InterviewSolution
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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.
| 51. |
Which of the following is not a convex set ?A. B. C. D. |
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Answer» Correct Answer - B Recall the definition of convex set. |
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| 52. |
Simplify: `cot^(-1)""(1)/(sqrt(x^(2)-1))"for" c lt-1.` |
| Answer» Correct Answer - `pi-sec^(-1)x,as0ltpi-thetalt(pi)/(2)` | |
| 53. |
Which of the following points belongs to the region indicated by the ineqation `2x+3y lt -6` ?A. (0,2)B. (-3,8)C. (3,-2)D. (-2,-2) |
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Answer» Correct Answer - D Check the point which stisfies the given inequation . |
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| 54. |
L.P.P. is a process of findingA. maximum value of objective functionB. minimum value of objective functionC. optimal value of objective functionD. only maximum value of objective function |
| Answer» Correct Answer - C | |
| 55. |
The maximum value of the function, f=3x+5y, subject to the constraints `x ge 5 and y ge 5` , is ______A. 40B. 24C. 8D. Does not exist. |
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Answer» Correct Answer - D The given constraints `x gt 5 and y ge 5` form an open- convex polygon. `:.` The maximum value does not exist. |
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| 56. |
The solution set of `3x+2yle6` isA. half plane not containing originB. half plane containing the points lying on line `3x+2y=6` and originC. XY-plane except points on line `3x+2y=6`D. half plane not containing the points lying on line `3x+2y=6` and origin |
| Answer» Correct Answer - B | |
| 57. |
The distance of a point P from the positive X axis and positive Y axis are 3 units and 5 units , respectively . Find the coordinates of P. |
| Answer» Correct Answer - P=(5,3) | |
| 58. |
The construction company uses concrete blocks made up of cement and sand. The weight of a concrete block has to be at least 5kg. Cement costs Rs. 20 per kg. while sand costs Rs. 6 per kg. Strength consideration dictate that the concrete block should contain minimum 4 kg. of cement and not more than 2 kg. of sand. Form the LPP for the cost to be minimum.A. Maximize `z=20x+6y` subject to `x+yge5,xle4,yle2,xge0,yge0`B. Maximize `z=20x+6y` subject to `x+yge5,xle4,yge2,xge0,yge0`C. Maximize `z=20x+6y` subject to `x+yge5,xge4,yge2,xge0,yge0`D. Maximize `z=20x+6y` subject to `x+yge5,xge4,yle2,xge0,yge0` |
| Answer» Correct Answer - D | |
| 59. |
State whether the point (-3,4) lies on the line, 3x+2y+1=0 or not ? |
| Answer» Correct Answer - The point lies on the line | |
| 60. |
The solution set of the inequation `x+2yge3` isA. half plane containing the originB. half plane not containing the originC. the whole XY-plane except point lying on line `x+2y-3=0`D. open half plane not containing the origin |
| Answer» Correct Answer - B | |
| 61. |
The solution set of the inequation `2x+y gt 5` isA. half plane that contains the originB. open half plane not containing the originC. whole XY-plane except the points lying on line `2x+y=5`D. half plane not containing the origin |
| Answer» Correct Answer - B | |
| 62. |
The cost of each table or each chair cannot exceed Rs. 9. If the cost of 4 table and 5 chairs cannot exceed Rs. 120, then the inequation which best represents the above information are :A. `x lt 9, y lt 9, 5x+4x ge 120`B. ` x gt 9, y gt 9, 4x+5y ge 120`C. `0 lt x le 9, 0 lt y lt 9, 4x+5y le 120`D. `0 lt le 9, 0 lt y le9, 5x+4y ge 120` |
| Answer» Correct Answer - C | |
| 63. |
Discuss the differentiability of the function `f(x)={{:(2x-1,whenx,lt1/2),(3-6x,when x, ge1/2):} at x=1/2.` |
| Answer» Correct Answer - Not differentiable Or, k=2 | |
| 64. |
The region specified by the inequality `4x+6y le 12` contains the origin . ( True/ False ) |
| Answer» Correct Answer - True | |
| 65. |
The cost of each table and each chair cannot exceed Rs. 7. If the cost of 3 tables and 4 chairs cannot exceed Rs. 30, form the inequation for the above data.A. `x gt 0, y gt 0, x le 7, y ge 7 , 3x + 4y le 30`B. `x lt 0, y lt 0, x le 7, y le 7, 3x+4y le 30`C. `0 lt x lt 7, 0 lt y le7, 3x+4y le 30`D. `x gt 0, le y gt 0, x ge 7, y ge 7 and 3x+4y le 30` |
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Answer» Correct Answer - C (i) Let the cost of each table and chair be x and y. (ii) Consider the cost of each table and each chair as Rs. x and Rs. y respectively. (iii) Frame the inequations according to the given conditions. |
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| 66. |
