If the middle term of the expansion of (3x3+x3)8 is 5670 then sum of all real values of x is equal to (A) 6 (B) 3 (C) 0 (D) 2
A path of length n is a sequence of points (x1,y1), (x2,y2),….,(xn,yn) with integer coordinates such that for all i between 1 and n−1 both inclusive,
either xi+1=xi+1 and yi+1=yi (in which case we say the ith step is rightward)
or xi+1=xi and yi+1=yi+1 ( in which case we say that the ith step is upward ).
This path is said to start at (x1,y1) and end at (xn,yn). Let P(a,b), for a and b non-negative integers, denotes the number of paths that start at (0,0) and end at (a,b).
Number of ordered pairs (i,j) where i=j for which P(i,100−i)=P(i,100−j) is
In the binomial
The coefficients of the (r−1)th,rth and (r+1)th terms in the expansion of (x+1)n are in the ratio 1 : 3 : 5. Find n and r.