Sujeet Kumar

I) Select the appropriate alternatives for each of the following :Question 1.The value of objective function is maximum under linear constraints _______.(A) at the centre of feasible region(B) at (0, 0)(C) at a vertex of feasible region(D) the vertex which is of maximum distance from (0, 0)Solution:(C) at a vertex of feasible region Question 2.Which … Read more

Question 1.Maximize : z = 11x + 8y subject to x ≤ 4, y ≤ 6,x + y ≤ 6, x ≥ 0, y ≥ 0.Solution:First we draw the lines AB, CD and ED whose equations are x = 4, y = 6 and x + y = 6 respectively. The feasible region is shaded … Read more

Question 1.A manufacturing firm produces two types of gadgets A and B, which are first processed in the foundry and then sent to machine shop for finishing. The number of man hours of labour required in each shop for production of A and B per unit and the number of man hours available for the … Read more

I) Find the feasible solution of the following inequations graphically.Question 1.3x + 2y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0Solution:First we draw the lines AB and CD whose equations are 3x + 2y = 18 and 2x + y = 10 respectively. The feasible solution is OCPBO which is … Read more

Question 1.Solve graphically :(i) x ≥ 0Solution:Consider the line whose equation is x = 0. This represents the Y-axis.To find the solution set, we have to check any point other than origin.Let us check the point (1, 1)When x = 1, x ≥ 0∴ (1, 1) lies in the required regionTherefore, the solution set is … Read more

Question 1.Solution: Question 2.The vector equation of line 2x – 1 = 3y + 2 = z – 2 is Solution: Question 3.The direction ratios of the line which is perpendicular to the two lines  (A) 4, 5, 7(B) 4, -5, 7(C) 4, -5, -7(D) -4, 5, 8Solution:(A) 4, 5, 7 Question 4. Question 5. … Read more

Question 1. Question 2. Question 3. Question 4. Question 5.Find the vector equation of the line which passes through the origin and the point (5, -2, 3).Solution: Question 6.Find the Cartesian equations of the line which passes through points (3, -2, -5) and (3, -2, 6).Solution:Let A = (3, -2, -5), B = (3, -2, … Read more

Question 1. Question 2. Question 3.Show that Solution: Question 4. Question 5.Find the distance of the point (1, 1, -1) from the plane 3x + 4y – 12z + 20 = 0.Solution:

Question 1. Question 2.Find the perpendicular distance of the origin from the plane 6x – 2y + 3z – 7 = 0.Solution:Alternative Method:The equation of the plane is 6x – 2y + 3z – 7 = 0 i.e. 6x – 2y + 3z = 7This is the normal form of the equation of plane.∴ perpendicular … Read more

Question 1.Solution:Let PM be the perpendicular drawn from the point P (2, -3, 1) to the line  The coordinates of any point on the line are given by x = -1 + 2λ, y = 3 + 3λ, z = -1 – λLet the coordinates of M be(-1 + 2λ, 3 + 3λ, -1 – … Read more