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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Objective function of an LPP isA. a constraintB. a function to be optimisedC. a relation between the variableD. feasible region |
| Answer» Correct Answer - B | |
| 2. |
The objective function off LPP defined over the convex set attains it optimum value atA. at least two of the corner pointsB. all the corner pointsC. at least one of the corner pointsD. none of the corner points |
| Answer» Correct Answer - C | |
| 3. |
Feasible region is represented by A. `2x+5yge80,x+yle20,xge0,yge0`B. `2x+5yle80,x+yge20,xge0,yge0`C. `2x+5yge80,x+yge20,xge0,yge0`D. `2x+5yle80,x+yle20,xge0,yge0` |
| Answer» Correct Answer - D | |
| 4. |
The feasible solution of a LPP belongs toA. first and secondB. first and thirdC. only secondD. only first |
| Answer» Correct Answer - D | |
| 5. |
The vertices of a closed- convex polygon representing the feasible region of the objective function f are (5,1) (3,5) (4,3) and (2,5) . Find the maximum value of the function f=8x+9y.A. 61B. 69C. 59D. 49 |
| Answer» Correct Answer - B | |
| 6. |
The maximum or minimum of the objective funtion occurs only at the corner points of the feasible region. This theorem is known as fundamental theorem ofA. AlgebraB. ArithmeticC. CalculusD. Extreme point |
| Answer» Correct Answer - D | |
| 7. |
Region represented by the inequalities `xge0,yge0` isA. first quadrantB. second quadrantC. third quadrantD. fourth quadrant |
| Answer» Correct Answer - A | |
| 8. |
The objective function `z=2x+4y` subject to `2x+yge3,x+2yge6,xge0yge0` can be minimizedA. at infinite number of pointsB. at two points onlyC. at one points onlyD. at three points only |
| Answer» Correct Answer - A | |
| 9. |
In a mid-day meal porogramme, an NGO wants to provide vitamin-rich diet to the students of an MCD school. The dietician of the NGO wishes to mix two types of dood in such a way that vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food 1 contains 2 units per kg of vitamin A and 1 unit per kg of vitamin C. Food 2 contains 1 units per kg of vitamin A and 2 units per kg of vitamin C. It costs Rs.50 per kg to purchase Food 1 and Rs.70 per kg to purchase Food 2. Formulate the problems as LPP and solve it graphically for the imnimum cost of such a mixture ? |
| Answer» Correct Answer - Minimum cost = Rs. 380 | |
| 10. |
The minimum value of `z=6x+21y` subject to `x+2yge3,x+4yge4,3x+yge3,xge0,yge0` isA. 20.5B. 28.8C. 24D. 22.5 |
| Answer» Correct Answer - D | |
| 11. |
The corner points of the feasible region determined by the following system of linear inequalities: `2x+yge10, x+3yle15,x,yge0` are `(0,0),(5,0),(3,4)` and `(0,5)`. Let `Z=px+qy`, where `p,qge0`. Condition on `p` and `q` so that the maximum of `Z` occurs at both `(3,4)` and `(0,5)` is: (a) `p=q` (b) `p=2q` (c) `p=eq` (d) `q=3p` |
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Answer» (d) Maximum value of `Z` is unique. Given that the maximum value of `Z` is obtained at two points `(3,4)` and `(0,5)`. `:.` Value of `Z` at `(3,4)=` value of `Z` at `(0,5)` `impliesp(3)+q(4)=p(0)+q(5)` `implies3p+4q=5qimplies3p=q` |
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| 12. |
The minimum value of `z=7x+y` subject to `5x+yge5,x+yge3,xge0,yge0` isA. 5B. 2.5C. 6D. 3.5 |
| Answer» Correct Answer - A | |
| 13. |
The constraints `x+yge5,x+2yge6,xge3,yge0` and the objective function `z=-x+2y` hasA. unbounded solutionB. concave solutionC. bounded solutionD. unique solution |
| Answer» Correct Answer - A | |
| 14. |
The region represented by the inequations `2x+3yle18,x+yge10,xge0,yle0` isA. a polygonB. unboundedC. bondedD. null region |
| Answer» Correct Answer - D | |
| 15. |
Shaded, region of the constraints `10x+2yge20,x+yge6` isA. B. C. D. |
| Answer» Correct Answer - C | |
| 16. |
Show that the minimum of Z occurs at more than two points : Maximise `Z = x + y`, subject to `x-ylt=-1,-x+ylt=0,x , ygeq0`. |
