Question 1 :
The necessary condition for third quadrant region in {tex} x y {/tex}-plane, is
Question 3 :
The region represented by {tex} 2 x + 3 y - 5 \leq 0 {/tex} and {tex} 4 x - 3 y + 2 \leq 0 {/tex}, is
Question 4 :
The intermediate solutions of constraints must be checked by substituting them back into
Question 6 :
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}
Question 7 :
The region represented by the inequation system {tex} x ,\ y \geq 0 ,\ y \leq 6 ,\ x + y \leq 3 ,{/tex} is
Question 8 :
The vertex of common graph of inequalities {tex} 2 x + y \geq 2 {/tex} and {tex} x - y \leq 3 , {/tex} is
Question 9 :
The minimum value of objective function {tex} c = 2 x + 2 y {/tex} in the given feasible region, is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd682ccf197791516a5f2b1"><br>
Question 11 :
For the L.P. problem {tex} { Min }\ z = 2 x + y {/tex} subject to {tex} 5 x + 10 y \leq 50 ,\ x + y \geq 1 ,\ y \leq 4 {/tex} and {tex} x ,\ y \geq 0 ,\ z = {/tex}
Question 12 :
The point at which the maximum value of {tex} ( 3 x + 2 y ) {/tex} subject to the constraints {tex} x + y \leq 2 ,\ x \geq 0 ,\ y \geq 0 {/tex} is obtained, is
Question 13 :
{tex} z = a x + b y ,\ a ,\ b {/tex} being positive, under constraints {tex} y \geq 1 {/tex}, {tex} x - 4 y + 8 \geq 0 ,\ x ,\ y \geq 0 {/tex} has
Question 15 :
The maximum value of {tex} \mu = 3 x + 4 y , {/tex} subject to the conditions {tex} x + y \leq 40 ,\ x + 2 y \leq 60 ,\ x ,\ y \geq 0 {/tex} is
Question 16 :
For the following feasible region, the linear constraints are<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd6821cf197791516a5f229"><br>
Question 17 :
For the L.P. problem {tex} { Min }\ z = - x _ { 1 } + 2 x _ { 2 } {/tex} such that {tex} - x _ { 1 } + 3 x _ { 2 } \leq 0 ,\ x _ { 1 } + x _ { 2 } \leq 6 ,\ x _ { 1 } - x _ { 2 } \leq 2 {/tex} and {tex} \ x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex}, {tex} x _ { 1 } = {/tex}
Question 18 :
On maximizing {tex} z = 4 x + 9 y {/tex} subject to {tex} x + 5 y \leq 200 {/tex}, {tex} 2 x + 3 y \leq 134 {/tex} and {tex} x , y \geq 0 {/tex}, {tex} z = {/tex}
Question 19 :
If a point {tex} ( h , k ) {/tex} satisfies an inequation {tex} a x + b y \geq 4 , {/tex} then the half plane represented by the inequation is