We provide linear programming practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on linear programming skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of linear programming Questions

Question No | Questions | Class |
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1 | If the replacement set ( = ) {-6,-3,0,3,6,9}( ; ) find the truth set of the following: ( 2 x-1>9 ) A ( cdot{6,9} ) в. {2,6} c. {7,3} D. {5,8} | 12 |

2 | Solve the inequalities for real ( x ) ( 3(2-x) geq 2(1-x) ) | 12 |

3 | The solution set of ( 6 x-1>5 ) is ( mathbf{A} cdot{x mid x<1, x in R} ) B . ( {x mid x1, x in W} ) D cdot ( {x mid x>1, x in R} ) | 12 |

4 | Solve the following problem graphically: Minimise and Maximise ( boldsymbol{z}=mathbf{3} boldsymbol{x}+mathbf{9} boldsymbol{y} ) Subject to the constraints: ( boldsymbol{x}+mathbf{3} boldsymbol{y} leq mathbf{6 0} ) ( boldsymbol{x}+boldsymbol{y} geq mathbf{1 0} ) ( boldsymbol{x} leq boldsymbol{y} ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

5 | The velocity of an object fired directly upward is given by ( V=80-32 t ), where ( t ) is in seconds. When will the velocity be between 32 and 64 feet per second? A. The velocity will be between 32 and 64 feet per second between 0.8 seconds after launch and 1.5 seconds after launch. B. The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch. C. The velocity will be between 32 and 64 feet per second between 0.4 seconds after launch and 1.2 seconds after launch. D. None of the above | 12 |

6 | A dietician wishes to mix two types of foods in such away that the vitamin contents of the mixture contains at least 8 units of vitamin ( A ) and 10 units of vitamin C. Food I contains 2 units/kg of vitamin ( A ) and 1 unit/kg of vitamin ( C ) while Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin 1 unit/kg of vitamin C. It costs ( R s .5 ) per kg to purchase food I and ( R s .7 ) per kg to purchase Food II. Determine the maximum cost of such a mixture. Formulate the above as a LPP and solve t graphically. | 12 |

7 | Solve the inequality and represent the solution graphically on number line. ( 5(2 x-7)-3(2 x+3) leq 0,2 x+19 leq ) ( mathbf{6} boldsymbol{x}+mathbf{4 7} ) | 12 |

8 | Construct the graphs of the following functions. ( boldsymbol{y}=mathbf{1} /|boldsymbol{x}| ) | 12 |

9 | Show that the minimum of ( Z ) occurs at more than two points. Minimise and Maximise ( Z=x+2 y ) subject to ( x+2 y geq 100,2 x-y leq ) ( mathbf{0}, mathbf{2} boldsymbol{x}+boldsymbol{y} leq mathbf{2 0 0} ; boldsymbol{x}, boldsymbol{y} geq mathbf{0} ) | 12 |

10 | Solve the given inequalities graphically: ( boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 0}, boldsymbol{x}+boldsymbol{y} geq mathbf{1}, boldsymbol{x}-boldsymbol{y} leq mathbf{0}, boldsymbol{x} geq ) | 12 |

11 | Lovish has 6 hours to spend in Ha Ha Tonka State Park. He plans to drive around the park at an average speed of 20 miles per hour, looking for a good trail to hike. Once he finds a trial he likes, he will spend the remainder of his time hiking it. He hopes to travel more than 60 miles total while in the park. If he hikes at an average speed of 1.5 miles per hour, which of the following systems of inequalities can be solved for the number of hours Lovish sends driving d, and the number of hours he spends hiking, h while he is at the park? A. ( 1.5 h+20 d>60, h+d leq 6 ) B. ( 1.5 h+20 d>60, h+d geq 6 ) ( c cdot 1.5 h+20 d6, h+d leq 60 ) | 12 |

12 | Find solution of following inequality, also show it graphically: [ boldsymbol{x}+mathbf{3} leq mathbf{5}, boldsymbol{x} in boldsymbol{Z} ] ( A ) begin{tabular}{rrrrrrrrrr} hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 end{tabular} B. begin{tabular}{rrrrrr} hline & & & & & & \ hline-2 & -1 & 0 & 1 & 2 & 3 end{tabular} ( c ) ( underbrace{longleftarrow}_{-2}-1 quad_{0} quad_{1} quad_{2} quad_{1} ) ( D ) begin{tabular}{rrrrrr} hline & 1 & 1 & & & 1 \ -2 & -1 & 0 & 1 & 2 & 3 end{tabular} | 12 |

13 | A sweet-shop makes gift packet of sweets by combining two special types of sweets ( A ) and ( B ) which weigh ( 7 k g ) Atleast ( 3 k g ) of ( A ) and no more than ( 5 k g ) of ( B ) should be used. The shop makes a profit of Rs. 15 on ( A ) and ( operatorname{Rs} .20 ) on ( B ) per kg. Determine the product mix so as to obtain maximum profit | 12 |

14 | Solve the inequality and show the graph of the solution on number line: ( 3 x-2<2 x+1 ) | 12 |

15 | If the system of inequalities ( y geq 2 x+1 ) and ( y>frac{1}{2} x-1 ) is graphed in the ( x y ) plane above, which quadrant contains no solutions to the system? B. Quadrant III c. Quadrant IV D. There are solutions in all four quadrants | 12 |

16 | Solve the inequalities for real ( x ) ( frac{3(x-2)}{5} leq frac{5(2-x)}{3} ) | 12 |

17 | Solve by graphical method: ( y-2 x leq ) ( mathbf{1}, boldsymbol{x}+boldsymbol{y} leq mathbf{3}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

18 | Use graphical method Maximize: ( boldsymbol{z}=mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y} ) Subject to: ( x+2 y leq 40 ) ( 6 x+5 y leq 150 ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

19 | Using graphical method Find the corner points for ( 2 x+5 y leq 25 ) ( 6 x+5 y leq 45 ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

20 | Solve: ( 6 leq-3(2 x-4)<12 ) | 12 |

21 | The quantity of ( A ) and ( B ) in one day for which profit will be maximum is: A .25,30 B. 30,25 c. 25,25 D. 30,30 | 12 |

22 | Solve the following inequalities. ( frac{2-5 x}{x+1}>2 ) | 12 |

23 | a) A manufacturing company makes two models ( A ) and ( B ) of a product. Each piece of model ( A ) requires 9 labor hours for fabricating and 1 labor hour for finishing. Each piece of model ( boldsymbol{B} ) requires 12 labor hours for finishing and 3 labor hours for finishing. For fabricating and finishing, the maximum labor hours available are: 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model ( A ) and Rs. 12000 on each piece of model ( B ). How many pieces of model ( A ) and model ( B ) should be manufactured per week to realize a maximum profit? What is the maximum profit per week? b) Find the value of ( K ) so that the function ( f(x)=left{begin{array}{ll}K x+1, & text { if } x leq 5 \ 3 x-5, & text { if } x leq 5end{array} ) at right. ( x=5 ) is a continuous function. | 12 |

24 | ( 4 x+1 geq 17, ) where ( x in N ) A ( cdot{5,6,7, ldots} ) в. ( {4,5,6, ldots} ) c. ( {1,2,3, ldots} ) D. None of these | 12 |

25 | If ( 3 x+7 leq 1, ) where ( x in Z, ) then find values of ( x ) A ( cdot{2,2} ) в. ( {-2,-3,-4, ldots} ) c. ( {-2,-1,0,1, ldots} ) D. None of these | 12 |

