Binomial Theorem questions
776 published questions with worked solutions.
- If p and q be positive, then the coefficients of x^p and x^q in the expansion of (1+x)^ p+q will be
- If n is odd, then C_0^2-C_1^2+C_2^2-C_3^2+ +(-1)^nC_n^2 is equal to
- The sum of the coefficients in the expansion of (x+y)^n is 4096. The greatest coefficient in the expansion is
- 1+ 2 1 3 2 + 2 5 3 6 ( 12 )^2+ 2 5 8 3 6 9 ( 12 )^3+ is equal to
- Statement 1: The number of terms in the expansion (x+ 1x+1 )^n is 2n+1. Statement 2: The number of terms in the expansion...
- If S be the sum of coefficients in the expansion of ( x+ y- z)^n, where ( , , >0), then the value of _ n S (S^ 1/n +1 )^n is
- The middle term in the expansion of (x+ 1 2x )^ 2n is
- The value of ^ 4n C_0+ ^ 4n C_4+ ^ 4n C_8+ + ^ 4n C_ 4n is
- The coefficient of x^n in the expansion of (1+x+x^2+ )^ -n is
- The number of terms in the expansion of (a+b+c)^n will be
- If in the expansion of (a-2b)^n, the sum of 4^ th and 5^ th term is zero, then the value of ab is
- The sum _ i=0 ^m 10 i 20 m-i , (where pq=0 if p<q) is maximum, when m is
- If the last term in the binomial expansion of (2^ 1/3 - 1 2 )^n is ( 1 3^ 5/3 )^ _38 , then the 5^ th term from the beginning is
- If in the expansion of (1+x)^n, the coefficient of r^ th and (r+2)^ th term be equal, then r is equal to
- Statement 1: The term independent of x in the expansion of (x+ 1x+2 )^m is (4m)! (2m)!^2 . Statement 2: The coefficient of x^6 in...
- The value of x, for which the 6^ th term in the expansion of 2^ _2 9^ x-1 +7 + 1 2^ (1/5) _2 (3^ x-1 +1 ) ^7 is 84, is equal to
- Assuming to be small that x^2 and higher powers of x can be neglected, then (1+ 34x )^ -4 (16-3x)^ 1/2 (8+x)^ 2/3 is...
- If for positive integers r>1, n>2, the coefficient of the (3r)^ th and (r+2)^ th powers of x in the expansion of (1+x)^ 2n are...
- If the ratio of the coefficient of third and fourth term in the expansion of (x- 1 2x )^n is 1:2, then the value of n will be
- Statement 1: If n is an odd prime, then the integral part of ( 5+2 )^n-2^ n+1 is divisible by 2n. Statement 2: If n is prime,...
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