At an infinite number of points

Both bounded and unbounded feasible space

JEE Questions for Maths Miscellaneous Quiz 15

A ball is thrown vertically upwards from the ground with velocity 15 m/s and rebounds from the ground with one-third of its striking velocity. The ratio of its greatest heights before and after striking the ground is

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4:1
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9:1
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5: 1
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3:1

particle possess two velocities simultaneously at an angle of tan^-1(12/to each other. Their resultant is 15 rn/s. If one velocity is 13 m/s, then the other will be

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5 m/s
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4 m/s
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12 m/s
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13 m/s

Two masses are projected with equal velocity u at angle 30^o and 60^o respectively. If the ranges covered by the masses be R₁ and R₂, then

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0%
2)
0%
0%

The amount of force that is needed to accelerate a truck of mass 36000 kg from rest to a velocity of 60 km/h in 20 seconds is

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6 kN
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30 kN
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60 kN
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30000 kN

A train is running at 5 m/s and a man jumps out of it with a velocity 10 m/s in a direction making an angle of 60° with the direction of the train. The velocity of the man relative to the ground is equal to

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12.24 m/s
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11.25 m/s
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14.23 m/s
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13.23 m/s

Inequations 3x – y ≥ 3 and 4x – y > 4

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Have solution for positive x and y
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Have no solution for positive x and y
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Have solution for all x
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Have solution for all y

Shaded region is represented by

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0%
2)
0%
0%

A Firm makes pents and shirts. A shirt takes 2 hours on machine and 3 hour of man labour while a pent takes 3 hour on machine and 2 hour of man labour. In a week there are 70 hour machine and 75 hour of man labour available. If the firm determine to make x shirts and y pents per week, then for this the linear constraints are

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0%
2)
0%
0%

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0%
2)
0%
0%
All of these

A company manufactures two types of products A and B. The storage capacity of its godown is 100 units. Total investment amount is Rs. 30,000. The cost price of A and B are Rs. 400 and Rs. 900 respectively. If all the products have sold and per unit profit is? Rs. 100 and? Rs. 120 through A and B respectively. If x units of A and y units of B be produced, then two linear constraints and iso-profit line are respectively

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0%
2)
0%
0%

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One solution
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Three solution
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An infinite no. of solution
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None of the above

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10
0%
15
0%
12
0%
8

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320
0%
300
0%
230
0%
None of these

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0%
2)
0%
0%

A cold drink factory has two plants located at Bhopal and Gwalior. Each plant produces three different types of drinks A, B, C. The production capacity of the plants per day is as follows,
A demand of 80,000 bottles of A, 22,000 bottles of B and 40,000 bottles of C in the month of June is forecasted. The operating costs per day of plants at Bhopal and Gwalior are Rs. 6,000 and Rs. 4,000 respectively. The number of days for which each plant must be run in June so as to minimize the operating costs in meeting the demand are

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12, 4
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4, 12
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40, 0
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None of these

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(0, 2)
0%
(0,
0%
(3,
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None of these

The intermediate solutions of constraints must be checked by substituting them back into

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Objective function
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Constraint equations
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Not required
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None of these

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(1000, 0)
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(0, 500)
0%
(2, 0)
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(2000,

A basic solution is called non-degenerate, if

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All the basic variables are zero
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None of the basic variables is zero
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At least one of the basic variables is zero
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None of the above

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then

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The objective function can be optimized
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The constraints are short in number
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The solution is problem oriented
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None of the above

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(2, 3)
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(3, 2)
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(3, 4)
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(4, 3)

The graph of x ≤ 2 and y ≥ 2 will be situated in the

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First and second quadrant
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Second and third quadrant
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First and third quadrant
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Third and fourth quadrant

The feasible solution of a L.P. P belongs to

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First and second quadrant
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First and third quadrant
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Second quadrant
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Only first quadrant

The position of points 0(0,and P(2, -in the region of graph of inequation 2x — 3y <5, will be

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0 inside and P outside
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0 and P both inside
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0 and P both outside
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0 outside and P inside

