“Learn about linear inequalities and linear programming, techniques used to solve optimization problems by finding the best outcome within given constraints.”
Mathematic 12 Class Chapter 5 Notes
The inequality x < a is the closed half plane to the _________ of the boundary line x = a: Left
A function which is to be maximized or minimized is called: Objective function
A solution of a linear inequality in x and y is an ordered pair of numbers, which _______ the inequality: Satisfies
The inequality x > a is the open half plane to the ____________ of the bounding line x = a: Right
The system of _______ involved in the problem concerned is called problem constraints: Linear inequalities
The variables used in the system of linear inequality relating to the problems of every day life are: Non-negative
ax+by+c > 0 is an: Inequality
ax + b < c is linear inequality in: one variables
The maximum or minimum values of the objective function occur in feasible region at: Corner points
Ax2 + By2 + Gx + Fy + C = 0 form hyperbola if: A
ax + b > c is an inequality of: One variable
The centre of the circle (x – 5)2 + (y-3)2 = 8 is: (5, 3)
The feasible region is _______ if it cannot be enclosed in a circle: Unbounded
A point of a solution region where two of its boundary lines intersects is called a ______ of the solution region: Vertex
Point (1, 2) lies in the region of inequality: 2x + y < 5
A function which is to be maximized or minimized is called an: Objective function
Non-vertical lines divide the plane into ________ half plane: Upper and lower
The graph of the inequality ax + by < c is: Half plane
The graph of 2x + y > 2 is the closed half plane the region is _________ the origin side of 2x + y =2: Not on
ax = by < c is an inequality of two variables: Two variable
The inequality x < a is the open half plane to the ___________ of the boundary line x = a: Left
There are _________ ordered pairs that satisfy the inequality ax + by < c: ax + by = c
x = 01 is solution of inequality: 2x + 3 > 0
A non-vertical line divides the plane into two half planes: Upper & lower
The feasible solution which maximum or minimize the objective function is called the: Feasible solution
The operation _________ by a positive constant to each side of inequality will not effect the order (or sense) of inequality: Dividing
(0, 0) is in the solution of inequality: 3x + 5y > 7
ax+by<c is a linear inequality in: Two variables
Solution of inequality x + 2y < 6 is: (1, 1)
ax+b<0 is an: Inequality
(1,3) is one of the solutions of the inequality: 3x+5y>29
An expression involving any one of the symbols <,<,>,> is called: Inequality
(2, 1) is in the solution of inequality: 2x + y < 6
A point (x,y) which satisfy a linear inequality in teo variables x & y form its: Solution
The vertex of parabola x2 – 4x – 8y + 4 = 0 is: (2, 0)
The point (-1, 2) satisfied the inequality: x + y < 4
The solution of ax + by ? c is: closed half plane
For inequalities 2x + y < 10 and x + 4y < 12, the corner point: (4, 2)
The order (or sense) of an inequality is change by ____________, it each side by a negative constant: Dividing
A point of a solution region where two of its boundary lines intersects is called a ____________ of the solution region: Vertex
Ax2 + By2 + Gx + Fy + C = 0 form ellipse if: A
(1,0) is in the solution of inequality: 3x +5y < 7
(0,1) is not the solution of inequality: x +3y < 0
The graph of 2x + y > 2 is the open half plane the region is ________ the origin side of 2x + y = 2: Not on
ax + by > c is an inequality of two variables: Two variable
There are _______ ordered pairs that satisfy the inequality ax + by > c: Infinitely many
If ax+by: Associated equation
The graph of linear equation of the form ax + by = c is a line, which divides the plane into _________ disjoint regions, where a, b and c are constants and a, b are not both zero: Two
Which one satisfies the inequality x + 2y < 6: (3, 1)
There are ______ ordered pairs that satisfy the inequality ax + by > c: Infinitely many
For different values of k, the equation 4x + 5y = k represents lines ________ to the line 4x + 5y = 0: Parallel
The graph of 2x + y <2is the closed half plane the region is _________ the origin side of 2x + y = 2: On
If equations of sides of the triangle are given, then intersection of any two lines give a: Vertex of the triangle
The graphs of ax+by: Closed half plane
The operation ________ by a positive constant to each side of inequality will not effect the order (or sense) of inequality: Dividing
A vertical line divides a plane into ______ half planes: Left and right
(2,1) is one of the solutions of the inequality: 2x+y<7
ax + by < C is linear inequality in variables”: 2
If a function f(x, y) have same maximum value at any two points, then it is _________ at all the points of the line segment between these point: Maxnimum
Medians of a triangle are: Concurrent
x = 0 is not in the solution of inequality: x + 4 > 0
The region of the graph ax + by > c is called _________ half plane: Open
The inequality ax +by < C when a = 0 represents __________ half plane:Upper or lower
y = b is a horizontal line perpendicular to: y-axis may be
Point (1, 2) lies in the solution region of the inequality: x + 3y > 5
The region of the graph ax + by < is called __________ half plane: Closed
(1, 0) is the solution of inequality: 3x + 5y < 6
If the segment obtained by joining any two points of a region lies entirely with in the region, then the region is called: Convex
Which one is a solution of inequality 2x + 3y < 0: (-1, -2)
ax + b < c is an inequality of one variable: One variable
ax+b ? 0 is an: Inequality
The region of the graph ax + by < c is called ________ half plane: Closed
x = 4 is the solution of inequality: x + 3 > 0
(0,1) is in the solution of inequality: x +y < 2
Each point of the feasible region is called: Feasible solution
The graph of the inequality ax+by<c is: Half plane
A point does not lie in the feasible region is ________ corner point of the feasible region: Not a
Two non-parallel lines interest each other at: Only one point
The point (1, 2) satisfies inequality: x + 2y > 3
If r = 0 then x2 + y2 = r2 is called ————— circle: Point
There are ________ ordered pairs that satisfy the inequality ax + by < c: Infinitely many
x = – 5 is in the solution of: 2x + 3 < 0
The region of the graph ax + by < c is called ______ half plane: Open
The inequality y < b is the open half plane to the __________ of the boundary line y = b: Below
The operation ___________ a constant to each side of inequality will not affect the order (or sense) of inequality: Adding
x = c is a vertical line parallel to: y-axis
The non-negative constraints are called: Decision variables
To find the optimal solution evaluate the objective function at: Corner points
ax+b>0 is an: Inequality
The ordered pair _____ is a solution of the inequality x + 2y < 6: (1, 1)
ax+by+c ? 0 is an: Inequality
The focus of parabola y2 = -8x is: (-2, 0)
The feasible region is __________ if it can easily be enclosed within a circle: Bounded
(3, 2) is not in the solution of inequalit: 3x + 5y < 8
ax + b < c is an inequality of one variable: One variable
A vertical line divides the plane into two half planes: Left & right
ax < b is an inequality of one variable: One variable
There are ___________ ordered pairs that satisfy the inequality ax + by < c: Infinitely many
The operation __________ a constant to each side of inequality will not effect the order (or sense) of inequality: Subtracing
x = a is a vertical line perpendicular to: x – axis
Important : Review all previous years’ 12 Class Past Papers for comprehensive practice and better exam preparation.