26 | Find graphically, the maximum value of ( z=2 x+5 y, ) subject to constraints given below: ( 2 x+4 y leq 8 ) ( mathbf{3} boldsymbol{x}+boldsymbol{y} leq mathbf{6} ) ( boldsymbol{x}+boldsymbol{y} leq mathbf{4} ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} leq mathbf{0 . 6} ) | 12 |

27 | Choose correct option which suitably represents value of ( boldsymbol{x} ) ( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{N} ) A ( cdot{0,1,2,3,4} ) в. {1,2,3,4} c. {1,2,3,4,5} D. {0,1,2,3,4,5} | 12 |

28 | ( boldsymbol{x}+mathbf{1} leq mathbf{7}, ) where ( boldsymbol{x} in boldsymbol{N} ) A ( cdot{1,2,3,4,5,6,7} ) в. {1,2,3,4,5,6} c. Data insufficient D. None of these | 12 |

29 | Identify the region described by the shaded part in the graph above. This question has multiple correct options A. ( y=4 x-6 ) B. ( y neq 4 x-6 ) c. ( y4 x-6 ) | 12 |

30 | Solve: ( frac{mathbf{2} boldsymbol{x}-mathbf{3}}{mathbf{4}}+mathbf{8} geq mathbf{2}+frac{mathbf{4} boldsymbol{x}}{mathbf{3}} ) | 12 |

31 | Solve the inequality and show the graph of the solution on number line: ( 5 x-3 geq 3 x-5 ) | 12 |

32 | Find solution of following inequality also show it graphically. [ boldsymbol{x}+mathbf{3}<mathbf{5}, boldsymbol{x} in boldsymbol{R} ] ( A ) begin{tabular}{lllllllll} hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 end{tabular} B. ( c ) begin{tabular}{llllll} hline & & & & & & \ -2 & -1 & 0 & 1 & 2 & 3 \ hline & & & & & & \ & & & & & & \ hline-2 & -1 & 0 & 1 & 2 & 3 end{tabular} D. begin{tabular}{cccccc} hline & 1 & & & & \ -2 & -1 & 0 & 1 & 2 & 3 end{tabular} | 12 |

33 | An aeroplane can carry a maximum of 200 passengers. A profit of Rs.1000 is made on each executive class ticket and a profit of Rs.600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit? A . 136000 в. 1360000 c. 13600 D. 1360 | 12 |

34 | Find ( boldsymbol{x} ) ( -(x-3)+4<5-2 x ) | 12 |

35 | Minimise ( Z=3 x+2 y ) subject to the constraints: ( boldsymbol{x}+boldsymbol{y} geq mathbf{8} ldots(mathbf{1}) ) ( 3 x+5 y leq 15 dots(2) ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ldots(mathbf{3}) ) | 12 |

36 | Solve the given inequalities graphically: ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 2}, boldsymbol{x} geq mathbf{1}, boldsymbol{y} geq mathbf{2} ) | 12 |

37 | Solve and graph the inequality. Give answer in interval notation. ( 15<4 x+3 leq 31 ) A ( cdot(3,7) ) в. [3,7) ( c .(3,7] ) D・ [3,7] | 12 |

38 | Identify the solution set for ( -(x-3)+ ) ( 4<5-2 x ) ( A cdot(-infty, 0) ) в. ( (-infty,-1) ) c. ( (-infty,-2) ) D. ( (-infty,-5) ) | 12 |

39 | toppr Q Type your question Minimum value of ( y= ) ( A ) ( 4 sec ^{2} x+cos ^{2} x ) for permissible real values of ( x ) is equal to If ( m, n ) are positive integers and ( m+n sqrt{2}= ) B. ( quad sqrt{41+24 sqrt{2}} ), then ( (m+ ) to ( n) ) is equal Number of solutions of then equation ( mathrm{C} ) ( log _{left(frac{3 x-x^{2}-14}{7}right)}(sin 3 x-sin x) ) 3. ( =log _{left(frac{9 x-x^{2}-14}{7}right)} cos 2 x ) is equal to Consider arithmetic sequence of positive the integers. If the sum of first ten terms is al to D. equal 4. the ( 58^{n} ) term, then the e of the least possible value first term is equal to 5. ( mathbf{A} cdot A-4, B-5, C-1, D-3 ) ( mathbf{B} cdot A-4, B-5, C-3, D-1 ) ( mathbf{c} cdot A-5, B-4, C-1, D-3 ) D . ( A-1, B-5, C-4, D-3 ) | 12 |

40 | If ( (boldsymbol{x} boldsymbol{y})^{boldsymbol{a}-1}=boldsymbol{z} ) ( (boldsymbol{y} boldsymbol{z})^{boldsymbol{b}-1}=boldsymbol{x} ) ( (boldsymbol{z} boldsymbol{x})^{c-1}=boldsymbol{y} ) then ( boldsymbol{a} boldsymbol{b}+boldsymbol{b} boldsymbol{c}+boldsymbol{c} boldsymbol{a}=? ) | 12 |

41 | Maximize: ( boldsymbol{z}=mathbf{3} boldsymbol{x}+mathbf{5} boldsymbol{y} ) Subject to: ( boldsymbol{x}+boldsymbol{4} boldsymbol{y} leq mathbf{2 4} ) ( mathbf{z} boldsymbol{x}+boldsymbol{y} leq mathbf{2 1} ) ( boldsymbol{x}+boldsymbol{y} leq mathbf{9} ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

42 | Find the solution of the following: If ( 5 x+4>8 x-11, ) then ( x<? ) | 12 |

43 | For a linear programming equations, convex set of equations is included in region of A . feasible solutions B. disposed solutions C. profit solutions D. loss solutions | 12 |

44 | Solve the system of inequalities graphically: ( mathbf{2} boldsymbol{x}+boldsymbol{y} geq mathbf{4}, boldsymbol{x}+boldsymbol{y} leq mathbf{3}, mathbf{2} boldsymbol{x}-mathbf{3} boldsymbol{y} leq mathbf{6} ) | 12 |

45 | Find solution of following inequality, also show it graphically. ( boldsymbol{x}-mathbf{5} geq-mathbf{7}, boldsymbol{x} in boldsymbol{R} ) ( A ) ( begin{array}{cccccc} & 1 & 1 & 1 & & & 1 \ -2 & -1 & 0 & 1 & 2 & 3end{array} ) B. begin{tabular}{lllllll} hline-2 & -1 & 0 & 1 & 2 & 3 end{tabular} ( c ) begin{tabular}{lllllll} & & & & & & & ( bullet ) \ hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 end{tabular} ( D ) ( longleftrightarrow )begin{tabular}{ccccccc} & & & & & ( rightarrow ) & ( rightarrow ) \ hline-2 & -1 & 0 & 1 & 2 & 3 & 4 end{tabular} | 12 |

46 | Show the solution of the problem of linear programming under the following restrictions by graphical method: ( boldsymbol{x}+ ) ( boldsymbol{y} leq mathbf{4}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

47 | Solve the system of inequalities graphically: ( 5 x+4 y leq 20, x geq 1, y geq 2 ) | 12 |

48 | A diet of a sick person must contains at least 48 units of vitamin ( A ) and 64 units of vitamin ( B ). Two foods ( F_{1} ) and ( F_{2} ) are available. Food ( F_{1} ) costs Rs. 6 per unit and Food ( F_{2} ) costs Rs. 10 per unit. One unit of food ( F_{1} ) contains 6 units of vitamin ( A ) and 7 units of vitamin ( B ). One unit of food ( F_{2} ) contains 8 units of vitamin ( A ) and 12 units of vitamin ( B ). Find the minimum cost for the diet that consists of mixture of these two foods and also meeting the minimum nutritional requirements. | 12 |

