Binomial Theorem questions
776 published questions with worked solutions.
- Statement-1: _ r=0 ^ n (r + 1)^nC_r = (n + 2)2^ n-1 Statement -2: _ r=0 ^ n (r + 1)^nC_rx^r = (1 + x)^n + nx(1 + x)^ n-1 .
- Let S_1 = _ j=1 ^ 10 j(j - 1)^ 10 C_j, S_2 = _ j=1 ^ 10 j^ 10 C_j and S_3 = _ j=1 ^ 10 j^2 , ^ 10 C_j. Statement-1: S_3 = 55 2^9...
- The coefficient of x^7 in the expansion of (1 - x - x^2 + x^3 )^6 is
- The number of terms in the expansion of (y^ 1/5 + x^ 1/10 )^ 55 , in which powers of x and y are free from radical signs are
- If n is a positive integer, then ( 3 + 1)^ 2n - ( 3 - 1)^ 2n is
- If the 7th term in the binomial expansion of ( 3 [3] 84 + 3 x )^9, x > 0, is equal to 729 , then x can be:
- The sum of the rational terms in the binomial expansion of (2^ 12 + 3^ 15 )^ 10 is :
- The number of terms in the expansion of (1 + x)^ 101 (1 - x + x^2 )^ 100 in powers of x is
- The coefficient of x^ 50 in the binomial expansion of (1 + x)^ 1000 + x(1 + x)^ 999 + x^2(1 + x)^ 998 + + x^ 1000 is:
- If (2 + x3 )^ 55 is expanded in the ascending powers of x and the coefficients of powers of x in two consecutive terms of the...
- If ^ n C_ r-1 = 56, ^ n C_ r = 28 and ^ n C_ r+1 = 8 then r is equal to
- The number of terms in the expansion of (1+3x+3x^2+x^3)^6 is
- The number of distinct terms in the expansion of (x+y-z)^ 16 is
- The number of real negative terms in the binomial expansion of (1+ix)^ 4n-2 , n N , x>0, is
- The number of rational terms in the expansion of (1+ 2+ [3] 3 )^6 is
- The sum of the rational terms in the expansion of ( 2+ [5] 3 )^ 10 is
- If the 4th term in the expansion of (px+x^ -1 )^m is 2.5 for all x R then
- In the expansion of (1+ax)^n, n N , the coefficients of x and x^2 are 8 and 24 respectively. Then
- In the expansion of (x^3- 1 x^2 )^n, n N , if the sum of the coefficients of x^5 and x^ 10 is 0 then n is
- If the coefficients of the (m+1)th term and the (m+3)th term in the expansion of (1+x)^ 20 are equal then the value of m is
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