Mathematics - Online Test

We have 2 + x < 6

⇒2 + x −2< 6−2

 ⇒x<4

Now 2−3x<−1⇒2−3x−2<−1−2⇒−3x<−3⇒−3x−3>−3−3⇒x>1

Hence the solution of the given system of equations is given by 1<x<4,xϵZ⇒x=2,3

Objective function is Z = 3x + 5 y ……………………(1).
The given constraints are : x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0 .

The corner points obtained by drawing the lines x+3y=3 and x+y=2 are (0,0), (3,0),(0,2) and (3/2,1/2)

Here Z = 7 is minimum at ( 3/2 , ½ ) .

Let R and S be two relations from sets A to B and B to C respectively.Then we can define a relation S∘R

from A to C such that  (a,c)∈S∘R this relation is called the composition of R and S.

Rhombus is a parallelogram in which the opposite sides are equaland parallel.

Therefore the lines y = mx and y = -2x are parallel, similarly y = 2x+ λ and y = -mx + λ are parallel.

If two lines are equal, then their slopes are qual

This implies  m = -2