49 | If ( boldsymbol{x} geq mathbf{0} ) ( 3 y-2 x geq-12 ) ( 2 x+5 y leq 20 ) The area of the triangle formed in the ( x y ) plane by the system of inequalities above is: ( mathbf{A} cdot 60 ) B . 30 c. 40 D. 50 | 12 |

50 | Feasible region’s optimal solution for a linear objective function always includes A. downward point B. upward point c. corner point D. front point | 12 |

51 | Find solution of following inequality also show it graphically. ( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{W} ) ( A ) B. ( c ) ( D ) | 12 |

52 | Solve the system of inequalities graphically: ( x-2 y leq 3,3 x+4 y geq 12, x geq 0, y geq 1 ) | 12 |

53 | Solve: ( 5 x-7<3(x+3), 1-frac{3 x}{2} geq ) ( x-4 ) | 12 |

54 | The graph of which inequality is shown below: A. ( y-x leq 0 ) B . ( x-y leq 0 ) c. ( y+x leq 0 ) D. None of the above | 12 |

55 | Solve ( frac{6 x^{2}-5 x-3}{x^{2}-2 x+6} leq 4 ) | 12 |

56 | Solve: ( mathbf{1 0} leq-mathbf{5}(boldsymbol{x}-mathbf{2})<mathbf{2 0} ) | 12 |

57 | A solution of ( 8 % ) boric acid is to be diluted by adding a ( 2 % ) boric acid solution to it. The resulting mixture is to be more than ( 4 % ) but less than ( 6 % ) boric acid. If we have 640 litres of the ( 8 % ) solution, how many litres of the ( 2 % ) solution will have to be added? | 12 |

58 | Find solution of following inequality also show it graphically. ( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{Z} ) ( A ) в. ( c ) ( D ) | 12 |

59 | Solve the following inequalities: ( frac{2 x-3}{4}+8 geq 2+frac{4 x}{3} ) A . ( x leq 6.3 ) в. ( x leq 7 ) c. ( x leq 7.3 ) D. ( x leq 8.3 ) | 12 |

60 | Which of the following is not true about feasibility? A. It cannot be determined in a graphical solution of an LPP B. It is independent of the objective function C. It implies that there must be a convex region satisfying all the constraints D. Extreme points of the convex region gives the optimum solution. | 12 |

61 | State True or False and write the correct statement. 1. In the cartesian plane the horizontal line is called Y-axis. 2. In the cartesian plane the vertical line is called Y-axis. 3. The point which lies both the axes is called origin. 4. The point (2,-3) lies in the third quadrant. 5. (-5,-8) lies in the fourth quadrant. 6. The point ( (-x,-y) ) lies in the first quadrant where ( boldsymbol{x}<mathbf{0}, boldsymbol{y}, mathbf{0} ) | 12 |

62 | Find the pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23 | 12 |

63 | Solve: ( frac{4+2 x}{3} geq frac{x}{2}-3 ) | 12 |

64 | Solve the following inequality and show it graphically: ( -2<x+3<5, x in Z ) ( A ) в. ( c ) D. | 12 |

65 | Solution of ( frac{x}{3}>frac{x}{2}+1 ) is | 12 |

66 | Solve the inequalities for real ( x ) ( 37-(3 x+5) geq 9 x-8(x-3) ) | 12 |

67 | Solve the inequalities for real ( x ) ( frac{3(x-2)}{5} leq frac{5(2-x)}{3} ) | 12 |

68 | 62. The area in sq. unit. of the trian- gle formed by the graphs of x = 4, y = 3 and 3x + 4y = 12 is (1) 12 (2) 8 (3) 10 (4) 6 | 12 |

69 | Q Type your question orgamisıng nis graduated cymnaers In the hopes of keeping his office tidy and setting a good example for his students. He has beakers with diameters, in inches, of ( frac{1}{2}, frac{3}{4}, frac{4}{5}, 1 ) and ( frac{5}{4} . ) With his original five cylinders, professor Buckingham realises that he is missing a cylinder necessary for his upcoming lab demonstration for Thursday’s class. He remembers that the cylinder he needs when added to the original five, will create a median diameter value of for the set of six total cylinders. He ( overline{mathbf{1 0}} ) also knows that the measure of the sixth cylinder will exceed the value of the range of the current five cylinders by a width of anywhere from ( frac{1}{4} ) inches to ( frac{1}{2} ) inches, inclusive. Based on the data, what is one possible value of ( y ), the diameter of this missing sixth cylinder? A ( .1 leq y leq 1.25 ) в. ( 2 leq y leq 2.25 ) c. ( 3 leq y leq 3.25 ) D. ( 4 leq y leq 4.25 ) | 12 |

70 | state ( quad ) Minimum Wage per Hour daho ( $ 7.25 ) Montana [ $ 7.90 ] Orego ( $ 9.10 ) Wahington ( quad $ 9.32 ) The table above shows the 2014 minim wages for several states that share a border. Assuming an average workweek of between 35 and 40 hours, which inequality represents how much more a worker who earns minimum wages can earn per week in Oregon than in Idaho? A ( . x geq 1.85 ) в. ( 7.25 leq x leq 9.10 ) c. ( 64.75 leq x leq 74 ) D. ( 253.75 leq x leq 364 ) | 12 |

71 | The constraints ( -boldsymbol{x}_{1}+boldsymbol{x}_{2} leq 1 ) ( -boldsymbol{x}_{1}+mathbf{3} boldsymbol{x}_{2} leq mathbf{9} ) ( boldsymbol{x}_{1}, boldsymbol{x}_{2} geq mathbf{0} ) defines on A. Bounded feasible space B. Unbounded feasible space C. Both bounded and unbounded feasible D. None of the above | 12 |

72 | Solve the following Linear programming problems graphically: Maximize ( z=3 x+4 y ) subject to the constraints ( : boldsymbol{x}+boldsymbol{y} leq mathbf{4}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

73 | Consider the linear inequalities ( 2 x+3 y leq 6,2 x+y leq 4, x geq 0, y geq 0 ) (a) Mark the feasible region. (b) Maximise the function ( z=4 x+5 y ) subject to the given constraints. | 12 |

74 | Find solution of following inequality, also show it graphically: [ boldsymbol{x}+mathbf{3} leq mathbf{5}, boldsymbol{x} in boldsymbol{N} ] ( A ) begin{tabular}{rrrrrrrrrr} hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 end{tabular} B. begin{tabular}{rrrrrr} hline & & & & & & \ hline-2 & -1 & 0 & 1 & 2 & 3 end{tabular} ( c ) ( underbrace{longleftarrow}_{-2}-1 quad_{0} quad_{1} quad_{2} quad_{1} ) ( D ) begin{tabular}{rrrrrr} hline & 1 & 1 & & & 1 \ -2 & -1 & 0 & 1 & 2 & 3 end{tabular} | 12 |

75 | Solve the following inequality and show it graphically: ( -2<x+3<5, x in N ) ( A ) B. ( c ) D. | 12 |

76 | Solve the following linear programming problem graphically: Maximize ( Z=7 x+10 y ) subject to the constraints ( 4 x+6 y leq 240 ) ( 6 x+3 y leq 240 ) ( x geq 10 ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

77 | Construct the graphs of the following functions. ( boldsymbol{y}=(boldsymbol{x}+mathbf{3}) /(boldsymbol{x}-mathbf{1}) ) | 12 |