The feasible solution that maximizes an objective function is called _____ |
| Answer» Correct Answer - optimum solution | |
| 67. |
If an isoprofit line coincides with the edge of the polygon, then the problem hasA. no solutionB. one solutionC. infinite solutionD. None of these |
| Answer» Correct Answer - C | |
| 68. |
Does the point (0,0) lie in the region specified by `x+y ge 6` ? |
| Answer» Correct Answer - No | |
| 69. |
The solution of the inequations ` x ge 0, y ge 0, y=2 and x=2` form the polygonal region with the vertices (0,0),(0,2),(2,0) and (2,2) and the polygon so formed by joining the vertices is a _____A. parallelogramB. rectangleC. squareD. rhombus |
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Answer» Correct Answer - C Check which quadrilateral is formed by the points (0,0) ,(0,2),(2,0) and (2,2) |
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| 70. |
If the isoprofit line moves away from the origin, then the value of the objective functions ______A. incresesB. DecreaseC. does not changeD. become zero |
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Answer» Correct Answer - A Increase ( standard result ). |
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| 71. |
Find the maximum value of x+y subjected to the condition `4x+3y le 12, 2x + 5y le 10, x le 0, x ge 0, y ge 0`.A. 3B. `(20)/(7)`C. `4`D. `(23)/(7)` |
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Answer» Correct Answer - D Find the closed- convex polygon formed by the given inequations and proceed. |
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| 72. |
The solution of the system of inequalities `x ge 0, x-5 le 0 and x ge y` is a polygonal region with the vertices asA. (0,0),(5,0),(5,5)B. (0,0),(0,5),(5,5)C. (5,5), (0,5), (5,0)D. (0,0), (0,5), (5,0) |
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Answer» Correct Answer - A Check the point which belongs the given inequations. |
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| 73. |
Which of the following is a point in the feasiable region determined by the linear inequalities `3x+2y ge 6 and 8x + 7y le 56` ?A. (3,1)B. (-3,1)C. (1,-3)D. (-3,1) |
| Answer» (3,1) satisfies both the given inequations. | |
| 74. |
The length and breadth of a rectangle ( in cm ) are x and y respectively `x le30, y le 20, x ge0 and y ge 0`. If a rectangle has a maximum perimeter , then its are is _______.A. `400 cm^(2)`B. `600 cm^(2)`C. `900 cm^(2)`D. None of these |
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Answer» The perimeter function is p=2(x+y) p is maximum, when x=30 and y=20 `implies p=2(50)=100` `:.` The area of the rectangle `=30xx20=600cm^(2)`. |
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| 75. |
Which of the following is a point in the feasiable region determined by the linear inequalities `2x+3y le 6 and 3x-2y le 16` ?A. (4,-3)B. (-2,4)C. (3,-2)D. (3,-4) |
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Answer» Correct Answer - C (i) Check the point which satisfies the given inequations. (ii) Substitute the value in the options in the given inequations. (iii) The point which satisfies the given inequations is the required point. |
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| 76. |
The vertices of the closed - convex polygon determined by the inequations `3x+2y ge 6, 4x+ 3y le 12 , x gt 0 and y ge 0` areA. (1,0),(2,0),(0,2),(0,1)B. (2,0),(3,0),(0,4) and (0,3)C. (1,0),(2,0),(0,2) and (2,2)D. (1,0),(0,2),(2,2) and (1,1) |
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Answer» Correct Answer - B (i) Check the points which belong to the given inequation. (ii) Represent the given inequations on the graph. (iii) Detect the closed - convex polygon and its vertices. |
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| 77. |
The objective function `z=4x+3y` subject to `3x+4yle24,8x+6yle48,xle5,yle6,xge0,yge0` can be maximizedA. at only one pointB. at two points onlyC. at infinite number of pointsD. at three points only |
| Answer» Correct Answer - C | |
| 78. |
The objective function `z=15x+30y` subject to `3x+yle12,x+2yle10,xge0,yge0,` can be maximizedA. at infinite number of pointsB. at two points onlyC. at one points onlyD. at three points only |
| Answer» Correct Answer - A | |
| 79. |
The lines `5x+4yge20,xle6,yle4,xge0,yge0` formA. a squareB. a rhombusC. a triangleD. a quadrilateral |
| Answer» Correct Answer - D | |
| 80. |
The maximum value of `z=x+y` subject to `x+yle10,3x-2yle15,xle6,xge0,yge0` isA. 5B. 7.5C. 12D. 10 |
| Answer» Correct Answer - D | |
| 81. |
