published questions with worked solutions.
- 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, then n+m is...
- Suppose _ r=0 ^ 2023 r^2 , ^ 2023 C_r=2023 2^ 2022 . Then the value of is
- The mean of the coefficients of x,x^2, ,x^7 in the binomial expansion of (2+x)^9 is
- Let [ 3n-1 2 ] be the constant term in the binomial expansion of _ j=0 ^2a_ 2j+1 = 12 (f(1)-f(-1) )=0. If the sum of the...
- Let [t] denote the greatest integer t. If the constant term in the expansion of (3x^2- 1 2x^5 )^7 is , then [ ] is equal to
- If the coefficient 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
- Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)^n be in the ratio 2:5:8. Then the coefficient...
- Let the sum of the coefficients of the first three terms in the expansion of (x- 3 x^2 )^n, x 0, n N, be 376. Then the...
- 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)...
- If the term without x in the expansion of 10^ 100 =x is 7315, then (1+ 1x )^x (2,e) is equal to
- The coefficient of x^4 in the expansion of (1+x+x^2 )^ 10 is
- The number of rational terms in the binomial expansion of (4^ 14 +5^ 16 )^ 120 is
- If the constant term, in binomial expansion of (2x^r+ 1 x^2 )^ 10 is 180, then r is equal to
- If _ k=1 ^ 10 K^2 ( ^ 10 C_K )^2=22000L, then L is equal to
- The coefficient of x^ 18 in the expansion of (x^4- 1 x^3 )^ 15 is
- The sum of the series 1+3x+6x^2+10x^3+ will be
- If y=3x+6x^2+10x^3+ , then the value of x in terms of y is
- 1 n! + 1 2! ,(n-2)! + 1 4! ,(n-4)! + is
- The sum of the series 3 4.8 - 3.5 4.8.12 + 3.5.7 4.8.12.16 - is
- The expansion of (1+3x+2x^2 ) is
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