78 | Represent ( x ) on number line or find ( x ) ( frac{3 x-2}{5}>frac{4 x-3}{2} ) | 12 |

79 | Solve the following Linear Programming Problems graphically: Minimise ( Z=-3 x+4 y ) subject to ( x+2 y leq 8,3 x+2 y leq ) ( mathbf{1 2}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

80 | Find ( x ) satisfying ( |x-5| leq 3 ) | 12 |

81 | ( boldsymbol{z}=mathbf{3 0} boldsymbol{x}+mathbf{2 0} boldsymbol{y}, boldsymbol{x}+boldsymbol{y} leq mathbf{8}, boldsymbol{x}+mathbf{2} boldsymbol{y} geq ) ( 4,6 x+4 y geq 12, x geq 0, y geq 0 ) has A. Unique solution B. Infinitely many solution C . Minimum at (4,0) D. Minimum 60 at point (0,3) | 12 |

82 | Find the number of real numbers in the solution set of following ( frac{2 x}{5}+1<-3 ) A . 10 B. 11 ( c cdot 9 ) D. Infinite | 12 |

83 | Solve the following inequalities graphically in two-dimensional plane: ( 2 x-3 y>6 ) | 12 |

84 | ( x in{text { real numbers }} ) and ( -1<3-2 x leq ) ( 7, ) evaluate ( x ) and represent it on a number line. | 12 |

85 | Minimize and maximize ( boldsymbol{z}=mathbf{5} boldsymbol{x}+mathbf{1 0} boldsymbol{y} ) subject to the constraints ( x+2 y leq 120 ) ( boldsymbol{x}+boldsymbol{y} geq mathbf{6 0} ) ( x-2 y geq 0 ) and ( x geq 0, y geq 0 ) by graphical method. | 12 |

86 | State true or false: The statement ( 0>1 rightarrow sin x=2 ) A. True B. False | 12 |

87 | The region represented by the inequation system ( boldsymbol{x}, boldsymbol{y} geq mathbf{0}, boldsymbol{y} leq mathbf{6}, boldsymbol{x}+ ) ( y leq 3 ) is A. Unbounded in first quadrant B. Unbounded in first and second quadrants C. Bounded in first quadrant D. None of the above | 12 |

88 | Study the graph carefully and answer the question given below it. The import in 1976 was approximately how many times that of the year ( 1971 ? ) | 12 |

89 | Determine graphically the minimum value of the objective function ( Z=50 x+20 y ldots(1) ) subject to the constraints: ( 2 x y geq 5 dots(2) ) ( mathbf{3} boldsymbol{x}+boldsymbol{y} geq mathbf{3} dots(mathbf{3}) ) ( 2 x-3 y leq 12 dots(4) ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ldots(mathbf{5}) ) | 12 |

90 | Find the number of whole numbers in the solution set of following ( x-5<-2 ) | 12 |

91 | Solve the following linear programming problem: [ begin{array}{c} text { Maximise: } boldsymbol{z}=mathbf{1 5 0} boldsymbol{x}+mathbf{2 5 0} boldsymbol{y} \ text { Subject to: } mathbf{4} boldsymbol{x}+boldsymbol{y} leq mathbf{4 0} \ mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{6 0} \ boldsymbol{x} geq mathbf{0} \ boldsymbol{y} geq mathbf{0} end{array} ] | 12 |

92 | Number of integral solutions satisfy inequality ( |boldsymbol{x}-mathbf{3}|-|mathbf{2 x}+mathbf{5}| geq|boldsymbol{x}+mathbf{8}| ) is A . 5 B. 6 ( c cdot 7 ) D. | 12 |

93 | Solve the following inequalities graphically in two-dimensional plane: ( x+y<5 ) | 12 |

94 | The solution set for ( (x+3)+4> ) ( -2 x+5 ) is ( ^{A} cdotleft(-frac{2}{3}, inftyright) ) B. ( (2, infty) ) ( c cdot(infty,-2) ) D. (-2,2) | 12 |

95 | Solve the following minimal assignment problem and hence find minimum time where ( ^{prime}-^{prime} ) indicates that job cannot be assigned to the machine: ( – ) | 12 |

96 | Kritika needs to receive completed surveys from at least 3800 potential voters in her city. She notices that for every 5 surveys she sends out, only 1 survey is completed. Last week she received 1350 completed surveys, and this week she received 900 completed surveys. Kritika plans to send out ( s ) additional surveys. Find the inequality which shows all possible for ‘s’ that would ensure that she received 3800 completed surveys? A ( . s geq 1550 ) B . ( s geq 2250 ) ( mathbf{c} cdot s geq 7750 ) D. ( s geq 12250 ) | 12 |

97 | Construct the graphs of the following functions. ( boldsymbol{y}=(|mathbf{1}-boldsymbol{x}|+mathbf{2})(boldsymbol{x}+mathbf{1}) ) | 12 |

98 | Solve: ( x-3(2+x)>2(3 x-1) ) | 12 |

99 | A solution is to be kept between ( 68^{circ} F ) and ( 77^{circ} F . ) What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by ( boldsymbol{F}=frac{mathbf{9}}{mathbf{5}} boldsymbol{C}+mathbf{3 2} ? ) | 12 |

100 | Which equation has the solution shown on the number line? ( mathbf{A} cdot x geq 1 ) в. ( x geq-6 ) c. ( x neq 1 ) D. ( x<0 ) | 12 |

101 | Solve the given inequalities graphically: ( boldsymbol{x}+boldsymbol{y} leq mathbf{9}, boldsymbol{y}>boldsymbol{x}, boldsymbol{x} geq mathbf{0} ) | 12 |

102 | Which quadrant does the solution lie in? A . ( I ) в. ( I I ) ( c . I I I ) D. ( I V ) | 12 |

103 | Solve the following system of inequalities graphically: ( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{6 0}, quad boldsymbol{x}+mathbf{3} boldsymbol{y} leq mathbf{3 0}, quad boldsymbol{x} geq ) ( 0 . y geq 0 ) | 12 |

104 | If the replacement set is the set of real numbers, solve ( :-4 x geq-16 ) | 12 |

105 | In solving LP problem : minimize ( boldsymbol{z}= ) ( 6 x+10 y, ) subject to ( x geq 6, y geq 2,2 x+ ) ( boldsymbol{y} geq mathbf{1 0}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0}, ) which constraints are reduntant? | 12 |

106 | Minimize ( z=6 x+2 y, ) Subject to ( x+ ) ( 2 y geq 3, x+4 y geq 4,3 x+y geq 3, x geq ) ( mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

107 | Two tailors, ( A ) and ( B ), earn Rs. 300 and Rs. 400 per day, respectively. ( A ) can stitch 6 shirts and 4 pairs of trousers while ( B ) can stitch 10 shirts and 4 pairs of trousers per day. To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost, formulate this as an LPP and find the number of days ( A ) and ( B ) worked. | 12 |

108 | Minimize ( Z=7 x+y ) subject to ( mathbf{5} boldsymbol{x}+boldsymbol{y} geq mathbf{5}, boldsymbol{x}+boldsymbol{y} geq mathbf{3}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

109 | Ordered pair that satisfy the equation ( boldsymbol{x}+boldsymbol{y}+mathbf{1}<mathbf{0} ) is: в. (-2,0) c. (2,-4) D. Both (B) and (C) | 12 |

