Let the four consecutive compartments made by the lines `2x-3y+1=0 and 3x-5y+2=0` be I, II, III and IV respectively. Let (0, 0) belong to compartment I. We associate four numbers 100, 200, 300 and 400 to the compartments I, II, III and IV respectively. Then the number associated to the compartment in which `(-1, 1)` belong is ...

Two lines 2x-3y=1 and x+2y+3=0 divide the xy plane in four compartments which are named as shown in the figure. Consider the locations of the points (2,-1),(3,2) and (-1,-2)

Three dice having digits 1,2,3,4,5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die-I die-II and die-III respectively. What is the number of possible outcomes such that x gt y gt z ?

The number of solutions of the equations 2x - 3y = 5, x+2y=7 is (i) 1 (ii)2 (iii)4 (iv) 0

Find the cube of each of the following (i) (-7) (ii) 1 2/3 (iii) 2.5 (iv) 0.05

Represent the following complex numbers in the complex plane: (i) 1+2i (ii) 5+7i (iii) 0+0i (iv) i .

A container is divided into two compartments. One compartment contains 2 moles of N_(2) gas at 1 atm and 300 K and other compartment contains H_(2) gas at the same temperature and pressure. Volume of H_(2) compartment is four times the volume of N_(2) compartment [Assuming no reaction under these conditions] If the container containing N_(2) and H_(2) are further heated to 1000 K, forming NH_(3) with 100% yeild calculate the final total pressure.

The oxidation number of hyrogen is (i) 0 (ii) +1 (iii) -1 (iv) + 1 only.