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The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form

1) an isosceles triangle 2) an equilateral triangle 3) a scalene triangle 4) a right angled triangle Solution: Given x + y = 0 ..(i) 5x + y... View Article

A straight line perpendicular to the line 2x + y = 3 is passing through (1, 1). Its y-intercept is

1) 1 2) 2 3) 3 4) 1/2 Solution: Equation of given line is 2x + y = 3 => y = -2x + 3 Here slope is m1 = -2 The perpendicular line will... View Article

The points (2, 5) and (5, 1) are two opposite vertices of a rectangle. If the other two vertices are points on the straight line y = 2x + k, then the value of k is

1) 4 2) 3 3) -4 4) -3 Solution: The given points (2,5) and (5,1) will form a diagonal of the rectangle. so, the midpoint of these points... View Article

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

1) isosceles 2) equilateral 3) right angled 4) none of these Solution: Given x + y = 0 …(i) 3x + y - 4 = 0 …(ii) x + 3y - 4 = 0 …(iii) From... View Article

A wholesale merchant wants to start the business of cereal with Rs 24000. Wheat is Rs 400 per quintal and rice is Rs 600 per quintal. He has the capacity to store 200 quintal cereal. He earns the profit of Rs 25 per quintal on wheat and Rs 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then maximum profit of the objective function is

1) 25x + 40y 2) 40x + 25y 3) 400x + 600y 4) (400 / 40) x + (600 / 25) y Solution: (2) 40x + 25y Let rice be represented by ‘x’ quintals and... View Article

The region represented by the inequation system x, y ≥ 0, y ≤ 6, x + y ≤ 3 is

1) unbounded in the first quadrant 2) unbounded in first and second quadrants 3) bounded in the first quadrant 4) None of the above Solution:... View Article

For the LPP, minimise z = x₁ + x₂ such that inequalities 5x₁ + 10x₂ ≤ 0, x₁ + x₂ ≥ 1, x₂ ≤ 4 and x₁, x₂ ≥ 0

1) There is a bounded solution 2) There is no solution 3) There are infinite solutions 4) None of the above Solution: (3) There are infinite... View Article

For an LPP, minimise z = 2x + y subject to constraints 5x + 10y ≤ 50 , x + y ≥ 1, y ≤ 4 and x,y ≥ 0, then z is equal to

1) 0 2) 1 3) 2 4) 12 Solution: (2) 1 Z = 2x + y Subject to constraints 5x + 10y ≤ 50 x + y ≥ 1 y ≤ 4 x, y ≥ 0 Z = 2x + y The minimum... View Article

A vertex of a feasible region by the linear constraints 3x + 4y ≤ 18, 2x + 3y ≥ 3 and x, y ≥ 0 is

1) (0, 2) 2) (4.8, 0) 3) (0, 3) 4) None of these Solution: (4) None of these... View Article

The maximum value of z = 10x + 6y, subject to constraints x ≥ 0, y ≥ 0, 3x + y ≤ 12, 2x + 5y ≤ 34 is

1) 72 2) 80 3) 104 4) 56 Solution: (4) 56 Z = 10x + 6y Subject to constraints 3x + y ≤ 12 2x + 5y ≤ 34. Consider the lines L1 and L2. L1 :... View Article

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 ≥ 0, y ≥ 0, x + y ≤ 5 x + y = 5 x 0... View Article

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

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