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Answer» We can draw the graph for these two lines, `x-y = -1` and `-x+y=0` Please refer to video for the graph. As shown in the video, there is no common area between these two inequalities. So, there can not be any maximum value for Z. |
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| 17. |
Solve the following linear programming problem graphically :Minimise `Z = 200 x + 500 y`. . . (1)subject to the constraints:`x+2ygeq10` . . .(2)`3x+4ylt=24` . . .(3)`xgeq0,ygeq0` . . .(4) |
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Answer» corner point method`` `(0,6)=3000` `(0,5)=2500` `(4,3)=2300` `(Z)=(4,3)=2300` |
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| 18. |
A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the tune (in minutes) required for each toy on the machines is given below:Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. show that 15 toys of type A and 30 of the B should be manufactured m a day to get maximum profit. |
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Answer» let type A `= x` let type B `= y` Acc to question `12x + 6y <= 360` `18x <= 360` `6x + 9y <= 300` Acc to graph `a(0,40) , b(15,30) ,c(20, 20) , d(20, 0)` to maximize, `7.5x + 5y= 200` `7.5 xx 15 + 5 xx 30 = 262.5` when `A= 15` `B= 30` Answer |
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| 19. |
Shaded, region of the constraints `x+yge5,2x+3yle18,4x+3yle24,xge0,yge0` isA. B. C. D. |
| Answer» Correct Answer - B | |
| 20. |
Solve the Following Linear Programming Problem graphically : Maximise `Z = 3x + 4y`subject to the constraints : `x+ylt=4,xgeq0,ygeq0`. |
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Answer» We can create a triangle with the given constraints. Please refer to video for the graph. From, the graph, coordinates of triangle are, `A(0,0),B(4,0) and C(0,4)` As `Z = 3x+4y` At `A(0,0), Z = 0` At `B(4,0), Z = 12` At `C(0,4), Z = 16` So, maximum value of `Z` will be `16` at `C(0,4)`. |
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| 21. |
The solution set of the constraints `x+yle11,3x+2yge25,2x+5yge20,xge0,yge0` includes the pointA. (2,3,)B. (3,2)C. (3,8)D. (4,3) |
| Answer» Correct Answer - C | |
| 22. |
The area of the feasible region for the following constraints ` 3y +x ge 3, x ge 0, y ge 0 ` will beA. boundedB. unboundedC. convexD. concave |
| Answer» Correct Answer - B | |
| 23. |
Which of the term is not used in a linear programming problem ?A. Slack variableB. Objective funcitonC. Concave regionD. Feasible region |
| Answer» Correct Answer - C | |
| 24. |
By graphical method, the solutions of linear programming problem maximise `Z=3x_(1)+5x_(2)` subject to constraints `3x_(1)+2x_(2) le 18, x_(1) le 4, x_(2) le 6 x_(1) ge0,x_(2) ge 0 ` areA. `x_(1)=2,x_(2)=0,z=6`B. `x_(1)=2,x_(2)=6,z=36`C. `x_(1)=4,x_(2)=3,z=27`D. `x_(1)=4,x_(2)=6,z=42` |
| Answer» Correct Answer - B | |
| 25. |
The constraints `-x+yle1,-x+3yle9,xge0,yge0` definesA. bounded feasible regionB. unbounded feasible regionC. both bounded and unbounded regionD. unique solution |
| Answer» Correct Answer - B | |
| 26. |
The maximum value of `z=6x+4y` subject to `xle2,x+yle3,-2x+yle1,xge0,yge0,` isA. 13B. 16C. 13.33D. 16.33 |
| Answer» Correct Answer - B | |
| 27. |
The constraints `3x+2yge9,x-yle3,xge0,yge0` and the objective function `z=4x+2y` hasA. unbounded solutionB. concave solutionC. bounded solutionD. unique solution |
| Answer» Correct Answer - A | |
| 28. |
The constraints `x+yle8,2x+3yle12,xge0,yge0` and the objective function `z=4x+6y` hasA. concave solutionB. no unique solutionC. bounded solutionD. unique solution |
| Answer» Correct Answer - B | |
| 29. |
The minimum value of `z=6x+2y` subject to `5x+9yle90,x+yge4,yle8,xge0,yge0` isA. 24B. 6C. 8D. 16 |
| Answer» Correct Answer - C | |
| 30. |
Minimize `Z=2x+3y.` subjeft ot the constraints `xge0,yge0,x+2yge1 and x+2yle10.` |
| Answer» Correct Answer - Minimum `Z=3/2at(0,(1)/(2))` | |
| 31. |
