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

If n parallel straight line in a plane are intersected by a family of m parallel lines, how many parallelograms are there in the network thus formed?

If n parallel straight lines in a plane are intersected by a family of m parallel lines , how many parallelograms are there in the network thus formed ?

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

A rectangle with sides of lengths (2n-1) and (2m-1) units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) m^2n^2 (b) mn(m+1)(n+1) (c) 4^(m+n-1) (d) non of these

m men and n women are to be seated in a row so that no two women sit together. If (m>n) then show that the number of ways in which they can be seated as (m!(m+1)!)/((m-n+1)!) .

m men and n women are to be seated in a row that no two women sit together . If m gt n, then show that the mumber of ways in which they can be sated is (m!(m+1)!)/((m-n+1)!)

If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m+n) terms is (a). m n (b). -m n (c). 1//m n (d). 0

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

sum_(m=1)^(n) tan^(-1) ((2m)/(m^(4) + m^(2) + 2)) is equal to