MCQ 11 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The linear programming problem,maximize $z = 2x + 3y$ subject to constraints $\text{x}+\text{y}\leq4,\text{x}\geq0,\text{y}\geq0$ It gives the maximum value of $Z$ as $8 .$
Reason: To obtain maximum value of $Z,$ we need to compare value of $Z$ at all the corner points of the feasible region.
- A
$A$ is true$, R$ is true$; R$ is a correct explanation for $A.$
- B
$A$ is true$,R$ is true$; R$ is not a correct explanation for $A.$
- C
$A$ is true$, R$ is false.
- ✓
$A$ is false$, R$ is true.
AnswerCorrect option: D. $A$ is false$, R$ is true.
View full question & answer→MCQ 21 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ Consider the linear programming problem. Maximise $Z = 4x + y$ Subject to constraints $\text{x}+\text{y}\leq50;\text{x}+\text{y}\geq100$ and $\text{x},\text{y}\geq0,$ Then, maximum value of $Z$ is $50.$
Reason $(R):$ If the shaded region is bounded then maximum value of objective function can be determined.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 31 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following: Consider, the graph of constraints stated as linear inequalities as below: $5\text{x}+\text{y}\leq100,\text{x}+\text{y}\leq60,\text{x},\text{y}\geq0.$
Assertion $(A):$ The points $(10, 50), (0, 60) , (10, 10)$ and $(20, 0)$ are feasible solutions.
Reason $(R):$ Points within and on the boundary of the feasible region represent feasible solutions of the constraints. - ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
View full question & answer→MCQ 41 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following: Consider, the graph of constraints stated as linear inequalities as below: $5\text{x}+\text{y}\leq100,\text{x}+\text{y}\leq60,\text{x},\text{y}\geq0.$
Assertion $(A): (25, 40)$ is an infeasible solution of the problem.
Reason $(R):$ Any point inside the feasible region is called an infeasible solution. - A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- ✓
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 51 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Maximise $Z = 3x + 4y,$ subjectto constraints: $\text{x}+\text{y}\leq1,\text{x}\geq0,\text{y}\geq0$ Then maximum value of $Z$ is $4.$
Reason: If the shaded region is not bounded then maximum value cannot be determined.
- A
$A$ is true$,R$ is true$; R$ is a correct explanation for $A.$
- B
$A$ is true$,R$ is true$; R$ is not a correct explanation for $A.$
- ✓
$A$ is true$, R$ is false.
- D
$A$ is false$, R$ is true.
AnswerCorrect option: C. $A$ is true$, R$ is false.
View full question & answer→MCQ 61 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ If an $\text{LPP}$ attains its maximum value at two corner points of the feasible region then it attains maximum value at infinitely many points.
Reason $(R):$ if the value of the objective function of a $\text{LPP}$ is same at two corners then it is same at every point on the line joining two corner points.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
View full question & answer→MCQ 71 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ The region represented by the set $\{(\text{x},\text{y}):4\leq\text{x}^2+\text{y}^2\leq9\}$ is a convex set.
Reason $(R):$ The set $\{(\text{x},\text{y}):4\leq\text{x}^2+\text{y}^2\leq9\}$ represents the region between two concentric circles of radii $2$ and $3.$
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 81 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ Feasible region is the set of points which satisfy all of the given constraints.
Reason $(R):$ The optimal value of the objective function is attained at the points on $X -$ axisonly.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- ✓
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 91 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following
Assertion $(A):$ The graph of $\text{x}\leq2$ and $\text{y}\geq2$ will be situated in the first and second quadrants.
Reason $(R):$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
View full question & answer→MCQ 101 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Maximum value of $z = 11x + 7y,$ subjectto constraints $2\text{x}+\text{y}\leq6,\text{x}\leq2,\text{x}\geq0,\text{y}\geq0$ will be obtained at $(0, 6).$
Reason: In a bounded feasible region, it always exist a maximum and minimum value.
- A
$A$ is true$, R$ is true$: R$ is a correct explanation for $A.$
- ✓
$A$ is true$,R$ is true$; R$ is not a correct explanation for $A.$
- C
$A$ is true$: R$ is false.
- D
$A$ is false$: R$ is true.
AnswerCorrect option: B. $A$ is true$,R$ is true$; R$ is not a correct explanation for $A.$
View full question & answer→MCQ 111 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A):$ For the constraints of a $\text{LPP}$ problem given by $\text{x}_1+2\text{x}_2\leq2000,\text{x}_1+\text{x}_2\leq1500,\text{x}_2\leq600$ and $\text{x}_1,\text{x}_2\geq0$ the points $(1000, 0), (0, 500), (2, 0)$ lie in the positive bounded region, but point $(2000, 0)$ does not lie in the positive boundedregion.
Reason $(R):$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is $\text{NOT}$ the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
View full question & answer→MCQ 121 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion $(A): $ The linear programming problem, maximize $Z = x + 2y$ subject to constraints $\text{x}-\text{y}\leq10,2\text{x}+3\text{y}\leq20$ and $\text{x}\geq0; \text{y}\geq0.$ It gives the maximum value of $Z$ as $\frac{40}{3}.$
Reason $(R) :$ To obtain maximum value of $Z,$ we need to compare value of $Z$ at all the corner points of the shaded region.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 131 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion $(A) :$ The maximum value of $Z = 11x + 7y$ Subject to the constraints are $2\text{x}+\text{y}\leq6,\text{x}\leq2,\text{x,y}\geq0. x,y 0$. Occurs at the point $(0,6).$
Reason $(R) :$ If the feasible region of the given $\text{LPP}$ is bounded, then the maximum and minimum values of the objective function occurs at corner points.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 141 Mark
Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion $(A) :$ For the $\text{LPP} \ Z= 3x + 2y,$ subject to the constraints $\text{x}+2\text{y}\leq2;\text{x}\geq;\text{y}\geq0$ both maximum value of $Z$ and Minimum value of $Z$ can be obtained.
Reason $(R) :$ If the feasible region is bounded then both maximum and minimum values of $Z$ exists.
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→