CUET Mathematics Algebra > Linear Programming PYQs

(A) and (C) only

(A), (C) and (D) only

(B), (C) and (D) only

(A), (B) and (D) only

13

10

22

14

is a bounded region in the first quadrant

is an unbounded region in the first and second quadrant

is an unbounded region in the first quadrant

has no point which satisfies all the inequalities

$(0, 0), (10, 0), (6, 12), (0, 20)$

$(0, 20), (0, 30), (4, 18)$

$(0, 20), (6, 12), (4, 18)$

$(15, 0), (40, 0), (4, 18), (6, 12)$

$2p = q$

$p = 3q$

$2p = 3q$

$3p = 2q$

$(\frac{30}{7}, \frac{60}{7})$

$(0,12)$

$(10,0)$

$(3,8)$

only maximum value in the feasible region

only minimum value in the feasible region

both maximum and minimum values in the feasible region

neither maximum nor minimum value in the feasible region

$2p = 3q$

$13p = 27q$

$q = 3p$

$p = 3q$

30

20

34

24

$2\max\{a, \beta\}$

$|a - \beta|$

0

$\max\{a, \beta\}$

8

4

10

$\frac{3}{2}$

(A) and (C) only

(A) only

(C) and (D) only

(A), (C) and (D) only

10

60

50

40

$4x + 3y \leq 12, 3x + 4y \leq 12, x \geq 0, y \geq 0$

$4x + 3y \geq 12, 3x + 4y \geq 12, x \geq 0, y \geq 0$

$4x + 3y \leq 12, 3x + 4y \geq 12, x \geq 0, y \geq 0$

$4x + 3y \geq 12, 3x + 4y \leq 12, x \geq 0, y \geq 0$

$x + 2y \leq 10$

$x + y \geq 2$

$x - y \geq 1$

$x - y \leq 1$

60

90

120

180

360

150

60

No Minimum value of Z

$3\frac{10}{11}$

$3\frac{9}{11}$

$4\frac{10}{11}$

$4\frac{9}{11}$

$3x + 4y ≤ 24, x + 2y \leq 10, x \geq 0, y \geq 0$

3x + 4y ≥ 24, x + 2y ≥ 10, x ≥ 0, y ≥ 0

3x + 4y ≥ 24, x + 2y ≤ 10, x ≥ 0, y ≥ 0

3x + 4y ≤ 24, x + 2y ≥ 10, x ≥ 0, y ≥ 0

Unbounded in first quandrant

Bounded in first quadrant

Unbounded in second quadrant

Not possible (Empty)

$p = q$

$p = 2q$

$q = 2p$

$q = 3p$

(A) and (C) only

(A) and (B) only

(B) and (C) only

(C) and (D) only

Region A

Region B

Region C

(Region A) ∪ (Region B)

$p = q$

$p = 2q$

$q = 2p$

$q = 3p$

$\phi$

$\{(-1,0), (0,2)\}$

$\{(-1,0), (0,2), (0, 0)\}$

unbounded region in first quadrant

$3q = 5p$

$8p = 3q$

$5p = 8q$

$3p = 5q$

₹480

₹560

₹640

₹600

$x + y \leq 800, 2x + y \leq 1000, x \leq 400, y \leq 700, x \geq 0, y \geq 0$

$x + y \geq 800, 2x + y \leq 1000, x \leq 400, x \geq 700, x \geq 0, y \geq 0$

$x + y \leq 800, 2x + y \geq 1000, x \geq 400, y \geq 700, x, y \geq 0$

$x + y \geq 800, 2x + y \geq 1000, x \leq 400, y \leq 700, x \geq 0, y \geq 0$

(0,2) only

(3,0) only

the mid point of the line segment joining (0,2) and (3,0)

every point on the line segment joining (0,2) and (3,0)

$\alpha = \frac{2}{3}\beta$

$p = \frac{4}{3}\alpha$

$\alpha + \beta = \frac{1}{2}$

$\alpha = \frac{4}{3}\beta$

24

30

36

28

24

42

100

23

(0,0), (0, 15), (0,20), (15,0), (10, 20)

(0, 15), (20,0), (15,0), (10, 20)

(15,0), (15,15), (10, 20), (0, 20), (0,15)

(0, 0), (20,0), (0, 15), (15, 15)

Only maximum in the feasible region

Only minimum in the feasible region

both maximum and minimum in the feasible region

either maximum or minimum but not both in the feasible region.