A manufacture produceds two types of steel trunks. He has two machines, A and B. The first type of book case requires 3 hours on machine A and 3 hours on machine B for completion whereas the second type required 3 hours on machine A and 2 hours n machine B. Machines A and B can work at most for 18 hours and 15 hours per day respectively. He earns a profit of Rs.30 and Rs.25 per trunk of the first type and second type respectively. How many trunks of each type must he make each day to make the maximum profit? |
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Answer» Correct Answer - For getting a maximum profit of Rs. 165, 3 trunks of each type should be manufactured. Let x trunks of the first type and y rrunks of the second type be manufactured. Then, `3x+3yle18, 3x+2yle15, xge0andyge0.` Maximize `Z=30x+25y.` |
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| 32. |
A manufure of a line f patent meducines is preparing a prodiction plan on medicines A and B. There are sufficient ingredients available to make 20000 bottes of A and 40000 bottles of B but there are only 45000 bottles int which either of the medicines can be put. Furthermore, it takes 3 horus to prepare enough material to fill 1000 bottles of B, and there are 66 hours available for this operation. The profit Rs. 8 per bottle for A and Rs.7 per bottle for B. How should the manufacturer schedule the production in order to maximize his profit? Also find the maximum profit. |
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Answer» Correct Answer - 12500 bottles of A and 34500 bottles of B, and maximum profit is Rs.325500 Maximize `Z=8x+7y"subject to"3x+y le66000, x+yle45000,le20000,yle40000,xge0andy ge0.` |
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| 33. |
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes 1 hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs 100 and that on a bracelet is Rs 300, how many of each should be produced daily to maximize the profit? |
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Answer» Correct Answer - `x=16and y=8` Maximize `P=100x+300y "subject to"x gt0,ygt0,x+y le24,(1)/(2)x+yle16.` |
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| 34. |
A firm manufactures two types of products, A and B, and sells them at a profil of 3 per unit to type B product and 5 perunit of type A product. Both product is processed on two machines M1and M2 One unit of type A requires one minute of processing time on M1 and two minutes of processing time on M2i whereas one unit of type B requires one minute of processing time on M1 and one minute on M Machines sells them at a profit of 5 per unit of type A and M, and M, are respectively available for at most 5 hours and 6 hours in a day. Find out how many units of each type of product the firn should produce a day in order to maximize the profit. Solve the problem graphically [CHSE 2000] |
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Answer» Correct Answer - 200200 Maximum `Z=2x+2y "subject to" x ge0,yge0,x+yle400,2x+y le600.` |
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| 35. |
A dealer wishes to purchase a number of fans and sewing machines. He has only Rs.5,760 to invest and has a space for at most 20 items. A fan costs him Rs. 360and a sewing machine Rs. 240. His expectation is that he can sell a fan at aprofit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that hecan sell all the items that he can buy, how should he invest his money inorder to maximize the profit? Formulate this as a linear programming problem and solve it graphically. |
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Answer» Correct Answer - 24 sewing machines only Maximize `P=22x+18y` subject to `x ge0,yx+yle20,360x+240yle5760.` |
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| 36. |
The minimum cost of each table is Rs. 10 and each capsule is Rs. 10. If the cost of 8 table and 5 capsules is not less than Rs. 150, frame the inequations for the given data.A. `x ge 10 , y ge 10, 8x+5y ge 150`B. `x ge 10, y ge 10 ,8s+5y le 150`C. `x le 10, y le 10, 8x+5y ge 150`D. ` x le 10, y le 10, 8x+5y le 150` |
