Binomial Theorem questions
776 published questions with worked solutions.
- The sum of the series x-1 x+1 + 12 x^2-1 (x+1)^2 + 13 x^3-1 (x+1)^3 + , is equal to
- The value of (x+y)(x-y)+ 1 2! (x+y)(x-y) (x^2+y^2 )+ 1 3! (x+y)(x-y) (x^4+y^4+x^2y^2 )+ , is
- The sum of the series 12 2! + 28 3! + 50 4! + 78 5! + , is
- If a= _ n=0 ^ x^ 3n (3n)! , b= _ n=1 ^ x^ 3n-2 (3n-2)! and c= _ n=1 ^ x^ 3n-1 (3n-1)! , then the value of a^3+b^3+c^3-3abc is
- If S= _ n=2 ^ ^nC_2 (n+1)! , then S equals
- The sum of the series 1+ 1^2+2^2 2! + 1^2+2^2+3^2 3! + 1^2+2^2+3^2+4^2 4! + , is
- If S= _ n=0 ^ ( x)^ 2n (2n)! , then S equals
- If S= _ n=2 ^ ^nC_2 3^ n-2 n! , then S equals
- Statement-1: The sum of the series q=16, r=16, s=1 q+5CC_r-5= ^ 17 C_ 15 +400 is 8000. Statement-2: =136 for any natural number =...
- Let S_n=1+q+q^2+ +q^n and T_n=1+ ( q+1 2 )+ ( q+1 2 )^2+ + ( q+1 2 )^n where q is a real number and q 1. If ^ 101 C_1+ ^ 101 C_2...
- 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...
- If the coefficients of x^7 in (x^2+ 1 bx )^ 11 and x^ -7 in (x- 1 bx^2 )^ 11 , b 0, are equal, then the value of b is equal to :
- Let ^ 10 C_s(25^ (s-1) +7)×(5^ (s-1) +1)^ -1 = 180, is: A possible value of 'x', for which the ninth term in the expansion of 3^...
- If ( 3^6 4^4 )k is the term, independent of x, in the binomial expansion of ( x 4 - 12 x^2 )^ 12 then k is equal to_____.
- The sum of all those terms which are rational numbers in the expansion of (2^ 1/3 +3^ 1/4 )^ 12 is:
- If the greatest value of the term independent of 'x' in the expansion of (x + a x )^ 10 is 10! (5!)^2 , then the value of 'a' is...
- Let n N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ^nC_0, 3.^nC_1, 5.^nC_2,...
- If the co-efficient of x^7 and x^8 in the expansion of (2+ x 3 )^n are equal, then the value of n is equal to________.
- If b is very small as compared to the value of a, so that the cube and other higher powers of b a can be neglected in the...
- The ratio of the coefficient of the middle term in the expansion of (1+x)^ 20 and the sum of the coefficients of two middle terms...
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