Maximum value of Z = 12x + 3y, subject to constraints x ≥ 0, y ≥ 0, x + y ≤ 5 and 3x + y ≤ 9 is
1) 15 2) 36 3) 60 4) 40 Solution: (2) 36 Z = 12x + 3y, Subject to constraints x... View Article
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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... 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... 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
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... 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... 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 )... 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... View Article
Which of the following sets are not convex?
1) {(x , y) : 8x2 + 6y2 ≤ 24} 2) {(x , y) : 6 ≤ x2 + y2... 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)... 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... 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... 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)... 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)... 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]... 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)... 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... 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 :... 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)... 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... View Article
