# JEE Main

Explore popular questions from Linear Programming for JEE Main. This collection covers Linear Programming previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Linear Programming

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Q 1. Shaded region is represented by A

{tex} 4 x - 2 y \leq 3 {/tex}

{tex} 4 x - 2 y \leq - 3 {/tex}

C

{tex} 4 x - 2 y \geq 3 {/tex}

D

{tex} 4 x - 2 y \geq - 3 {/tex}

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Q 2. For the constraint of a linear optimizing function {tex} z = x _ { 1 } + x _ { 2 } , {/tex} given by {tex} x _ { 1 } + x _ { 2 } \leq 1,3 x _ { 1 } + x _ { 2 } \geq 3 {/tex} and {tex} x _ { 1 } , x _ { 2 } \geq 0 {/tex}

A

There are two feasible regions

B

There are infinite feasible regions

There is no feasible region

D

None of these

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Q 3. The intermediate solutions of constraints must be checked by substituting them back into

A

Objective function

Constraint equations

C

Not required

D

None of these

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Q 4. A basic solution is called non-degenerate, if

A

All the basic variables are zero

None of the basic variables is zero

C

At least one of the basic variables is zero

D

None of these

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Q 5. The feasible solution of a L.P.P. belongs to

A

First and second quadrant

B

First and third quadrant

C

Second quadrant

Only first quadrant

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Q 6. The true statement for the graph of inequations {tex} 3 x + 2 y \leq 6 {/tex} and {tex} 6 x + 4 y \geq 20 {/tex}, is

Both graphs are disjoint

B

Both do not contain origin

C

Both contain point {tex} ( 1,1 ) {/tex}

D

None of these

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Q 7. The value of objective function is maximum under linear constraints

A

At the centre of feasible region

B

At {tex} ( 0,0 ) {/tex}

C

At any vertex of feasible region

The vertex which is at maximum distance from {tex} ( 0,0 ) {/tex}

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Q 8. The region represented by {tex} 2 x + 3 y - 5 \leq 0 {/tex} and {tex} 4 x - 3 y + 2 \leq 0 {/tex}, is

A

Not in first quadrant

Bounded in first quadrant

C

Unbounded in first quadrant

D

None of these

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Q 9. Objective function of a L.P.P, is

A

A constraint

A function to be optimized

C

A relation between the variables

D

None of these

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Q 10. Shaded region is represented by A

{tex} 2 x + 5 y \geq 80 ,\ x + y \leq 20 ,\ x \geq 0 ,\ y \leq 0 {/tex}

B

{tex} 2 x + 5 y \geq 80 ,\ x + y \geq 20 ,\ x \geq 0 ,\ y \geq 0 {/tex}

{tex} 2 x + 5 y \leq 80 ,\ x + y \leq 20 ,\ x \geq 0 ,\ y \geq 0 {/tex}

D

{tex} 2 x + 5 y \leq 80 ,\ x + y \leq 20 ,\ x \leq 0 ,\ y \leq 0 {/tex}

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Q 11. The graph of inequations {tex} x \leq y {/tex} and {tex} y \leq x + 3 {/tex} is located in

A

II quadrant

B

I, II quadrants

I, II, III quadrants

D

II, III, IV quadrants

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Q 12. 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{tex}\% {/tex} on saving certificate and 10{tex} \% {/tex} on national saving bonds per annum. He invest Rs. {tex} x {/tex} in saving certificates and Rs. {tex} y{/tex} in national saving bonds. Then the objective function for this problem is

{tex} 0.08 x + 0.10 y {/tex}

B

{tex} \frac { x } { 2000 } + \frac { y } { 2500 } {/tex}

C

{tex} 2000 x + 2500 y {/tex}

D

{tex} \frac { x } { 8 } + \frac { y } { 10 } {/tex}

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Q 13. The minimum value of {tex} z = 2 x _ { 1 } + 3 x _ { 2 } {/tex} subject to the constraints {tex} 2 x _ { 1 } + 7 x _ { 2 } \geq 22 ,\ x _ { 1 } + x _ { 2 } \geq 6,\ 5 x _ { 1 } + x _ { 2 } \geq 10 {/tex} and {tex} x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex} is

14

B

20

C

10

D

16

##### Explanation 