`n` lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. `sum_(k=1)^(n-1)k` b. `n(n-1)` c. `n^2` d. none of these

25 lines are drawn in a plane. Such that no two of them are parallel and no three of them are concurrent. The number of points in which these lines intersect, is:

If 20 lines are drawn in a plane such that no two of them are parallel and so three are concurrent, in how many points will they intersect each other?

If n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent, such that these lines divide the planein 67 parts, then find number of different points at which these lines will cut.

sum_(k=1)^ook(1-1/n)^(k-1)=>? a. n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is a. 1/4m n(m-1)(n-1) b. 1/4m n(m-1) c. 1/4m^2n^2 d. none of these

There are n 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 1/8n(n-1)(n-2)(n-3)

There are n 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 1/8n(n-1)(n-2)(n-3)

There are n straight lines in a plane such that n_(1) of them are parallel in onne direction, n_(2) are parallel in different direction and so on, n_(k) are parallel in another direction such that n_(1)+n_(2)+ . .+n_(k)=n . Also, no three of the given lines meet at a point. prove that the total number of points of intersection is (1)/(2){n^(2)-sum_(r=1)^(k)n_(r)^(2)} .

The value of sum_(r=0)^(n-1)^n C_r//(^n C_r+^n C_(r+1)) equals a. n+1 b. n//2 c. n+2 d. none of these

If n is a whole number such that n+n=n ,\ t h e n\ n=? (a) 1 (b) 2 (c) 3 (d) none of these