Only maximum value of Z attained in the feasible region

Only minimum value of Z attained in the feasible region

both maximum and minimum value of Z attained in the feasible region

either maximum or minimum of Z attained in the feasible region but not both

21

42

33

60

Region A

Region B

Region C

Region D

900

1650

1620

1680

$a - 5b = 0$

$a - 3b = 0$

$a - 2b = 0$

$a - 8b = 0$

150

228

120

100

(A) - (IV), (B) - (II), (C) - (III), (D) - (I)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (I), (B) - (II), (C) - (IV), (D) - (III)

there exists only maximum value of Z

there exists only minimum value of Z

there exists both maximum and minimum values of Z

there is neither maximum value nor minimum value of Z

46

54

56

92

Point B and D

Point F only

Point A and C

Point E only

$3p = 2q + 1$

$3p = 4q$

$6p = q$

$2p = 3q$

$(0,0), (25,0), (0,20), \left(\frac{50}{3}, \frac{40}{3}\right)$

$(25,0), (20,0), \left(\frac{50}{3}, \frac{40}{3}\right), (50,0)$

$(0,20), (0,40), (50,0), (25,0)$

$(0,0), (50,0), (0,20), \left(\frac{50}{3}, \frac{40}{3}\right)$

(3,0) only

(0,2) only

Every point on the line segment joining the points (0,2) and (3,0)

Only the mid point of the line segment joining the points (0,2) and (3,0)

2.5

4.5

5.5

3.5

$(2,0)$ only

neither $(2,0)$ nor $\left(\frac{20}{19}, \frac{45}{19}\right)$

$(0,3)$ only

$\left(\frac{20}{19}, \frac{45}{19}\right)$ only

$b = 2a$

$a = 2b$

$a = b$

$a = -2b$

50

52.5

61.3

72.4

60

38

30

34

14

20

26

30

$a = 2b$

$2a = b$

$a = b$

$3a = b$

Max $z > 400$

Max $z < 400$

Max $z = 400$

Max $z = 350$

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (III), (B) - (I), (C) - (II), (D) - (IV)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

24

10

12

14

35

25

40

20

region A

region B

region C

region D

$(0, 0)$

$(5, 0)$

$(0, 8)$

$(4, 10)$

The feasible region is bounded.

The corner points of the feasible region are $(0,0)$, $(20,0)$, $(15,10)$, $(10,15)$ and $(0,20)$

The optimal value of the objective function is attained at the point $(15, 10)$.

The LPP has a unique optimal solution.

(A), (B) and (D) only

(A), (C) and (D) only

(A), (B), (C) and (D)

(B) and (C) only

$5p = 2q$

$2p = 5q$

$p = 2q$

$2p = q$

(0, 0)

(0, 8)

(5, 0)

(4, 10)

$3q = p$

$q = p$

$2q = p$

$2p = q$

(A) and (C) only

(B) and (C) only

(A) and (D) only

(A) and (B) only

12

10

8

4

(A), (B) and (C) only

(A), (C) and (D) only

(A), (B), (C) and (D)

(B) and (D) only

$x + 2y \leq 40$

$3x + y \geq 30$

$4x + 3y \leq 60$

$x \geq 0, y \geq 0$

Maximum $z = 3$ at $(1, 2)$

There is no solution

Maximum $z = 15$ at $(7, 8)$

Maximum $z = 10$ at all points on the line $x - y = -1$

is bounded in the first quadrant

is unbounded in the first quadrant

is unbounded in first and second quadrants

does not exist

$3a = b$

$a = b$

$a = 2b$

$2a = b$

Maximize $z = 150x + 250y$;

Subjected to constants,

$x + y \leq 35, x + 2y \geq 50, x \geq 0, y \geq 0$

Maximize $z = 150x + 250y$;

Subjected to constants,

$x + y \leq 35, x + 2y \leq 50, x \geq 0, y \geq 0$

Maximize $z = 150x + 250y$;

Subjected to constants,

$x + y \geq 35, 2x + y \leq 50, x \geq 0, y \geq 0$

Maximize $z = 150x + 250y$;

Subjected to constants,

$x + y \geq 35, 2x + y \geq 50, x \geq 0, y \geq 0$

(0, 2) only

the mid-point of the line segment joining the points (2, 3) and (3, 1) only

(2, 3) and (3, 1) only

every point on the line segment joining the points (2, 3) and (3, 1)

$p - 8q$ = 0

$q - 5p$ = 0

$p - 5q$ = 0

$p - 3q$ = 0

Its feasible region is bounded and optimal point is (60, 30)

Its feasible region is unbounded and optimal point is (60, 30)

Its feasible region is bounded and optimal point is (0, 110)

Its feasible region is unbounded and optimal point is (30, 70)

Its feasible region is bounded and has 4 corner points

Its feasible region is bounded and has 3 corner points

Its feasible region is unbounded and has 4 corner points

Its feasible region is unbounded and has 3 corner points

(0, 20)

(20, 40)

(10, 20)

(0, 15)

a+2b

2a=b

3a = 2b

3a = 4b

(A), (B) and (D) only

(A), (B) and (C) only

(A) and (C) only

(B) and (D) only

Region D

Region B

Region A

Region C

$b = 3a$

$a = 3b$

$a = 2b$