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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 3451. |
The maximum value of \[z=4x+2y\] subject to the constraints \[2x+3y\le 18,\ x+y\ge 10\]; \[x,\ y\ge 0\], is [MP PET 2001] |
| A. | 36 |
| B. | 40 |
| C. | 20 |
| D. | None of these |
| Answer» E. | |
| 3452. |
The maximum value of \[P=x+3y\] such that \[2x+y\le 20\], \[x+2y\le 20\], \[x\ge 0,\ y\ge 0\], is [MP PET 1995] |
| A. | 10 |
| B. | 60 |
| C. | 30 |
| D. | None of these |
| Answer» D. None of these | |
| 3453. |
The maximum value of \[P=6x+8y\] subject to constraints \[2x+y\le 30,\ x+2y\le 24\] and \[x\ge 0,\ y\ge 0\] is [MP PET 1994; 95] |
| A. | 90 |
| B. | 120 |
| C. | 96 |
| D. | 240 |
| Answer» C. 96 | |
| 3454. |
If the number of available constraints is 3 and the number of parameters to be optimized is 4, then |
| A. | The objective function can be optimized |
| B. | The constraints are short in number |
| C. | The solution is problem oriented |
| D. | None of these |
| Answer» C. The solution is problem oriented | |
| 3455. |
The solution of a problem to maximize the objective function \[z=x+2y\] under the constraints \[x-y\le 2\], \[x+y\le 4\] and \[x,\ y\ge 0\], is |
| A. | \[x=0,\ y=4,\ z=8\] |
| B. | \[x=1,\ y=2,\ z=5\] |
| C. | \[x=1,\ y=4,\ z=9\] |
| D. | \[x=0,\ y=3,\ z=6\] |
| Answer» B. \[x=1,\ y=2,\ z=5\] | |
| 3456. |
The solution for minimizing the function \[z=x+y\] under a L.P.P. with constraints \[x+y\ge 1\], \[x+2y\le 10\], \[y\le 4\] and \[x,\ y\ge 0\], is |
| A. | \[x=0,\ y=0,\ z=0\] |
| B. | \[x=3,\ y=3,\ z=6\] |
| C. | There are infinitely solutions |
| D. | None of these |
| Answer» D. None of these | |
| 3457. |
The minimum value of linear objective function \[c=2x+2y\] under linear constraints \[3x+2y\ge 12\], \[x+3y\ge 11\] and \[x,\ y\ge 0\], is |
| A. | 10 |
| B. | 12 |
| C. | 6 |
| D. | 5 |
| Answer» B. 12 | |
| 3458. |
The point at which the maximum value of \[(3x+2y)\] subject to the constraints \[x+y\le 2,\ x\ge 0,\ y\ge 0\] is obtained, is [MP PET 1993] |
| A. | (0, 0) |
| B. | (1.5, 1.5) |
| C. | (2, 0) |
| D. | (0, 2) |
| Answer» D. (0, 2) | |
| 3459. |
For the L.P. problem Min\[z=2x-10y\] subject to \[x-y\ge 0,\ \ x-5y\ge -5\] and \[x,\ y\ge 0\], \[z=\] |
| A. | ?10 |
| B. | ?20 |
| C. | 0 |
| D. | 10 |
| Answer» B. ?20 | |
| 3460. |
For the L.P. problem Min\[z=2x+y\] subject to \[5x+10y\le 50,\] \[x+y\ge 1,\ \ y\le 4\] and \[x,\ y\ge 0\], \[z=\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | ½ |
| Answer» C. 2 | |
| 3461. |
On maximizing \[z=4x+9y\] subject to \[x+5y\le 200,\] \[x+5y\le 200,\ \ 2x+3y\le 134\] and \[x,\ y\ge 0\], \[z=\] |
| A. | 380 |
| B. | 382 |
| C. | 384 |
| D. | None of these |
| Answer» C. 384 | |
| 3462. |
For the L.P. problem Min\[z={{x}_{1}}+{{x}_{2}}\] such that \[5{{x}_{1}}+10{{x}_{2}}\le 0,\ \ {{x}_{1}}+{{x}_{2}}\ge 1,\ \ {{x}_{2}}\le 4\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] |
| A. | There is a bounded solution |
| B. | There is no solution |
| C. | There are infinite solutions |
| D. | None of these |
| Answer» D. None of these | |
| 3463. |