110 | A cooperative society of farmers has 50 hectares of land to grow two crops ( A ) and B. The profits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops ( A ) and ( B ) at the rate of 20 litres and 10 litres per hectare, respectively. Further not more than 800 litres of herbicide should be used in order to protect fish and wildlife using a pond which collects drainage from this land. Keeping in mind that the protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance in environment? | 12 |

111 | Solve, and express the answer graphically. ( frac{4 x+4}{x-4} leq 0 ) | 12 |

112 | Find the number of integer solutions of ( boldsymbol{x}_{1}+boldsymbol{x}_{2}+boldsymbol{x}_{3}+boldsymbol{x}_{4}=mathbf{2 0} ) where ( boldsymbol{x}_{1} geq ) ( -5, x_{2} geq 3, x_{3} geq 0, x_{4} geq 1 ) | 12 |

113 | Solve: ( frac{x}{3}>frac{x}{2}+1 ) | 12 |

114 | Find solution of following inequality, also show it graphically: ( boldsymbol{x}-mathbf{5} geq-mathbf{7}, boldsymbol{x} in boldsymbol{Z} ) ( A ) begin{tabular}{lllllll} hline-2 & -1 & 0 & 1 & 2 & 3 end{tabular} B. ( quad-3 quad-2-1 quad 0 quad+quad bullet quad longrightarrow rightarrow ) ( quad-3 quad-1 quad 0 quad 1 quad 2 quad 3 quad 4 ) ( c ) begin{tabular}{ccccccc} & & & & & ( rightarrow ) & ( rightarrow ) \ hline-2 & -1 & 0 & 1 & 2 & 3 & 4 end{tabular} ( D ) begin{tabular}{rrrrrr} hline & 1 & 1 & 1 & & & 1 \ -2 & -1 & 0 & 1 & 2 & 3 end{tabular} | 12 |

115 | (Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops ( X ) and ( Y . ) The profit from crops ( X ) and ( Y ) per hectare are estimated at ( R s .10,500 ) and Rs.9, 000 respectively. To control weeds, a liquid herbicide has to be used for | 12 |

116 | Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11 | 12 |

117 | The statement written as value of ( x ) is less than 50 is represented as A ( .5050 ) c. ( x<50 ) D. None of these | 12 |

118 | Solve the following inequalities graphically in two-dimensional plane: ( 2 x+y geq 6 ) | 12 |

119 | Solve for ( boldsymbol{x}: frac{boldsymbol{x}^{2}-|boldsymbol{x}|-mathbf{1 2}}{boldsymbol{x}-mathbf{3}} geq mathbf{2} boldsymbol{x} ) | 12 |

120 | Solve the linear inequations: ( -2 leq frac{1}{2}-frac{2 x}{3} leq 1 frac{5}{6}, x in N ) Then ( frac{15}{4} geq x geq-2 ) A. True B. False | 12 |

121 | A firm has the cost function ( C=frac{x^{3}}{3}- ) ( 7 x^{2}+111 x+50 ) and demand function ( boldsymbol{x}=mathbf{1 0 0}-boldsymbol{p} ) Write the total revenue function in terms of ( boldsymbol{x} ) | 12 |

122 | (Diet problem) A dietician has to develop a special diet using two foods ( boldsymbol{P} ) and ( Q . ) Each packet (containing ( 30 g ) ) of food ( P ) contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food ( Q ) contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A? | 12 |

123 | Solve the following inequality and show it graphically: ( frac{boldsymbol{x}+mathbf{4}}{boldsymbol{x}-mathbf{3}}>mathbf{0}, boldsymbol{x} in boldsymbol{W} ) ( ^{A} cdot underbrace{0}_{-3-2-1} cdot 1,0 ) в. ( c_{1}+ )begin{tabular}{ccccccc} hline-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 end{tabular} | 12 |

124 | Solve graphically the linear inequalities ( 2 x+3 y leq 7, x+2 y leq 4 ) ( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) If ( z=6 x+5 y ) is the objective function find its maximum value. | 12 |

125 | Solve the inequation ( 8-2 x geq x- ) ( mathbf{5} ; boldsymbol{x} boldsymbol{epsilon} boldsymbol{N} ) | 12 |

126 | Solve the following inequation, write the solution set and represent it on the number line. ( -3(x-7) geq 15-7 x>frac{x+1}{3}, x in R ) | 12 |

127 | Solve the following system of inequalities graphically ( 3 x+2 y leq 12, x geq 1, y geq 2 ) | 12 |

128 | Which value of ( x ) is in the solution set of the inequality ( :-2 x+5>17 ? ) A ( . x>-8 ) в. ( x-4 ) D. ( x<12 ) | 12 |

129 | A manufacturer produces nuts and bolts. It takes 1 hour of work on machine ( A ) and 3 hours on machine ( B ) to produce a package of nuts. It takes 3 hours on machine ( A ) and 1 hour on machine ( B ) to produce a package of bolts. He earns a profit of ( R s .17 .50 ) per package on nuts and ( R s .7 .00 ) per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day? | 12 |

130 | Solve the inequalities for real ( x ) ( frac{(2 x-1)}{3} geq frac{(3 x-1)}{4}-frac{(2-x)}{5} ) | 12 |

131 | Solve the inequalities for real ( x ) ( mathbf{2}(mathbf{2} boldsymbol{x}+mathbf{3})-mathbf{1 0}<mathbf{6}(boldsymbol{x}-mathbf{2}) ) | 12 |

132 | Solve the following inequalities graphically in two-dimensional plane: ( -3 x+2 y geq-6 ) | 12 |

133 | Solve the following Linear Programming problems graphically: 1. Maximize ( Z=3 x+4 y quad ) Subject to the constraints ( : x+y leq 4, x geq 0, y geq ) ( mathbf{0} ) 2. Minimize ( Z=-3 x+4 y quad ) subject to ( x+2 y leq 8,3 x+2 y leq 12, x geq ) ( mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

134 | toppr Q Type your question pressure in atmospheres. For example if a substance at a particular temperature and pressure lies in gas area, the substance exists only as a gas. However, if the temperature-pressure | 12 |

135 | The specific set of real numbers that lies between two conditional numbers ( a ) and ( b ) is classified as A . interval B. break c. double interval D. equal interval | 12 |

136 | In North west corner rule, if the supply in the row is satisfied one must move A. down in the next row B. up in the next row c. right cell in the next column D. left cell in the next row | 12 |

137 | Solve the following system of inequalities graphically ( 2 x+y geq ) ( 8, x+2 y geq 10 ) | 12 |

138 | Pankaj is planning lunch for his wedding anniversary. At one restaurant, the cost per person for lunch is ( $ 15 ) with an additional one-time set-up charge of ( $ 35 . ) Pankaj has a maximum budget of ( $ 150 . ) If ( p ) represents the number of people (including Pankaj) who will attend the lunch, which of the following inequalities represents the number of people who can attend within budget? A. ( 15 p leq 150+35 ) B. ( 35 leq 150-15 p ) c. ( 15 p geq 150-35 ) D. ( 35 geq 150-15 p ) | 12 |

139 | Solve ( frac{|boldsymbol{x}-mathbf{3}|}{boldsymbol{x}^{2}-mathbf{5} boldsymbol{x}+mathbf{6}} geq mathbf{2} ) | 12 |

140 | An oll company nas two depots ( A ) and ( B ) with capacities of ( 7000 L ) and ( 4000 L ) respectively. The company is to supply oil to three petrol pumps ( D, E ) and ( F ) whose requirements are ( 4500 L, 3000 L ) and ( 3500 L ) respectively. The distance (in ( mathrm{km} ) ) between the depots and the petrol pumps is given in the following table: Distance (in km) From/To 1 ( boldsymbol{A} ) ( B ) 7 ( D ) 3 6 4 A Assuming that the transportation cost of 10 litres of oil is Re.1 per ( mathrm{km} ), how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost? | 12 |

