Binomial Theorem questions
776 published questions with worked solutions.
- The value of _ r=1 ^ 10 r ^ n C_r ^ n C_ r-1 is equal to
- The sum _ r=1 ^ n r ^ 2n C_r is equal to
- The sum 1 ^ 20 C_1-2 ^ 20 C_2+3 ^ 20 C_3- -20 ^ 20 C_ 20 is equal to
- The coefficient of a^ 8 b^ 6 c^ 4 in the expansion of (a+b+c)^ 18 is
- The term independent of x in the expansion of (1+x)^ n (1- 1x )^ n is
- The coefficient of the (r+1)th term of (x+ 1x )^ 20 when expanded in the descending powers of x is equal to the coefficient of...
- If (1+x)^ 2n =a_0+a_1x+a_2x^2+ +a_ 2n x^ 2n then
- In the expansion of ( [3] 4 + 1 [4] 6 )^ 20 ,
- Let n N. If (1+x)^ n =a_0+a_1x+a_2x^2+ +a_nx^ n , and a_ n-3 ,a_ n-2 ,a_ n-1 are in AP then
- Let R=(8+3 7)^ 20 and [R]= the greatest integer less than or equal to R. Then
- 1 1! ,(n-1)! + 1 3! ,(n-3)! + 1 5! ,(n-5)! + is equal to
- In the expansion of (x+y+z)^ 25
- (1-x)^ 3/2 can be expanded in ascending powers of x if
- (3+x)^ p/q can be expanded in ascending powers of x if
- If x is positive, the first negative term in the expansion of (1+x)^ 27/6 is the
- In the expansion of (2+x)^ -5/2 , the coefficient of x^4, if it exists, is
- If x^2+x 1-x = a_1x + a_2x^2 + to , |x| < 1, then
- If |x| < 1, the coefficient of x^3 in the expansion of 1 e^x (1+x) is
- The constant term in the expansion of x + _e(1-x) x^3 is
- In the expansion of _ 10 (1-x), |x| < 1, the coefficient of x^n is
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