For the L.P. problem Min\[z=-{{x}_{1}}+2{{x}_{2}}\] such that \[-{{x}_{1}}+3{{x}_{2}}\le 0,\]\[{{x}_{1}}+{{x}_{2}}\le 6,\ {{x}_{1}}-{{x}_{2}}\le 2\]and \[{{x}_{1}},\ {{x}_{2}}\ge 0\],\[{{x}_{1}}=\] |
| A. | 2 |
| B. | 8 |
| C. | 10 |
| D. | 12 |
| Answer» B. 8 | |
| 3464. |
A basic solution is called non-degenerate, if |
| A. | All the basic variables are zero |
| B. | None of the basic variables is zero |
| C. | At least one of the basic variables is zero |
| D. | None of these |
| Answer» C. At least one of the basic variables is zero | |
| 3465. |
For the L.P. problem Max\[z=3{{x}_{1}}+2{{x}_{2}}\] such that \[2{{x}_{1}}-{{x}_{2}}\ge 2\], \[{{x}_{1}}+2{{x}_{2}}\le 8\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\], \[z=\] |
| A. | 12 |
| B. | 24 |
| C. | 36 |
| D. | 40 |
| Answer» C. 36 | |
| 3466. |
In the above question the is o-profit line is |
| A. | \[3x+y=30\] |
| B. | \[x+3y=20\] |
| C. | \[3x-y=20\] |
| D. | \[4x+3y=24\] |
| Answer» B. \[x+3y=20\] | |
| 3467. |
A shopkeeper wants to purchase two articles A and B of cost price Rs. 4 and 3 respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total article worth more than Rs. 24. If he purchases the number of articles of A and B, x and y respectively, then linear constraints are |
| A. | \[x\ge 0,\ y\ge 0,\ 4x+3y\le 24\] |
| B. | \[x\ge 0,\ y\ge 0,\ 30x+10y\le 24\] |
| C. | \[x\ge 0,\ y\ge 0,\ 4x+3y\ge 24\] |
| D. | \[x\ge 0,\ y\ge 0,\ 30x+40y\ge 24\] |
| Answer» B. \[x\ge 0,\ y\ge 0,\ 30x+10y\le 24\] | |
| 3468. |
A factory produces two products A and B. In the manufacturing of product A, the machine and the carpenter requires 3 hour each and in manufacturing of product B, the machine and carpenter requires 5 hour and 3 hour respectively. The machine and carpenter work at most 80 hour and 50 hour per week respectively. The profit on A and B is Rs. 6 and 8 respectively. If profit is maximum by manufacturing x and y units of A and B type product respectively, then for the function \[6x+8y\] the constraints are |
| A. | \[x\ge 0,\ y\ge 0,\ 5x+3y\le 80,\ 3x+2y\le 50\] |
| B. | \[x\ge 0,\ y\ge 0,\ 3x+5y\le 80,\ 3x+3y\le 50\] |
| C. | \[x\ge 0,\ y\ge 0,\ 3x+5y\ge 80,\ 2x+3y\ge 50\] |
| D. | \[x\ge 0,\ y\ge 0,\ 5x+3y\ge 80,\ 3x+2y\ge 50\] |
| Answer» C. \[x\ge 0,\ y\ge 0,\ 3x+5y\ge 80,\ 2x+3y\ge 50\] | |
| 3469. |
The maximum value of objective function in the above question is |
| A. | 100 |
| B. | 92 |
| C. | 95 |
| D. | 94 |
| Answer» D. 94 | |
| 3470. |
The objective function for the above question is |
| A. | \[10x+14y\] |
| B. | \[5x+10y\] |
| C. | \[3x+5y\] |
| D. | \[5y+3x\] |
| Answer» D. \[5y+3x\] | |
| 3471. |
In a test of Mathematics, there are two types of questions to be answered?short answered and long answered. The relevant data is given below Type of questions Time taken to solve Marks Number of questions Short answered questions 5 minute 3 10 Long answered questions 10 minute 5 14 The total marks is 100. Students can solve all the questions. To secure maximum marks, a student solves x short answered and y long answered questions in three hours, then the linear constraints except\[x\ge 0,\ y\ge 0\], are |