The true statement for the graph of mequations 3x + 2y ≤ 6 and 6x + 4y ≥ 20, is

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Both graphs are disjoint
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Both do not contain origin
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Both contain point (1, 1)
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None of the above

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0%
2)
0%
0%

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(1, 1)
0%
(0,1)
0%
(3, 0)
0%
(0,

0%
0%
2)
0%
0%

In which quadrant, the bounded region for inequations x + y ≤ 1. and x – y ≤ 1 is situated

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I, II
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I, III
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II, III
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All the four quadrants

The necessary condition for third quadrant region in xy-plane is

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x > 0,y > 0
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x < 0,y < 0
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x < 0,y > 0
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x < 0,y = 0

For the following feasible region, the linear constraints are

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0%
2)
0%
0%
None of these

The value of objective function is maximum under the linear constraints

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At the centre of feasible region
0%
At (0, 0)
0%
At any vertex of feasible region
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The vertex which is at maximum distance from

The region represented by 2x + 3y – 5 = 0 and 4x – 3y + 2 = 0, is

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Not in first quadrant
0%
Bounded in first quadrant
0%
Unbounded in first quadrant
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None of these

The region represented by the inequation system x,y ≥ 0 ,y ≤ 6, x + y ≤ 3, is

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Unbounded in first quadrant
0%
Unbounded in first and second quadrants
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Bounded in first quadrant
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None of the above

The solution set of the inequation 2x + y > 5, is

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Half plane that contains the origin
0%
Open half plane not containing the origin
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Whole xy-plane except the points lying on the line 2x + y = 5
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None of the above

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At only one point
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At two points only
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At an infinite number of points
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None of the above

If a point (h, k) satisfies an inequation ax + by 4, then the half plane represented by the inequation is

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The half plane containing the point (ii, k) but excluding the points on ax + by =4
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The half plane containing the point (h, k) and the points on ax + by =4
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Whole xy-plane
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None of the above

Inequation y – x ≤ 0 represents

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The half plane that contains the positive x-axis
0%
Closed half plane above the line y = x which contains positive y-axis
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Half plane that contains the negative x-axis
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None of the above

Objective function of a L.P.P is

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A constraint
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A function to be optimized
0%
A relation between the variables
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None of the abov

The optimal value of the objective function is attained at the points

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Given by intersection of inequations with axes only
0%
Given by intersection of inequations with x-axis only
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Given by corner points of the feasible region
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None of the above

If the constraints in a linear programming problem are changed

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The problem is to be re-evaluated
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Solution is not defined
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The objective function has to be modified
0%
The change in constraints is ignored

Which of the following statements is correct

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Every L.P.P. admits an optimal solution
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A L.P.P. admits a unique optimal solution
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If a L.P.P admits two optimal solutions, it has an infinite number of optimal solutions
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The set of all feasible solutions of a L.P.P. is not a convex set

Shaded region is represented by

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0%
2)
0%
0%

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Bounded feasible space
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Unbounded feasible space
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Both bounded and unbounded feasible space
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None of the above

Which of the following is not true for linear programming problems

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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
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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
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A basic solution which is also in the feasible region is called a basic feasible solution
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A column in the simplex tableau that contains all of the variables in the solution is called pivot or key column

Which of the terms is not used in a linear programming problem

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Slack variables
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Objective function
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Concave region
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Feasible solution

The graph of inequations x ≤ y and y ≤ x + 3 is located in

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II quadrant
0%
I, II quadrants
0%
I, II, III quadrants
0%
II, Ill, IV quadrants

The area of the feasible region for the following constraints 3y + x ≤ 3, x ≤ 0, y ≤ 0 will be

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Bounded
0%
Unbounded
0%
Convex
0%
Concave

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Area DHF
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Area AUC
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Area EDHG
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Line segment GI
0%
line segment IC

whole sale 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 was capacity to store 200 quintaL cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 quintal on rice. If he stores x quintal rice and y quintal wheat, then for maximum profit the objective function is

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0%
2)
0%
0%

JEE Questions for Maths Miscellaneous Quiz 15 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Miscellaneous Quiz 15 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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