The objective function `z=x+y` subject to `x+yle10,3x-2yle15,xle6,xge0,yge0` can be maximizedA. at one point onlyB. at two points onlyC. at infinite number of pointsD. at three points only |
| Answer» Correct Answer - C | |
| 82. |
The objective function `z = x_1 + x_2`, subject to `x_1 + x_2 leq 10,-2x_1 + 3x_2 leq 15,x_1 leq 6,x_1 ,x_2 leq 0` has maximum value of the feasible region.A. 5B. 7.5C. 12D. 10 |
| Answer» Correct Answer - D | |
| 83. |
Maximize `Z=4x+9y,` subject to the constraints `x ge0,yge0,x+5yle200, 2x+3yle134,` |
| Answer» Correct Answer - Maximum `Z=382 when x=10and y=38` | |
| 84. |
Find the maximum vlue of `Z=7x+7y,` subject ot the constrainst `x ge0,yge0,x +y ge 2 and 2x+2yle6.` |
| Answer» Correct Answer - Maximum `Z=21at x=3,y=0` | |
| 85. |
The common region represented by inequalities `0lexle6,0leyle4` isA. a triangleB. a rectangleC. a squareD. a pentagon |
| Answer» Correct Answer - B | |
| 86. |
In the following figure, find AP and BP. |
| Answer» Correct Answer - AP=3 units, BP=4 units | |
| 87. |
A manufactures makes two products, A and B. Product A sell at Rs. 200 each and takes `1/2` hours to make. Product B shell at Rs. 300 each and takes 1 hour to make. There is a permanent order for 14 of product A and 16 of product B.A working week consists of 40 hours of production and the weekly turnover must not be less than Rs. 10000. If the profit on each of the product A is Rs.20 and on product B, it is Rs.30 then how many of each should be produced so that the profit is maximum? Asso, find the maximum profit. |
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Answer» Correct Answer - A=48, B=16; maximum profit =Rs.1440 Let the number of articles produced per week be x of A and y of B. Then, `1/2x+yle40,200x+300yge10000,xge14,yge16.` Profit functin is `Z=20x+30y.` Maximize `Z=20x+30y.` subject to the constraints `x+2yle80,2x+3yge1000,xge14,yge16.` |
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| 88. |
A profit of Rs. 300 is made on class I ticket , and Rs. 800 is made on class II ticket. If x and y are the number of tickets of class I and class II sold, then the profit function is _______ |
| Answer» Correct Answer - f=300x+800y | |
| 89. |
If (3,2), (2,3),(4,2) and (2,4) are the vertices of a polygonal region subject to certain constraint, then the minimum value of the objective function f=9x+5y is __________ |
| Answer» Correct Answer - 33 | |
| 90. |
State which of the following points belong to the region specified by the corresponding inequation that is ,`3x+4y lt 4`A. (0,2),B. (3,2)C. (1,-2)D. (4,5) |
| Answer» Correct Answer - A::B | |
| 91. |
If (0,0), (0,4), (2,4) and (3,2) are the vertices of a polygonal region subject to certain constraints , then the maximum value of the objective funciton f=3x+2y is __________ |
| Answer» Correct Answer - 14 | |
| 92. |
If the line segment joining any two point A and B, belonging to a subset Y of a plane , is contained in the subset Y, then Y is called ______. |
| Answer» Correct Answer - a convex set | |
| 93. |
State which of the following points belong to the region specified by the corresponding inequation that is ,`5x-6y+30 gt 0`.A. (0,2)B. (-4,8)C. (2,3)D. (4,5) |
| Answer» Correct Answer - D | |
| 94. |
In a rectangular coordinate system, the region specified by the inequlity `y ge1` lies below the X-axis ( True/ False ) |
| Answer» Correct Answer - False | |
| 95. |
Does the line y-x+3=0 pass through the point (3,0) ? |
| Answer» Correct Answer - Yes | |
| 96. |
If `x gt 0 and y lt 0`, then the point (x,y) lies in the _____ quadrant of a rectangular co-ordinate system. |
| Answer» Correct Answer - fourth `(Q_(4))` | |
| 97. |
If a motorcyclist rides at a speed of 50 km/hr, he has to spend Rs. 2 per km on petrol. If he rides at a faster speed of 70 km/hr, the petrol cost increases to Rs. 2.5 per km. He has Rs. 500 To spend on petrol and wishes to travel maximum distance within an hour. Formulate as LPP.A. Maximize `z=x+y` subject to `(x)/(50)+(y)/(70)le1,2x+2.5yge500,xge0,yge0`B. Maximize `z=x+y` subject to `(x)/(50)+(y)/(70)le1,2x+2.5yle500,xge0,yge0`C. Maximize `z=x+y` subject to `(x)/(50)+(y)/(70)ge1,2x+2.5yle500,xge0,yge0`D. Maximize `z=x+y` subject to `(x)/(50)+(y)/(70)ge1,2x+2.5yge500,xge0,yge0` |
| Answer» Correct Answer - B | |
| 98. |
If `|veca+vecb|=60,|veca-vecb|=40 and |veca|=22"then find"|vecb|.` |
| Answer» Correct Answer - `vec|b|=46` | |
| 99. |
If A is a square matrix of order `3 and |3A|=k|A|` then find the value of k, |
| Answer» Correct Answer - `k=27` | |
| 100. |
If `**` is a binary operation on the set R of all real numers difined by `a**b=a+b-3` then find the identity element for `**.` |
| Answer» Correct Answer - `e=3` | |