| A. | \[5x+10y\le 180\], \[x\le 10,\ y\le 14\] |
| B. | \[x+10y\ge 180\], \[x\le 10,\ y\le 14\] |
| C. | \[5x+10y\ge 180\], \[x\ge 10,\ y\ge 14\] |
| D. | \[5x+10y\le 180\], \[x\ge 10,\ y\ge 14\] |
| Answer» B. \[x+10y\ge 180\], \[x\le 10,\ y\le 14\] | |
| 3472. |
The objective function in the above question is |
| A. | \[2x+y\] |
| B. | \[x+2y\] |
| C. | \[2x+2y\] |
| D. | \[8x+10y\] |
| Answer» D. \[8x+10y\] | |
| 3473. |
For the constraints of a L.P. problem given by \[{{x}_{1}}+2{{x}_{2}}\le 2000\],\[{{x}_{1}}+{{x}_{2}}\le 1500\],\[{{x}_{2}}\le 600\]and \[{{x}_{1}},\ {{x}_{2}}\ge 0\], which one of the following points does not lie in the positive bounded region |
| A. | (1000, 0) |
| B. | (0, 500) |
| C. | (2, 0) |
| D. | (2000, 0) |
| Answer» E. | |
| 3474. |
A firm produces two types of products A and B. The profit on both is Rs. 2 per item. Every product requires processing on machines \[{{M}_{1}}\] and \[{{M}_{2}}\]. For A, machines \[{{M}_{1}}\] and \[{{M}_{2}}\] takes 1 minute and 2 minute respectively and for B, machines \[{{M}_{1}}\] and \[{{M}_{2}}\] takes the time 1 minute each. The machines \[{{M}_{1}},\ {{M}_{2}}\] are not available more than 8 hours and 10 hours, any of day, respectively. If the products made x of A and y of B, then the linear constraints for the L.P.P. except \[x\ge 0,\ y\ge 0\], are |
| A. | \[x+y\le 480\,,\ 2x+y\le 600\] |
| B. | \[x+y\le 8,\ 2x+y\le 10\] |
| C. | \[x+y\ge 480\,,\ 2x+y\ge 600\] |
| D. | \[x+y\le 8,\ 2x+y\ge 10\] |
| Answer» B. \[x+y\le 8,\ 2x+y\le 10\] | |
| 3475. |
Mohan wants to invest the total amount of Rs. 15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. He invest Rs. x in saving certificates and Rs. y in national saving bonds. Then the objective function for this problem is |
| A. | \[0.08x+0.10y\] |
| B. | \[\frac{x}{2000}+\frac{y}{2500}\] |
| C. | \[2000x+2500y\] |
| D. | \[\frac{x}{8}+\frac{y}{10}\] |
| Answer» B. \[\frac{x}{2000}+\frac{y}{2500}\] | |
| 3476. |
A wholesale merchant wants to start the business of cereal with Rs. 24000. Wheat is Rs. 400 per quintal and rice is Rs. 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then for maximum profit the objective function is |
| A. | \[25x+40y\] |
| B. | \[40x+25y\] |
| C. | \[400x+600y\] |
| D. | \[\frac{400}{40}x+\frac{600}{25}y\] |
| Answer» C. \[400x+600y\] | |
| 3477. |
The feasible region for the following constraints \[{{L}_{1}}\le 0,{{L}_{2}}\ge 0,\,{{L}_{3}}=0,\,x\ge 0,y\ge 0\] in the diagram shown is [Kerala (Engg.) 2005] |
| A. | Area DHF |
| B. | Area AHC |
| C. | Line segment EG |
| D. | Line segment GI |
| E. | Line segment IC |
| Answer» D. Line segment GI | |
| 3478. |
The graph of inequations \[x\le y\] and \[y\le x+3\] is located in |
| A. | II quadrant |
| B. | I, II quadrants |
| C. | I, II, III quadrants |
| D. | II, III, IV quadrants |
| Answer» D. II, III, IV quadrants | |
| 3479. |
Which of the terms is not used in a linear programming problem [MP PET 2000] |
| A. | Slack variables |
| B. | Objective function |
| C. | Concave region |
| D. | Feasible solution |
| Answer» D. Feasible solution | |