141 | Q Type your question brand ( Q ).The amounts (in ( mathrm{kg} ) ) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least ( 240 k g ) of phosphoric acid, at least 270 kg of potash and at most ( 310 k g ) of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? ( begin{array}{llll}text { Kg per bag } & & & \ & & text { Brand } P & text { Brand } Q \ & & & \ text { Nitrogen } & 3 & 3.5 & \ text { Phosphoric acid } & 1 & 2 & \ text { Potash } & 3 & 1.5 & \ text { Chlorine } & 1.5 & 2 & end{array} ) | 12 |

142 | Solve the following inequation: ( (x-5)(x+9)(x-8)<0 ) | 12 |

143 | Solve the inequalities for real ( x ) ( frac{x}{4}<frac{(5 x-2)}{3}-frac{(7 x-3)}{5} ) | 12 |

144 | Check, whether the half plane ( 3 x+ ) ( 6 y geq 0 ) contains ( (1,1), ) if so shade the plane containing ( (mathbf{1}, mathbf{1}) ) | 12 |

145 | Sai is ordering new shelving units for his store. Each unit is 7 feet in length and extends from floor to ceiling. Sai’s store has 119 feet of wall space that includes 21 feet of windows along the walls. If the shelving units cannot be placed in front of the windows, which of the following inequalities includes all possible values of ( r, ) the number of shelving units that Sai could use? A ( cdot r leq frac{119-21}{7} ) B. ( r geq frac{119+21}{7} ) c. ( r leq 119-21+7 r ) D. ( r geq 119+21-7 r ) ( r ) | 12 |

146 | Solve ( mathbf{7}>mathbf{3} boldsymbol{x}-mathbf{8} ; boldsymbol{x} in boldsymbol{N} ) В. {1,2,3,4} c. (1,15) D. None of these | 12 |

147 | A farmer plans to mix two types of food to make a mix of low cost feed for the animals in his farm. A bag of food ( boldsymbol{A} ) ( operatorname{costs} $ 10 ) and contains 40 units of proteins, 20 units of minerals and 10 units of vitamins. A bag of food ( B ) costs ( $ 12 ) contains 30 units of proteins, 20 units of minerals and 30 units of vitamins. How many bags of food ( A ) and ( B ) should the consumed by the animals each day in order to meet the minimum daily requirements of 150 units of proteins, 90 units of minerals and 60 units of vitamins at a minimum cost? | 12 |

148 | Solve the inequalities and represent the solution graphically on number line. ( 5 x+1>-24,5 x-1<24 ) | 12 |

149 | Solve and graph the inequality. Give answer in interval notation. ( -6 x+12>-7 x+17 ) ( A cdot(5, infty) ) В ( cdot(-infty, 5) ) ( c cdot(29, infty) ) ( mathbf{D} cdot(-infty, 29) ) | 12 |

150 | solve : ( frac{x^{2}-5 x+6}{|x|+7}<0 ) then ( x epsilon(alpha, beta) quad alpha+beta= ) | 12 |

151 | Suppose ( f ) is the collection of all ordered pairs of real numbers and ( x=6 ) is the first element of some ordered pair in ( f ) Suppose the vertical line through ( x=6 ) intersects the graph of ( f ) twice. Is ( f ) a function? Why or why not? | 12 |

152 | The above diagram shows a number line. The above number line represents the | 12 |

153 | Which region is described by the shade in the graph given? This question has multiple correct options A ( .2 x+3 y=3 ) B. ( 2 x+3 y>3 ) c. ( 2 x+3 y<3 ) D. None of these | 12 |

154 | Solve the following inequalities graphically in two-dimensional plane: ( 3 x+4 y leq 12 ) | 12 |

155 | Solve the following inequalities graphically in two-dimensional plane: ( y+8 geq 2 x ) | 12 |

156 | The point which does not belong to the feasible region of the LPP: Minimize: ( Z=60 x+10 y ) subject to ( 3 x+y geq 18 ) ( 2 x+2 y geq 12 ) ( x+2 y geq 10 ) ( x, y geq 0 ) is в. (4,2) D. (10,0) | 12 |

157 | The objective function ( z=x_{1}+x_{2} ) subject to ( boldsymbol{x}_{1}+boldsymbol{x}_{2} leq mathbf{1 0},-mathbf{2} boldsymbol{x}_{mathbf{1}}+mathbf{3} boldsymbol{x}_{2} leq ) ( mathbf{1 5}, boldsymbol{x}_{1} leq mathbf{6}, boldsymbol{x}_{1}, boldsymbol{x}_{2} geq mathbf{0} ) has maximum value ( ldots ldots . . . . . . . . . ) of the feasible region. A. at only one point B. at only two points c. at every point of the segment joining two points D. at every point of the line joining two points | 12 |

158 | Solve ( :-5(x+4)>30 ; x in Z ) | 12 |

159 | Dietician has to develop a special diet using two foods ( P ) and ( Q . ) Each packet (containing ( 30 g ) ) of food ( P ) contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin ( A ) while each packet of the same quality of food ( Q ) contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and almost 300 units of cholesterol. How many packets of each food should be used to maximize the amount of vitamin ( A ) in the diet? What is the maximum amount of vitamin A? | 12 |

160 | Reshma wishes to mix two types of food ( P ) and ( Q ) in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin ( A ) and 11 units of vitamin B. Food ( P ) costs Rs. ( 60 / k g ) and Food ( Q operatorname{costs} R s .80 / k g ) Food ( P ) contains 3 units/kg of Vitamin ( A ) and 5 units / kg of Vitamin ( B ) while food ( Q ) contains 4 units/kg of Vitamin ( A ) and 2 units / kg of vitamin ( B ) Determine the minimum cost of the mixture. | 12 |

161 | Solve: ( |2 x-5|<1 ) | 12 |

162 | Solve the following system of inequalities graphically ( 2 x-y> ) ( 1, x-2 y<-1 ) | 12 |

163 | Solve ( & ) graph the solution set of ( 3 x+ ) ( 6 geq 9 ) and ( -5 x>-15, x in R ) | 12 |

164 | Solve the following inequalities graphically in two-dimensional plane: ( boldsymbol{x}-boldsymbol{y} leq 2 ) | 12 |

165 | Which equation has the solution shown on the number line? в. ( -5<xx>0 ) D. ( -1>x>-6 ) | 12 |

166 | Suppose a manufacturer of printed circuits has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits. Type A requires 20 resistors, 10 transistors and 10 capacitors Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type ( A ) circuits is ( E 5 ) and that on type ( B ) circuits is ( E 12 ), how many of each circuit should be produced in order to maximize profit? | 12 |

167 | Maximize ( boldsymbol{f}=mathbf{4} boldsymbol{x}-boldsymbol{y}, ) subject to the constraints ( mathbf{7} boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{2 8}, mathbf{2 y} leq mathbf{7}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ) | 12 |

168 | Find the solution of following inequality, also show it graphically: ( boldsymbol{x}<mathbf{4}, boldsymbol{x} in boldsymbol{R} ) ( A ) в. c. D. | 12 |

169 | Solve the following equation: ( -8<-(3 x-5)<13 ) | 12 |

170 | Solve: ( 3 x^{2}-4>x(2 x-3) ) | 12 |

171 | While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because: A. the resources are limited in supply B. the objective function as a linear function c. the constraints are linear equations or inequalities D. all of the above | 12 |

