Binomial Theorem questions
776 published questions with worked solutions.
- The sum of the coefficients in the expansion of (1+2x+3x^2+ +nx^ n-1 )^2 is
- The first 3 terms in the expansion of (1+ax)^n (n 0) are 1, 6x and 16x^2. Then, the value of a and n are respectively
- The 6^ th term in the expansion of (2x^2- 1 3x^2 )^ 10 is
- If the 6^ th term in the expansion of ( 1 x^ 8/3 +x^2 _ 10 x )^8 is 5600, then value of x is
- The r^ th terms in the expansion of (a+2x)^n is
- The (r+1)^ th term in the expansion of (1-x)^ -4 will be
- The coefficient of x^7 in (1+3x-2x^3 )^ 10 is equal to
- The range of the values of the term independent of x in the expansion of (x ^ -1 + ^ -1 x )^ 10 , [-1,1] is
- The value of (1.002)^ 12 upto fourth place of decimal is
- If the sum of the coefficient in the expansion of (x-2y+3z)^n is 128, then the greatest coefficient in the expansion of (1+x)^n is
- The value of x in the expansion [x+x^ _ 10 x ]^5, if the third term in the expansion is 1000000, is
- The sum of 1+n (1- 1x )+ n(n+1) 2! (1- 1x )^2+ , will be
- If (1+ax)^n=1+8x+24x^2+ , then the values of a and n are
- The last positive integer n such that n-3 3+ n-1 4> n3 is
- If C_r stands for ^nC_r, the sum of the given series 2 ( n2 )! ( n2 )! n! [C_0^2-2C_1^2+3C_2^2- +(-1)^n(n+1)C_n^2 ], where n is...
- If x^ 2k occurs in the expansion of (x+ 1 x^2 )^ n-3 , then
- Statement 1: The coefficient of x^ 3 +2 in the expansion of (a+x)^ (b+x)^ +1 (c+x)^ +2 N is (a+b+c). Statement 2: The coefficient...
- If (1+x)^n=C_0+C_1x+C_2x^2+ +C_nx^n, then the value of C_0+2C_1+3C_2+ +(n+1)C_n will be
- The expansion of 1 (4-3x)^ 1/2 by Only One Correct Option will be valid, if
- The term independent of x in the expansion of ( x3 + 3 2x^2 )^ 10 will be
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