| 3480. |
Which of the following is not true for linear programming problems [Kurukshetra CEE 1998] |
| A. | A slack variable is a variable added to the left hand side of a less than or equal to constraint to convert it into an equality |
| B. | A surplus variable is a variable subtracted from the left hand side of a greater than or equal to constraint to convert it into an equality |
| C. | A basic solution which is also in the feasible region is called a basic feasible solution |
| D. | A column in the simplex tableau that contains all of the variables in the solution is called pivot or key column |
| Answer» E. | |
| 3481. |
The constraints \[-{{x}_{1}}+{{x}_{2}}\le 1\] \[-{{x}_{1}}+3{{x}_{2}}\le 9\] \[{{x}_{1}},\ {{x}_{2}}\ \ge 0\] define on [MP PET 1999] |
| A. | Bounded feasible space |
| B. | Unbounded feasible space |
| C. | Both bounded and unbounded feasible space |
| D. | None of these |
| Answer» C. Both bounded and unbounded feasible space | |
| 3482. |
The intermediate solutions of constraints must be checked by substituting them back into |
| A. | Objective function |
| B. | Constraint equations |
| C. | Not required |
| D. | None of these |
| Answer» C. Not required | |
| 3483. |
If the constraints in a linear programming problem are changed |
| A. | The problem is to be re-evaluated |
| B. | Solution is not defined |
| C. | The objective function has to be modified |
| D. | The change in constraints is ignored |
| Answer» B. Solution is not defined | |
| 3484. |
The optimal value of the objective function is attained at the points [MP PET 1998] |
| A. | Given by intersection of inequations with axes only |
| B. | Given by intersection of inequations with x-axis only |
| C. | Given by corner points of the feasible region |
| D. | None of these |
| Answer» D. None of these | |
| 3485. |
Objective function of a L.P.P. is |
| A. | A constraint |
| B. | A function to be optimized |
| C. | A relation between the variables |
| D. | None of these |
| Answer» C. A relation between the variables | |
| 3486. |
Inequation \[y-x\le 0\] represents |
| A. | The half plane that contains the positive x-axis |
| B. | Closed half plane above the line \[y=x\] which contains positive y-axis |
| C. | Half plane that contains the negative x-axis |
| D. | None of these |
| Answer» B. Closed half plane above the line \[y=x\] which contains positive y-axis | |
| 3487. |
If a point (h, k) satisfies an inequation \[ax+by\ge 4\], then the half plane represented by the inequation is |
| A. | The half plane containing the point (h, k) but excluding the points on \[ax+by=4\] |
| B. | The half plane containing the point (h, k) and the points on \[ax+by=4\] |
| C. | Whole xy-plane |
| D. | None of these |
| Answer» C. Whole xy-plane | |
| 3488. |
The region represented by the inequation system \[x,\ y\ge 0\], \[y\le 6,\ x+y\le 3\], is |
| A. | Unbounded in first quadrant |
| B. | Unbounded in first and second quadrants |
| C. | Bounded in first quadrant |
| D. | None of these |
| Answer» D. None of these | |
| 3489. |
The region represented by \[2x+3y-5\le 0\] and \[4x-3y+2\le 0\], is |