172 | Which point belongs to the region represented by ( boldsymbol{x}+boldsymbol{y} leq mathbf{0} ? ) This question has multiple correct options A. (4,5) (年) (4,5) в. (-7,9) c. (7,-9) D. (8,-12) | 12 |

173 | Which equation has the solution shown on the number line? ( mathbf{A} cdot 4>x geq 1 ) в. ( 0>x geq-3 ) c. ( x neq 1 ) D. ( x<0 ) | 12 |

174 | Each month a store owner can spend at most ( $ 100,000 ) on PC’s laptops. A PC costs the store owner ( $ 1000 ) and ( a ) laptop costs him ( $ 1500 . ) Each PC is sold for a profit of ( $ 400 ) while laptop is sold for a profit of ( $ 700 . ) The store owner estimates that at least 15 PC’s but no more than 80 are sold each month. He also estimates that the number of laptops sold is at most half the PC’s. How many PC’s and how many laptops should be sold in order to maximize the profit? | 12 |

175 | Solve the inequality and show the graph of the solution on number line: ( frac{x}{2} geq frac{(5 x-2)}{3}-frac{(7 x-3)}{5} ) | 12 |

176 | Find the largest value of ( x ) for which ( 2(x-1) leq 9-x ) and ( x in W ) | 12 |

177 | The shaded region in the figure is the solution set of the inequations. ( mathbf{A} cdot 5 x+4 y geq 20, x leq 6, y geq 3, x geq 0, y geq 2 ) B. ( 5 x+4 y geq 20, x geq 6, y leq 3, x geq 0, y geq 2 ) c. ( 5 x+4 y geq 20, x leq 6, y leq 3, x geq 0, y geq 0 ) D. ( 5 x+4 y leq 20, x leq 6, y leq 3, x geq 0, y geq 2 ) | 12 |

178 | f the solution set for the system is given by the above figure, then which of the following is NOT a solution to the system? A ( cdot(0,3) ) B. (1,2) c. (2,4) D. (3,3) | 12 |

179 | Find the relation between ( x ) and ( y ) from the following statements. ( -boldsymbol{x}= ) ( mathbf{5} ;-mathbf{5}<boldsymbol{y} ) A ( . xy ) D. none | 12 |

180 | Solve the inequality and represent the solution graphically on number line. ( mathbf{2}(boldsymbol{x}-mathbf{1})mathbf{2}-boldsymbol{x} ) | 12 |

181 | The shaded region is represented by the inequation: A ( . y geq x ) В . ( y geq-x ) c ( cdot y geq|x| ) D・ ( y leq|x| ) | 12 |

182 | Consider the linear inequations and solve them graphically: ( mathbf{3} boldsymbol{x}-boldsymbol{y}-mathbf{2}>mathbf{0} ; boldsymbol{x}+boldsymbol{y} leq mathbf{4} ; boldsymbol{x}> ) ( mathbf{0} ; boldsymbol{y} geq mathbf{0} ) Which of the following are corner points of the convex polygon region of the solution? A. (0,0) (年) ( 0,0,0,0,0,1, ) B. (2,3) c. (0,4) (年. ( (0,4)) ) D ( cdotleft(frac{3}{2}, frac{5}{2}right) ) | 12 |

183 | The set of values of ( ^{prime} x^{prime} ) which satisfies the inequation ( sqrt{x^{2}-18 x+72}<(x-1) ) is ( A cdot phi ) B ( cdot[1,2) ) ( mathrm{c} cdot[12, infty) ) D・(1,2) | 12 |

184 | Find the solution set to the inequality ( 2 x+1 geq 9 ? ) ( mathbf{A} ) B. c. D. | 12 |

185 | Solve the following inequality ( frac{-2 x+5}{x+6}>-2 ) | 12 |

186 | Solve the following inequation and write the solution set : [ begin{array}{r} 13 x-5<15 x+4<7 x+ \ 12, x in R end{array} ] Represent the solution on a real number line. | 12 |

187 | Solve the inequality and show the graph of the solution on number line: ( 3(1-x)<2(x+4) ) | 12 |

188 | Solve the following inequalities graphically in two-dimensional plane: ( x>-3 ) | 12 |

189 | Represent the set of real values of ( x ) on the number line satisfying ( frac{1}{2}(2 x- ) 1) ( leq 2 x+frac{1}{2} leq 5 frac{1}{2}+x . ) Also, find the greatest and the smallest values of ( x ) satisfying the inequations. ( mathbf{A} cdot x epsilon[-1,4] ) В. ( x in[-1,5] ) ( mathbf{c} cdot x epsilon[-2,5] ) D. ( x epsilon[-2,7] ) | 12 |

190 | The longest side of a triangle is 3 times the shortest side and the third side is 2 ( mathrm{cm} ) shorter than the longest side. If the perimeter of the triangle is at least 61 ( mathrm{cm}, ) find the minimum length in cm. of the shortest side. | 12 |

191 | The bar graph shows the number of cakes sold at a shop in four days. What is the difference in number of cakes between the highest and the lowest daily sale? 4.20 B. 35 ( c cdot 30 ) D. 40 | 12 |

192 | The set of all integral values of ( x ) for which ( 5 x-1<(x+1)^{2}<7 x-3, ) is ( A cdot phi ) B . {1} ( c cdot{2} ) D. {3} | 12 |

193 | In North west corner rule the allocation is done in A. upper left corner B. upper right corner c. middle cell in the transportation table D. cell with the lowest cost | 12 |

194 | Pankaj wants to create tests for SAT students. He wants to make some calculator and non calculator tests. He figures that each non-calculator test will take him 3 hours to create, and each calculator test will take 4 hours to create. Because of his time constraint, he can at most devote at most 6 hours per week of his time for the next 5 weeks to create the practice and he wants to provide at least 8 practice tests, which of the system of inequality represent how many of each type of test he can create? ( mathbf{A} cdot n+c geq 8 ) ( 3 n+4 c leq 6 ) B ( . n+c geq 8 ) ( 3 n+4 c leq 30 ) c. ( n+c leq 8 ) ( 3 n+4 c geq 30 ) D. ( n+c geq 6 ) ( 3 n+4 c leq 8 ) | 12 |

195 | Solve the given inequalities graphically: ( 2 x+y geq 8, x+2 y geq 10 ) | 12 |

196 | How many acres of each (wheat and rye) should the farmer plant in order to get maximum profit? A . (5,5) в. (4,4) c. (4,5) (年. (4,5) D. (4,3) | 12 |

197 | Solve the system of inequalities graphically ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 5 0}, boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{8 0}, boldsymbol{x} leq mathbf{1 5}, boldsymbol{y} ) | 12 |

198 | ( boldsymbol{x}={4,5,6} ) is the solution set for A. ( x geq 4 ) and ( x leq 7 ) B. ( x geq 4 ) and ( x4 ) and ( x4 ) and ( x leq 7 ) | 12 |

199 | Which region is described by the shade in the graph given above? This question has multiple correct options A ( .2 x+3 y=3 ) B . ( 2 x+3 y3 ) D. ( -2 x+3 y<3 ) | 12 |

200 | Find the relation between ( x ) and ( y ) from the following statement. ( boldsymbol{x}>-mathbf{3} ;-mathbf{6}>boldsymbol{y} ) A ( . xy ) c. ( x=y ) D. none | 12 |

