ECAT Pre General Science Mathematics Chapter 21 Linear Inequalities and Linear Programming Online Test

3x + 4 = 0 is

• not inequality A
• equation B
• identity C
• inequality D

A point of a solution region where two of its boundary lines intersect, is called

• Boundary A
• Inequality B
• Half plane C
• Vertex D

A point where two of its boundary lines intersect is called

• Corner point A
• Feasible point B
• Vertex C
• Feasible solution D

There may be ______ feasible solution in the feasible region

• Infinite A
• Finite B
• Defined C
• None of above D

A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivations of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours per hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 15 per hectometer for wheat. The profit function for the farmer is

• P(x, y) = 20x + 15y A
• P(x, y) = 2x + 3y B
• P(x, y) = x + y C
• P(x, y) = 3x + 2y D

x = 0 is in the solution of the inequality

• x > 0 A
• 3x + 4 < 0 B
• x + 3 < 0 C
• x - 2 < 0 D

Which is not a half plane

• ax + by < c A
• ax + by > c B
• Both A and B C
• None D

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None D

3x + 4 < 0 is

• not inequality A
• equation B
• identity C
• inequality D

3x + 4 > 0 is

• equation A
• inequality B
• identity C
• none of these D

Each point of the feasible region is called

• Solution A
• feasible solution B
• Both a & b C
• None D

ax + by < c is linear inequality in

• four variables A
• three variables B
• two variables C
• one variable D

• p < r A
• p > rr B
• p + r < 0 C
• p - r < 0 D

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is

• 120 A
• 100 B
• 140 C
• 160 D

If x < y, 2x = A, and 2y = B, then

• A = B A
• A < B B
• A < x C
• B < y D

The graph of the linear equation of the form ax =by = c is a line which divided the plane into:

• Two similar regions A
• Two disjoint regions B
• Four equal parts C
• One region D

The point (1,3) is one solution of

• 3x + 5y > 29 A
• 3x + 5y < 7 B
• x + 2y < 4 C
• x + 4y > 3 D

Order (or sense) of an inequality is changed by multiplying or dividing its each side by a:

• Zero A
• one B
• negative constant C
• Non negative constant D

The solution set of x < 4 is

• -∞< x < 4 A
• -∞> x > 4 B
• -∞< x < 2 C
• -∞> x > 2 D

Optimize means ______ a quantity under certain constraints

• Minimize A
• Maximize B
• Maximize or minimize C
• None of these D

The graph of y> 0 is the upper - half of:

• y-axis A
• x-axis B
• 1st and 4th quandrant C
• 2nd and 3rd quadrant D

(1, 1) is the in the solution of the inequality

• 3x + 4y > 3 A
• 2x + 3y < 2 B
• 4x = 3y > 5 C
• 2c - 3y > 2 D

The feasible region which can be enclosed within a circle is called

• Bounded region A
• Convex region B
• Unbounded region C
• None D

The corner point of the boundary lines, x-2y

2x + y = 2 is:

• (2,6) A
• (6,2) B
• (-2,2) C
• (2,-2) D

The points (x, y) which satisfy a linear inequality in two variables x and y from its

• domain A
• range B
• solution C
• none of these D

x = -1 is in the solution of the inequality

• x + 5 < 0 A
• 2x + 3 < 0 B
• x > 0 C
• 2x + 3 > 0 D

x = ________ is in the solution of 2x + 3 > 0

• 1 A
• -2 B
• -3 C
• -4 D

Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y≥ 2,x +2y≤ 8, x≥ 0,y ≥ 0

• (1,0) A
• (0,4) B
• (3,0) C
• (8,0) D

The liner equation ax + by = c is called _________ of the inequality ax +by > c.

• Associated equation A
• Non-associated equation B
• disjoint equation C
• Feasible equation D

ab > 0 and a > 0 then

• a > b A
• a < b B
• a = b C
• None D