#### Chapters

Chapter 1.2: Matrics

Chapter 1.3: Trigonometric Functions

Chapter 1.4: Pair of Lines

Chapter 1.5: Vectors and Three Dimensional Geometry

Chapter 1.6: Line and Plane

Chapter 1.7: Linear Programming Problems

Chapter 2.1: Differentiation

Chapter 2.2: Applications of Derivatives

Chapter 2.3: Indefinite Integration

Chapter 2.4: Definite Integration

Chapter 2.5: Application of Definite Integration

Chapter 2.6: Differential Equations

Chapter 2.7: Probability Distributions

Chapter 2.8: Binomial Distribution

## Chapter 2: Linear Programming Problems

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems MCQ

#### 2 marks each

The corner points of the feasible solutions are (0, 0) (3, 0) (2, 1) (0, 7/3) the maximum value of Z = 4x + 5y is

12

13

35/3

0

The half plane represented by 4x + 3y >14 contains the point

(0, 0)

(2, 2)

(3, 4)

(1, 1)

The feasible region is the set of point which satisfy.

The object functions

All the given constraints

Some of the given constraints

Only one constraint

**Choose the correct alternative:**

Objective function of LPP is

A constraint

A function to be maximized or minimized

A relation between the decision variables

A feasible region

Equation of straight line

The value of objective function is maximum under linear constraints

At the center of the feasible region

At (0, 0)

At vertex of feasible region

At (−1, −1)

If a corner point of the feasible solutions are (0, 10) (2, 2) (4, 0) (3, 2) then the point of minimum Z = 3x + 2y is

(2, 2)

(0, 10)

(4, 0)

(3, 2)

The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at

(30, 25)

(20, 35)

(35, 20)

(40, 15)

A solution set of the inequality x ≥ 0

Half plane on the Left of y-axis

Half plane on the right of y axis excluding the point on y-axis

Half plane on the right of y-axis including the point on y-axis

Half plane on the upword of x-axis

Which value of x is in the solution set of inequality − 2X + Y ≥ 17

− 8

− 6

− 4

12

The graph of the inequality 3X − 4Y ≤ 12, X ≤ 1, X ≥ 0, Y ≥ 0 lies in fully in

I quadrant

II quadrant

III quadrant

IV quadrant

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems Short Answers I

#### 2 marks

**Solve each of the following inequations graphically using XY-plane:**

4x - 18 ≥ 0

Sketch the graph of inequation x ≥ 5y in xoy co-ordinate system

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

Find the feasible solution of linear inequation 2x + 3y ≤ 12, 2x + y ≤ 8, x ≥ 0, y ≥ 0 by graphically

Solve graphically: x ≥ 0 and y ≥ 0

Find the solution set of inequalities 0 ≤ x ≤ 5, 0 ≤ 2y ≤ 7

**Find the feasible solution of the following inequation:**

3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥** **0

Draw the graph of inequalities x ≤ 6, y −2 ≤ 0, x ≥ 0, y ≥ 0 and indicate the feasible region

Check the ordered points (1, −1), (2, −1) is a solution of 2x + 3y − 6 ≤ 0

Show the solution set of inequations 4x – 5y ≤ 20 graphically

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 2 Linear Programming Problems Long Answers II

#### 4 Marks

Maximize z = 5x + 2y subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0

Maximize z = 7x + 11y subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0

Maximize z = 10x + 25y subject to x + y ≤ 5, 0 ≤ x ≤ 3, 0 ≤ y ≤ 3

Maximize z = 3x + 5y subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0 also find the maximum value of z

Minimize Z = 8x + 10y subject to 2x + y ≥ 7, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0

Minimize z = 7x + y subjected to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0

Minimize z = 6x + 21y subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points

Minimize z = 2x + 4y is subjected to 2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 show that the minimum value of z occurs at more than two points

Maximize z = −x + 2y subjected to constraints x + y ≥ 5, x ≥ 3, x + 2y ≤ 6, y ≥ 0 is this LPP solvable? Justify your answer

x − y ≤ 1, x − y ≥ 0, x ≥ 0, y ≥ 0 are the constant for the objective function z = x + y. It is solvable for finding optimum value of z? Justify?

## Chapter 2: Linear Programming Problems

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 - Linear Programming Problems

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 2 Linear Programming Problems are Linear Inequations in Two Variables, Linear Programming Problem (L.P.P.), Lines of Regression of X on Y and Y on X Or Equation of Line of Regression, Graphical Method of Solving Linear Programming Problems, Linear Programming Problem in Management Mathematics.

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