201 | State true or false: If ( x ) is a positive integer or a solution to ( x+3>4, ) then ( x>0 ) and ( x>frac{1}{2} ) A . True B. False | 12 |

202 | To receive Grade ( A ) in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunitas marks in first four examinations are 87,92,94 and 95 find minimum marks that Sunita must obtain in the fifth examination to get grade ( A ) in the course | 12 |

203 | Solve the given inequalities graphically: ( 2 x+y geq 6 ) and ( 3 x+4 y leq 12 ) | 12 |

204 | A graph and the system of inequalities are shown above. Which region of the graph could represent the solution for the system of in equations? ( boldsymbol{y}>boldsymbol{x} ) ( mathbf{3} boldsymbol{y} leq-mathbf{4} boldsymbol{x}+mathbf{6} ) ( A cdot A ) в. ( B ) ( c . c ) D. ( D ) | 12 |

205 | Solve ( & ) graph the solution set of ( -2< ) ( 2 x-4 ) and ( -2 x+5 geq 13, x epsilon R ) | 12 |

206 | Solve the following inequality and show it graphically: ( |boldsymbol{x}+mathbf{3}|<mathbf{4}, boldsymbol{x} in boldsymbol{R} ) ( A ) B. ( c ) D. | 12 |

207 | Find ( boldsymbol{x} ) ( frac{5 x}{2}+frac{3 x}{4} geq frac{39}{4} ) | 12 |

208 | Graph the solution set ( |x| geq 3 ) ( A cdot(-3,3) ) B ( cdot(-infty,-3] cap[3, infty) ) ( mathbf{c} cdot(-infty,-3) cap(3, infty) ) D. [-3,3] ( langle 1,1,-7,6-5,-4 ) | 12 |

209 | Given ( boldsymbol{x} in{text { integers }}, ) find the solution ( operatorname{set} ) of ( :-5 leq 2 x-3<x+2 ) | 12 |

210 | Solve: ( 3 x+4 y geq 12, x geq 0, y geq 1 ) and ( 4 x+7 y leq 28 ) | 12 |

211 | Which of the following inequations represents the shaded region? A. ( 2 x+y leq 4 ) B. ( 2 x+y geq 4 ) c. ( x+2 y leq 4 ) D. ( x+2 y geq 4 ) | 12 |

212 | Which of the following points lie in the solution set? A ( .(1,1) ) в. (1,2) c. (2,1) () D. (3,2) | 12 |

213 | Consider the linear inequations and solve them graphically: ( mathbf{3} boldsymbol{x}-boldsymbol{y}-mathbf{2}>mathbf{0} ; boldsymbol{x}+boldsymbol{y} leq mathbf{4} ; boldsymbol{x}> ) ( mathbf{0} ; boldsymbol{y} geq mathbf{0} ) The solution region of these inequations is a convex polygon with sides. ( A cdot 3 ) B. 4 ( c .5 ) D. 7 | 12 |

214 | In North west corner rule if the demand in the column is satisfied one must move to the A. left cell in the next column B. right cell in the next row c. right cell in the next column D. left cell in the next row | 12 |

215 | Solve the following inequality and show it graphically: ( |boldsymbol{x}+mathbf{3}|<mathbf{4}, boldsymbol{x} in boldsymbol{Z} ) ( A ) B. ( c ) D. | 12 |

216 | If ( x ) belongs to a set of integers, ( A ) is the solution set of ( 2(x-1)<3 x-1 ) and ( B ) is the solution set of ( 4 x-3 leq 8+x ) then find ( A cap B ) A ( cdot{0,1,2} ) в. {1,2,3} ( mathbf{c} cdot{0,1,2,3} ) D cdot {0,2,4} | 12 |

217 | Which equation has the solution shown on the number line? ( mathbf{A} cdot 4>x geq 1 ) B. ( x<1 ) c. ( x neq 1 ) D. ( x<0 ) | 12 |

218 | For a zoo to incur a profit,it needs to sell at least 350 admission tickets each day. Four student groups, each of which includes 48 students, have purchased tickets for admission. If ( z ) represents the number of additional ticket sold today, and the zoo made its daily profit goal successful, which of the following inequalities could represent all possible values for ( z ? ) ( mathbf{A} cdot 4(48)+z leq 350 ) B ( cdot 4(48)+z geq 350 ) ( mathbf{c} cdot 4(48)-z leq 350 ) ( mathbf{D} cdot 4(48)-z geq 350 ) | 12 |

219 | Solve the following linear inequality: ( frac{8 x-5}{2 x+11} geq 4 ) | 12 |

220 | The shaded region is represented by the inequality: A. ( y-2 x leq-1 ) B . ( x-2 y leq-1 ) c. ( y-2 x geq-1 ) D. ( x-2 y geq-1 ) | 12 |

221 | A worker uses a forklift to move boxes hat weigh either 40 pounds or 65 pound s each. Let ( x ) be the number of 40 pound boxes and ( y ) be the number of 65 pound. The forklift can carry upto either 45 boxes or a weight of 2400 pound Which of the following systems of inequalities represents this relationship? ( left{begin{array}{l}40 x+65 y leq 2,400 \ x+y leq 45end{array}right. ) в. ( left{frac{y}{40}+frac{y}{65} leq 2,400right. ) c. ( left{begin{array}{l}40 x+65 y leq 45 \ x+y leq 2,400end{array}right. ) D. ( left{begin{array}{l}x+y leq 2,400 \ 40 x+65 y leq 2,400end{array}right. ) | 12 |

222 | The number of points in ( (-infty, infty) ) for which ( x^{2}-x sin x- ) ( cos boldsymbol{x}=mathbf{0}, ) is ( mathbf{A} cdot mathbf{6} ) B. 4 ( c cdot 2 ) D. None of the above | 12 |

223 | Solve the following system of inequalities graphically ( x+2 y leq 8 ) ( 2 x+y leq 8 ) ( x geq 0 ) ( boldsymbol{y} geq mathbf{0} ) | 12 |

224 | Solve the system of in equations ( frac{x}{2 x+1} geq frac{1}{4} ; frac{6 x}{4 x-1}<frac{1}{2} ) | 12 |

225 | A retired person wants to invest an amount of Rs. ( 50,000 . ) His broker recommends investing in two type of bonds A and B yielding 10% and 9% return respectively on the invested amount. He decides to invest at least Rs.20, 000 in bond A and at least Rs. 10,000 in bond ( B . ) He also wants to | 12 |

226 | Solve: ( -(x-2)+4>-3 x+10 ) | 12 |

227 | Solve the following inequation and represent the solution set on a number line ( -8 frac{1}{2}<-frac{1}{2}-4 x leq 7 frac{1}{2}, x in 1 ) | 12 |

228 | Solve the given inequalities graphically: ( x+y geq 4 ) and ( 2 x-y>0 ) | 12 |

229 | Formulate the equations for the above problem. ( (x text { and } y text { are the number of units of } A ) and ( B ) manufactured in a day respectively) A. ( 15 x+5 y leq 10 ; 24 x+14 y geq 1000 ) B. ( 15 x+5 y leq 600 ; 24 x+14 y geq 1000 ) c. ( 5 x+15 y leq 600 ; 24 x+14 y geq 1000 ) D. ( 5 x+15 y leq 10 ; 24 x+14 y geq 1000 ) | 12 |

230 | Graph the solution set ( |boldsymbol{x}|=mathbf{1} ) ( A ) B. c. D. | 12 |

231 | A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is ( boldsymbol{R} boldsymbol{s} .5 ) and that from a shade is ( R s .3 . ) Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit? | 12 |

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