ECAT Mathematics Chapter 21 online mcq test with answers for chapter 21 (Linear Inequalities and Linear Programming)

Question # 1

A point where two of its boundary lines intersect is called

Corner point A
Feasible point B
Vertex C
Feasible solution D

Question # 2

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

Question # 3

x = 0 is in the solution of the inequality

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

Question # 4

x = -1 is in the solution of the inequality

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

Question # 5

Which is in the solution set of 4x - 3y < 2

(3, 0) A
(4, 1) B
(1, 3) C
None D

Question # 6

The solution set of x < 4 is

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

Question # 7

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

Question # 8

Optimal solution is found by evaluation the objective function at

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

Question # 9

Multiplying each side of an inequality by (-1) will:

Not effect A
Change the sign B
Become zero C
Not defined D

Question # 10

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

Question # 11

3x + 4 > 0 is

equation A
identity B
inequality C
none of these D

Question # 12

A function which is to be maximized or minimized is called an

Explicit function A
Implicit function B
Objective function C
None D

Question # 13

(0,1) is in the solution of the inequality

3x + 2y > 8 A
2x - 3y < 4 B
2x + 3y > 5 C
x -2y < -5 D

Question # 14

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

Question # 15

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

Boundary A
Inequality B
Half plane C
Vertex D

Question # 16

The point ________ is in the solution of the inequality 2x - 3y > 5

(1, -1) A
(2,2) B
(0,0) C
(3,0) D

Question # 17

The point (1,3) is one solution of

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

Question # 18

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

Question # 19

There may be ______ feasible solution in the feasible region

Infinite A
Finite B
Defined C
None of above D

Question # 20

The real numbers which satisfy an inequality form its

solution A
coefficient B
domain C
range D

Question # 21

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

2x + y > 7 A
x - y > 2 B
3x + 5y < 6 C
2x + y < 6 D

Question # 22

Sum of two quantities is at least 20 is denoted by

x +y =20 A
x +y≥ 20 B
x +y≠ 20 C
x +y≤20 D

Question # 23

Optimize means ______ a quantity under certain constraints

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

Question # 24

An expression involving any of the symbols <,>,< or > is called

equation A
inequality B
linear equation C
identity D

Question # 25

3x + 4 < 0 is

not inequality A
equation B
identity C
inequality D

Question # 26

A ________ divides the plane into left and right half planes.

Vertical line A
Horizontal line B
Non vertical line C
Inequality D

Question # 27

The graph of y < 2 is the

Left half plane A
upper half plane B
Right half plane C
Lower half plane D

Question # 28

Each point of the feasible region is called

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

Question # 29

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

Bounded region A
Convex region B
Unbounded region C
None D

Question # 30

Maximum value of z =15x +20y subject to 3x+ 4y≤ 12,x,y≥ 0 is given by

46 A
60 B
50 C
70 D

Sr.#	Question	Answer
1	The solution set of the inequality ax + by < c is	A. straight line B. half plane C. parabola D. none of these
2	The graph of y> 0 is the upper - half of:	A. y-axis B. x-axis C. 1st and 4th quandrant D. 2nd and 3rd quadrant
3	Which is not a half plane	A. ax + by < c B. ax + by > c C. Both A and B D. None
4	The corner point of the boundary lines, x-2y 2x + y = 2 is:	A. (2,6) B. (6,2) C. (-2,2) D. (2,-2)
5	(2, 1) is in the solution of the inequality	A. 2x + y > 7 B. x - y > 2 C. 3x + 5y < 6 D. 2x + y < 6
6	The real numbers which satisfy an inequality form its	A. solution B. coefficient C. domain D. range
7	A function which is to be maximized or minimized is called an	A. Explicit function B. Implicit function C. Objective function D. None
8	(1, 1) is the in the solution of the inequality	A. 3x + 4y > 3 B. 2x + 3y < 2 C. 4x = 3y > 5 D. 2c - 3y > 2
9	A point of a solution regions where two of its boundary lines intersect, is called:	A. Vertex of the solution B. Feasible point C. Point of inequality D. Null point of the solution region
10	Each point of the feasible region is called	A. Solution B. feasible solution C. Both a & b D. None

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