2nd Year Math Notes Chapter 5
Handwritten notes of 2nd year math notes chapter 5 written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of 2nd Year Math Chapter 5 Solution for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Important 2nd year math chapter 5 mcqs for Intermediate part-II students.
- Important Multiple Choice Questions (MCQs) of Chapter No. 5: Linear Inequalities and Linear Programming of 2nd Year Mathematics.
- 1. The equation y^2-16=0 represents two lines.
- (a) Parallel to x-axis (b) Parallel y-axis (c) not || to x-axis (d) not || to y-axis
- 2. The perpendicular distance of the line 3x+4y+10=0 from the origin is
- (a) 0 (b) 1 (c) 2 (d) 3
- 3. The lines represented by ax^2+2hxy+by^2=0 are orthogonal if
- (a) a-b=0 (b) a+b=0 (c) a+b>0 (d) a-b<0
- 4. Every homogenous equation of second degree ax^2+bxy+by^2=0 represents two straight lines
- (a) Through the origin (b) not through the origin (c) two || line (d) two ⊥ar lines
- Important 2nd year math ch 5 mcqs for Intermediate part-II students.
- 5. The equation 10x^2-23xy-5y^2=0 is homogeneous of degree
- (a) 1 (b) 2 (c) 3 (d) more than 2
- 6. The equation y^2-16=0 represents two lines.
- (a) Parallel to x-axis (b) Parallel y-axis (c) not || to x-axis (d) not || to y-axis
- 7. (0,0) is satisfied by
- (a) x-y<10 (b) 2x+5y>10 (c) x-y≥13 (d) None
- 8. The point where two boundary lines of a shaded region intersect is called _____ point.
- (a) Boundary (b) corner (c) stationary (d) feasible
- Important 2nd year maths chapter 5 mcqs solved for Intermediate part-II students.
- 9. If x>b then
- (a) –x>-b (b) –x (c) x (d) –x<-b
- 10. The symbols used for inequality are
- (a) 1 (b) 2 (c) 3 (d) 4
- 11. An inequality with one or two variables has ________ solutions.
- (a) One (b) two (c) three (d) infinitely many
- 12. ax+by
- (a) a=0,b=0 (b) a≠0 ,b≠0 (c) a=0,b≠0 (d) a≠0,b=0,c=0
- 13. The graph of corresponding linear equation of the linear inequality is a line called________
- (a) Boundary line (b) horizontal line (c) vertical line (d) inclined line
- 14. The graph of a linear equation of the form ax+by=c is a line which divides the whole plane into ______ disjoints parts.
- (a) Two (b) four (c) more than four (d) infinitely many
- Important 2nd year maths chapter 5 mcqs for Intermediate part-II students.
- 15. The graph of the inequality x≤b is
- (a) Upper half plane (b) lower half plane (c) left half plane (d) right half plane
- 16. The graph of the inequality y≤b is
- (a) Upper half plane (b) lower half plane (c) left half plane (d) right half plane
- 17. The feasible solution which maximizes or minimizes the objective function is called
- (a) Exact solution (b) optimal solution (c) final solution (d) objective function
- Important 2nd year maths chapter 5 mcqs with answers for Intermediate part-II students.
- 18. Solution space consisting of all feasible solutions of system of linear in inequalities is called
- (a) Feasible solution (b) Optimal solution (c) Feasible region (d) General solution
- 19. Corner point is also called
- (a) Origin (b) Focus (c) Vertex (d) Test point
- 20. For feasible region:
- (a) x≥0,y≥0 (b) x≥0,y≤0 (c) x≤0,y≥0 (d) x≤0,y≤0
- 21. x=0 is in the solution of the inequality
- (a) x<0 (b) x+4<0 (c) 2x+3>0 (d) 2x+3<0
- 22. Linear inequality 2x-7y>3 is satisfied by the point
- (a) (5,1) (b) (-5,-1) (c) (0,0) (d) (1,-1)
- 23. The non-negative constraints are also called
- (a) Decision variable (b) Convex variable (c) Decision constraints (d) concave variable
- 24. If the line segment obtained by joining any two points of a region lies entirely within the region , then the region is called
- (a) Feasible region (b) Convex region (c) Solution region (d) Concave region
- 25. A function which is to be maximized or minimized is called:
- (a) Linear function (b) Objective function (c) Feasible function (d) None of these
- Important 2nd year math chapter 5 important questions for Intermediate part-II students.
- Introduction of linear inequalities and linear programming with examples and key points.
- Linear inequality in two variables
- Half planes
- Associated equation with example
- What is the corner point or vertex of the solution region
- Indicate the solution region of the following system of linear inequalities by shading
- Important 2nd year math exercise 5.1 solution pdf for Intermediate part-II students.
- Problem constraints
- Non-negative constraints
- Feasible region
- Important 2nd year math chapter 5 for Intermediate part-II students.
- Decision variables
- Definition of feasible solution
- Definition of feasible solution set
- Definition of Convex
- Important 2nd year math chapter 5 definitions for Intermediate part-II students.
- Definition of an objective function
- Definition of an optimal solution
- Theorem of linear programming
- Important 2nd year maths chapter 5 exercise 5.1 for Intermediate part-II students.
- Important 2nd year maths chapter 5 exercise 5.2 for Intermediate part-II students.
- Important 2nd year maths chapter 5 exercise 5.3 for Intermediate part-II students.