There are three routes `R_1,R_2and R_3` from Madhu's home to her place of work. There are four parking lots `P_1, P_2, P_3, P_4` and three entrances `B_1, B_2, B_3` into the office building. There are two elevatos `E_1 and E_2` to her floor. Using the tree diagram explain how many ways can she reach her office?

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P.show that its sides are in A.P .

If P stands for P_(r) then the sum of the series 1 + P_(1) + 2P_(2) + 3P_(3) + …+ nPn is

Consider the sets A ={p,q,r,s} and B={1,2,3,4}. Are they equal?

The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , ba n dc are in AdotPdot

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_3=p vec r_1+q vec r_2, then show that p+q=1.

If a_1, a_2, a_3(a_1>0) are three successive terms of a G.P. with common ratio r , for which a_3>4a_2-3a_1 holds is given by

For the three events A ,B ,a n dC ,P (exactly one of the events AorB occurs) =P (exactly one of the two evens BorC ) =P (exactly one of the events CorA occurs) =pa n dP (all the three events occur simultaneously) =p^2w h e r e 0 < p < 1//2. Then the probability of at least one of the three events A ,Ba n dC occurring is a. (3p+2p^2)/2 b. (p+3p^2)/4 c. (p+3p^2)/2 d. (3p+2p^2)/4

There are three coplanar parallel lines. If any p points are taken on each of the lines, the maximum number of triangles with vertices on these points is a. 3p^2(p-1)+1 b. 3p^2(p-1) c. p^2(4p-3) d. none of these