| A. | Not in first quadrant |
| B. | Bounded in first quadrant |
| C. | Unbounded in first quadrant |
| D. | None of these |
| Answer» C. Unbounded in first quadrant | |
| 3490. |
Which of the following is not a vertex of the positive region bounded by the inequalities \[2x+3y\le 6\], \[5x+3y\le 15\] and \[x,\ y\ge 0\] |
| A. | (0, 2) |
| B. | (0, 0) |
| C. | (3, 0) |
| D. | None of these |
| Answer» E. | |
| 3491. |
The value of objective function is maximum under linear constraints |
| A. | At the center of feasible region |
| B. | At (0, 0) |
| C. | At any vertex of feasible region |
| D. | The vertex which is at maximum distance from (0, 0) |
| Answer» E. | |
| 3492. |
For the following feasible region, the linear constraints are |
| A. | \[x\ge 0,\ y\ge 0,\ 3x+2y\ge 12,\ x+3y\ge 11\] |
| B. | \[x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\ge 11\] |
| C. | \[x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\le 11\] |
| D. | None of these |
| Answer» B. \[x\ge 0,\ y\ge 0,\ 3x+2y\le 12,\ x+3y\ge 11\] | |
| 3493. |
The necessary condition for third quadrant region in xy-plane, is |
| A. | \[x>0,\ y<0\] |
| B. | \[x<0,\ y<0\] |
| C. | \[x<0,\ y>0\] |
| D. | \[x<0,\ y=0\] |
| Answer» C. \[x<0,\ y>0\] | |
| 3494. |
In which quadrant, the bounded region for inequations \[x+y\le 1\] and \[x-y\le 1\] is situated |
| A. | I, II |
| B. | I, III |
| C. | II, III |
| D. | All the four quadrants |
| Answer» E. | |
| 3495. |
A vertex of a feasible region by the linear constraints \[3x+4y\le 18,\ 2x+3y\ge 3\] and \[x,\ y\ge 0\], is |
| A. | (0, 2) |
| B. | (4.8, 0) |
| C. | (0, 3) |
| D. | None of these |
| Answer» E. | |
| 3496. |
A vertex of bounded region of inequalities \[x\ge 0\], \[x+2y\ge 0\] and \[2x+y\le 4\], is |
| A. | (1, 1) |
| B. | (0, 1) |
| C. | (3, 0) |
| D. | (0, 0) |
| Answer» E. | |
| 3497. |
The vertex of common graph of inequalities \[2x+y\ge 2\] and \[x-y\le 3\], is |
| A. | (0, 0) |
| B. | \[\left( \frac{5}{3},\ -\frac{4}{3} \right)\] |
| C. | \[\left( \frac{5}{3},\ \frac{4}{3} \right)\] |
| D. | \[\left( -\frac{4}{3},\ \frac{5}{3} \right)\] |
| Answer» C. \[\left( \frac{5}{3},\ \frac{4}{3} \right)\] | |
| 3498. |
The true statement for the graph of inequations \[3x+2y\le 6\] and \[6x+4y\ge 20\], is |
| A. | Both graphs are disjoint |
| B. | Both do not contain origin |
| C. | Both contain point (1, 1) |
| D. | None of these |
| Answer» B. Both do not contain origin | |
| 3499. |
The position of points O (0,0) and P (2, ? 2) in the region of graph of inequation \[2x-3y |
| A. | O inside and P outside |
| B. | O and P both inside |
| C. | O and P both outside |
| D. | O outside and P inside |
| Answer» B. O and P both inside | |
| 3500. |
For the constraint of a linear optimizing function \[z={{x}_{1}}+{{x}_{2}}\], given by \[{{x}_{1}}+{{x}_{2}}\le 1,\ 3{{x}_{1}}+{{x}_{2}}\ge 3\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] |
| A. | There are two feasible regions |
| B. | There are infinite feasible regions |
| C. | There is no feasible region |
| D. | None of these |
| Answer» D. None of these | |