Number of points of intersection of `n` straight lines if `n` satisfies `n+5P_(n+1)=(11(n-1))/2xx^(n+3)P_n` is a. `15` b. `28` c. `21` d. 10

Number of points of intersection of n straight lines if n satisfies .^(n+5)P_(n+1)=(11(n-1))/(2)xx.^(n+3)P_(n) is

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

If .^(n+1)P_(3)=10.^(n-1)P_(2) , find n.

The number of positive integers satisfying the inequality .^(n+1)C_(n-2) - .^(n + 1)C_(n - 1) le 100 is

If P_(n) denotes the product of all the coefficients of (1+x)^(n) and 9!P_(n+1)=10^(9)P_(n) then n is equal to

The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))+1)^(n) is (a) 2n (b) 3n (c) 2n+1 (d) 3n+1

There are n is straight lines in a plane in which no two are parallel and no three pass through the same point their points of intersection are joined show that the number of fresh lines thus introduced is (1/8)n(n-1)(n-2)(n-3)

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

If .^(n)P_(5)=20.^(n)P_(3) , find n.

If 16.^(15)P_(n)=13.^(16)P_(n) , find n.