Binomial Theorem questions
776 published questions with worked solutions.
- Suppose bmatrix _ k=0 ^ n k & _ k=0 ^ n ^nC_kk^2 _ k=0 ^ n ^nC_kk & _ k=0 ^ n ^nC_k3^k bmatrix =0 holds for some positive integer...
- The value of [C(7, 0)+C(7, 1)]+[C(7, 1)+C(7, 2)]+ +[C(7, 6)+C(7, 7)] is
- The expansion of (x-y)^n, n 5 is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then x y is...
- The number of terms in the expansion of (x+a)^ 100 +(x-a)^ 100 after simplification is
- In the expansion of (1+x)^ 50 , the sum of the coefficients of odd powers of x is
- In the expansion of (1+x)^ 43 , if the coefficients of (2r+1)^ th and (r+2)^ th terms are equal, then what is the value of r (r...
- If the coefficients of a^m and a^n in the expansion of (1+a)^ m+n are and , then which one of the following is correct?
- What is the number of non-zero terms in the expansion of (1+2 3 x)^ 11 +(1-2 3 x)^ 11 (after simplification)?
- What is C(n, r)+2C(n, r-1)+C(n, r-2) equal to?
- What is the coefficient of the middle term in the binomial expansion of (2+3x)^4?
- Let the coefficient of the middle term of the binomial expansion of (1+x)^ 2n be and those of two middle terms of the binomial...
- How many terms are there in the expansion of (1+2x+x^2)^5+(1+4y+4y^2)^5?
- If the middle term in the expansion of (x^2+ 1 x )^ 2n is 184756x^ 10 , then what is the value of n?
- If the constant term in the expansion of ( x - k x^2 )^ 10 is 405, then what can be the values of k?
- What is C(47, 4)+C(51, 3)+C(50, 3)+C(49, 3)+C(48, 3)+C(47, 3) equal to?
- The term independent of x in the binomial expansion of ( 2 x^2 - x )^ 10 is equal to
- If (1+2x-x^2)^6=a_0+a_1x+a_2x^2+ +a_ 12 x^ 12 , then what is a_0-a_1+a_2-a_3+a_4- +a_ 12 equal to?
- What is the sum of the last five coefficients in the expansion of (1+x)^9 when it is expanded in ascending powers of x?
- How many terms are there in the expansion of (1+ 2 x )^9 (1- 2 x )^9?
- Consider the following statements in respect of the expansion of (x+y)^ 10 : 1. Among all the coefficients of the terms, the...
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