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The maximum value of z = 9x + 13y, subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0 and y ≥ 0 is

1) 130 2) 81 3) 79 4) 99 Solution: (3) 79 Z = 9x + 13y, Subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0 and y ≥ 0 Z =9x+13y At O... View Article

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

1) given by the intersection of inequations with axes only 2) given by the intersection of inequations with X-axis only 3) given by corner... View Article

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

1) bounded 2) unbounded 3) convex 4) concave Solution: (2) unbounded... View Article

The linear programming problem: Maximise z = x₁ + x₂ subject to constraints x₁ + 2x₂ ≤ 2000, x₁ + x₂ ≤ 1500, x₂ ≤ 600 and x₁ ≥ 0. Which one of the following points do not lie in the positive bounded region

Maximise z = x1 + x2 Subject to constraints x1 + 2x2 ≤ 2000, x1 + x2 ≤ 1500, x2 ≤ 600 and x1 ≥ 0 Which one of the following points do not lie in... View Article

Variables of the objective function of the linear programming problem are

1) zero 2) zero or positive 3) negative 4) zero or negative Solution: (2) zero or positive Variables of the objective function of the linear... View Article

The point which provides the solution of the linear programming problem, maximise Z = 45x + 55y subject to constraints x, y ≥ 0, 6x + 4y ≤ 120 and 3x + 10y ≤ 180 is

1) ( 15, 10 ) 2) ( 10, 15 ) 3) ( 0, 18 ) 4) ( 20, 0 ) Solution: (2) ( 10 , 15 ) 3x + 10y = 180 (60, 0) and (0, 18) are the points. 6x + 4y =... View Article

Consider the linear programming problem: Maximise z = 4x + y Subject to constraints x + y ≤ 50, x + y ≥ 100, and x, y ≥ 0. Then, the maximum value of z is

Maximise z = 4x + y Subject to constraints x + y ≤ 50, x + y ≥ 100, and x, y ≥ 0 Then, the maximum value of z is 1) 0 2) 50 3) 100 4) does not... View Article

Which of the following sets are not convex?

1) {(x , y) : 8x2 + 6y2 ≤ 24} 2) {(x , y) : 6 ≤ x2 + y2 ≤ 36} 3) {(x , y): y ≥ 3, y ≥ 30} 4) {(x , y): x2 ≤ y Solution: (2) {(x , y) : 6 ≤ x2... View Article

If x + y ≤ 2 ; x ≥ 0, y ≥ 0 is the point at which maximum value of 3x + 2y attained will be

1) (0, 2) 2) (0, 0) 3) (2, 0) 4) (1 / 2, 1 / 2) Solution: (3) (2, 0) Given , x + y ≤ 2, x ≥ 0 and y ≥ 0 Let z = 3x + 2y The table for x + y... View Article

A Furniture dealer deals in only two items, table and chair. He has Rs. 5000 to invest and a space to store at most 60 pieces. A table costs him Rs. 250 and a chair Rs. 50. He can sell a table at a profit of Rs. 50 and a chair at a profit of Rs. 15. Assume that, he can sell all the items that he produced. The number of constraints in the problem is

1) 2 2) 3 3) 4 4) 5 Solution: (3) 4 Let x and y be the number of tables and chairs. The cost of x table = Rs. 250 and cost of y chair = Rs.... View Article

If a flagstaff subtends the same angle at the points A, B, C and D on the horizontal plane through its foot, then A, B, C and D form a

1) square 2) cyclic quadrilateral 3) rectangle 4) none of these Solution: (2) cyclic quadrilateral If O is the foot of the flagstaff, then... View Article

The angle of elevation of the top of a mountain observed from each of the three points A, B and C forming a triangle ABC on the plane is α. The height of the mountain is

1) (ɑ / 1) tan ɑ cot A 2) (ɑ / 2) cot ɑ tan A 3) (ɑ / 2) tan ɑ cosec A 4) (ɑ / 2) cosec ɑ tan A Solution: (3) (ɑ / 2) tan ɑ cosec A Let h be... View Article

ABCD is a rectangular park with AB = 50 m. A tower stands at the point C. The angles of elevation of the top of the tower at A and B are 15° and 30° respectively. The height of the tower is

1) 25 / [√3 + 1] m 2) 25 / (√√3 + 1) m 3) 25 / √3 m 4) none of these Solution: (2) 25 / (√√3 + 1) m Let h be the height of the tower at... View Article

From a point on a hill-side of constant inclination, the angle of elevation of the top of a flagstaff on its summit is observed to be α and α metre nearer the top of the hill, it is β. If h is the height of the flagstaff, the inclination of the hill to the horizon is

1) sin-1 [a sin α sin β] / [h sin (β - α)] 2) cos-1 [a sin α sin β] / [h sin (β - α)] 3) tan-1 [a sin α sin β] / [h sin (β - α)] 4) none of... View Article

Two straight roads OA and OB intersect at O. A tower is situated within the angles formed by them and subtends angles of 45° and 30° at the points A and B where the roads are nearest to it. If OA = α and OB = b, then the height of the tower is

1) √(a2 + b2) / 2 2) √(a2 + b2) 3) √(a2 - b2) / 2 4) √(a2 - b2) Solution: (3) √(a2 - b2) / 2 Let PQ be the tower of height h. Let PA, PB... View Article

ABC is an equilateral triangular plot. An electric pole stands at the vertex and makes an angle of 60° at either of the other two vertices. If the height of the triangle is 100 m, then the height of the pole is

1) 100 m 2) 150 m 3) 200 m 4) 300 m Solution: (3) 200 m Let AP be the electric pole of height h. AB / h = cot 60o AB = h / √3 = AC = BC... View Article

A flagstaff stands vertically on a pillar, the height of the flagstaff being double the height of the pillar. A man on the ground at a distance finds that both the pillar and the flagstaff subtend equal angles at his eyes. The ratio of the height of the pillar and the distance of the man from the pillar is

1) √2 : 1 2) 1 : 2 3) √3 : 1 4) 1 : √3 Solution: (4) 1 : √3 Let h / x = a tan θ = a, tan 2θ = 3h / x = 3a [2 tan θ] / [1 - tan2 θ] = 3a 2a /... View Article

A vertical lamp-post of height 9 metres stands at the corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30 degrees, while from another corner it is 45 degrees. The area of the field is

1) 81 sq. metres 2) 81 √2 sq. meters 3) 9 √2 sq. meters 4) none of these Solution: (2) 81 √2 sq. meters One side = 9 cot 45o = 9m... View Article

The angle of elevation of the top of a vertical pole when observed from each vertex of a regular hexagon is π/3. If the area of the circle circumscribing the hexagon be A sq. metre, then the area of the hexagon is

1) (3 √3 / 2) A sq.m 2) (3 √3 / π) A sq.m 3) (3 √3 / 2) (A / π) sq. m 4) none of these Solution: (3) (3 √3 / 2) (A / π) sq. m Assume... View Article

ABCD is a rectangular field. A vertical lamp post of height 12 m stands at the corner A. If the angle of elevation of its top from B is 60° and from C is 45°. then the area of the field is

1) 48√2 sq m 2) 48√3 sq m 3) 12√3 sq m 4) 12√2 sq m Solution: (1) 48√2 sq m AE is the vertical lamp-post. AE = 12m tan 45o = AE / AC AC... View Article

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