Binomial Theorem questions
776 published questions with worked solutions.
- ^nC_r+2 , ^nC_ r-1 + ^nC_ r-2 is equal to
- If n is even, ^nC_0< ^nC_1< ^nC_2< < ^nC_r> ^nC_ r+1 > ^nC_ r+2 > > ^nC_n, then r=
- The value of ^7C_0+2 ( ^7C_1+ ^7C_2+ + ^7C_6 )+ ^7C_7 is 2^m+n where m>7. Find m+n.
- In the expansion of (1+x+x^2+x^3 )^6, then coefficient of x^ 14 is
- The ninth term of the expansion (3x- 1 2x )^8 is
- In the expansion of (x- 1x )^6, the coefficient of x^0 is
- In the binomial expansion of (a-b)^n, n 5, the sum of 5^ th and 6^ th terms is zero, then ab equals
- If in expansion of (1+x)^ 21 , the coefficient of x^r and x^ r+1 be equal, then r is equal to
- If (1+x)^ 15 =a_0+a_1x+ +a_ 15 x^ 15 , then _ r=1 ^ 15 r a_r a_ r-1 is equal to
- If the second term in the expansion [ [13]a + a a^ -1 ]^n is 14a^ 5/2 , then the value of ^nC_3 ^nC_2 is
- 1+ 24+ 2 5 4 8 + 2 5 8 4 8 12 + 2 5 8 11 4 8 12 16 + is
- If x^ 2r occurs in (x+ 2 x^2 )^n, then n-2r must be of the form
- If the coefficient of x^7 in (ax^2+ 1 bx )^ 11 equal the coefficient of x^ -7 in (ax- 1 bx^2 )^ 11 , then a and b satisfy the...
- If the coefficient of r^ th and (r+1)^ th terms in the expansion of (3+7x)^ 29 are equal, then r equals
- If in the expansion of (a-2b)^n, the sum of the 5^ th and 6^ th term is zero, then the value of ab is
- If |x|< 12, then the coefficient of x^r in the expansion of 1+2x (1-2x)^2 is
- The coefficient of x^5 in the expansion of (1+x^2 )^5(1+x)^4 is
- If the fourth term in the expansion of (ax+ 1x )^n is 52, then
- The two consecutive terms in the expansion of (3+2x)^ 74 whose coefficient are equal, are
- If the coefficient of x^2 and x^3 in the expansion of (3+ax)^9 be same, then the value of a is
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