Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.

Total number of equivalence relations defined in the set S = {a, b, c} is ____________.

The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^-1 is given by ____________.

Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.

Find the position vector of a point A in space such that `vec"OA"` is inclined at 60º to OX and at 45° to OY and `|vec"OA"|` = 10 units.

Let `"f" ("x") = ("In" (1 + "ax") - "In" (1 - "bx"))/"x", "x" ne 0` If f (x) is continuous at x = 0, then f(0) = ____________.

If the feasible region for a linear programming problem is bounded, then the objective function Z = ax + by has both a maximum and a minimum value on R.

The minimum value of the objective function Z = ax + by in a linear programming problem always occurs at only one corner point of the feasible region

Determine the maximum value of Z = 11x + 7y subject to the constraints : 2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.

Maximise Z = 3x + 4y, subject to the constraints: x + y ≤ 1, x ≥ 0, y ≥ 0

Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2, x ≥ 0, y ≥ 0.

Minimise Z = 13x – 15y subject to the constraints: x + y ≤ 7, 2x – 3y + 6 ≥ 0, x ≥ 0, y ≥ 0

Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in Figure

Feasible region (shaded) for a LPP is shown in Figure. Maximise Z = 5x + 7y.

The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y

Refer to Exercise 7 above. Find the maximum value of Z.

The feasible region for a LPP is shown in figure. Evaluate Z = 4x + y at each of the corner points of this region. Find the minimum value of Z, if it exists.

In figure, the feasible region (shaded) for a LPP is shown. Determine the maximum and minimum value of Z = x + 2y.

A man rides his motorcycle at the speed of 50 km/hour. He has to spend Rs 2 per km on petrol. If he rides it at a faster speed of 80 km/hour, the petrol cost increases to Rs 3 per km. He has atmost Rs 120 to spend on petrol and one hour’s time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem

Refer to quastion 12. What will be the minimum cost?