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Answer» Correct Answer - A Let the cost of each tablet of x and the cost of each capsuel be y. Minimum cost of each tablet and each capsule is Rs. 10. `:. xge 10 and y ge 10` The cost of 8 tablet and 5 capsules should be greater than or equal to 150 ,i.e., ` 8x+5y gt 150`. |
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| 37. |
Evaluate: `int(sinx)/((cos^(2)x+1)(cos^(2)x+4))dx.` |
| Answer» Correct Answer - `-1/3tan^(-1)(cosx)+1/6tan^(-1)((cosx)/(2))+C` | |
| 38. |
Solve the differential equation `(1+e^(x//y))sx+e^(x//y)(1-(x)/(y))dy=0.` Or Find the general solution of the differential equation `(1+tany)(dx-dy)+2xdy=0.` |
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Answer» Correct Answer - `(e^(x)//y+(x)/(y))y=C` Or x(cosy+siny)e^(y)=e^(y)siny+C` |
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| 39. |
A magazine seller has 500 subscribers and collects annual subscription charges of Rs.300 per subscriber. Sh e proposes to increase the annual subscription charges and it is believed that for every increase of Re 1, one subscriber will discontinue. What increase will bring maximum income to her? M solution. Write one important role of magazines in our lives. ake appropriate assumptions in order to apply derivatives to reach the |
| Answer» Correct Answer - Increase subscription charges by Rs.100 to have maximum income. Through reading magazines, our mind and pint of vieq are consolidated and enriched. | |
| 40. |
Minimize ` z = 6x + 4y `, subject to ` 3x + 2y ge12, x + y ge5, 0 le x le 4, 0 le y le 4`.A. 22B. 24C. 40D. 28 |
| Answer» Correct Answer - B | |
| 41. |
The objective function `z=6x+4y` subjective to `3x+2yge12,x+yge5,0lexle4,0leyle4` can be minimizedA. at one point onlyB. at two points onlyC. at infinite number of pointsD. at three points only |
| Answer» Correct Answer - C | |
| 42. |
Minimize x+y , subject to the constraints : `2x+y ge 6` `x+2y ge 8` `x ge 0 and y ge 0` |
| Answer» Correct Answer - `(14)/(3)` | |
| 43. |
two cards are drawn successively with replacement from a pack of 52 cards. Find the probability distribution of the number of diamonds and the mean of the distribution. |
| Answer» Correct Answer - Mean `1/2,"Variance"=3/8` | |
| 44. |
The minimum value of 2x + 3y subject to the condition `x+4y ge 8, 4x+y ge 12, x ge 0 and y ge 0` isA. `(28)/(3)`B. `16`C. `(25)/(3)`D. `10` |
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Answer» Correct Answer - A Find the open- convex polygon formed by the given equations and proceeds . |
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| 45. |
The inequation represent by the following graph is A. `2x+3y+6 le 0`B. `2x+3y -6 ge 0`C. `2x+3 le 6`D. ` 2x +3y +6 ge 0` |
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Answer» Correct Answer - C The corresponding equation of the line is `(x)/(3)+(y)/(1)=1` |
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| 46. |
Which of the following is a convex set ?A. A triangleB. A squareC. A circleD. All of these |
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Answer» Correct Answer - D Recall the definition of convex set. |
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| 47. |
which of the following is not a convex set?A. `{(x,y):2x+2yle7}`B. `{(x,y):x^(2)+y^(2)le4}`C. `{x:|x|=5}`D. `{(x,y):2x^(2)+3y^(2)le6}` |
| Answer» Correct Answer - C | |
| 48. |
Which of the following set is convex?A. `{(x,y):x^(2)+y^(2)ge1}`B. `{(x,y):y^(2)gex}`C. `{(x,y):3x^(2)+4y^(2)ge5}`D. `{(x,y):yge2,yle4}` |
| Answer» Correct Answer - D | |
| 49. |
Which of the following set is not a convex set?A. `{(x,y):1lex^(2)+y^(2)le3}`B. `{(x,y):x^(2)+y^(2)le2}`C. `{(x,y):x+yle1}`D. `{(x,y):2x^(2)+3y^(2)le6}` |
| Answer» Correct Answer - A | |
| 50. |
If `A=[{:(3,4),(1,-1):}]"then using"A^(-1)` solve the following system of equatins: `3x+4y=5,x-y=-3.` |
| Answer» Correct Answer - `x=-1,y=2` | |