Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

A maximum or a minimum may not exist for a linear programming problem if ____________.

In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. If M and m respectively be the largest and smallest values at corner points then ____________.

In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case feasible region is unbounded, M is the maximum value of the objective function if ____________.

In Corner point method for solving a linear programming problem, one finds the feasible region of the linear programming problem, determines its corner points, and evaluates the objective function Z = ax + by at each corner point. Let M and m respectively be the largest and smallest values at corner points. In case the feasible region is unbounded, m is the minimum value of the objective function.

If two corner points of the feasible region are both optimal solutions of the same type, i.e., both produce the same maximum or minimum.

In a LPP, the objective function is always ____________.

Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0.

Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0.

Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0.

Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.

Maximize Z = 10 x₁ + 25 x₂, subject to 0 ≤ x₁ ≤ 3, 0 ≤ x₂ ≤ 3, x₁ + x₂ ≤ 5.

Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at ____________.

The feasible region for an LPP is shown shaded in the figure. Let Z = 3x - 4y be the objective function. Minimum of Z occurs at ____________.

Maximize Z = 10×1 + 25×2, subject to 0 ≤ x₁ ≤ 3, 0 ≤ x₂ ≤ 3, x₁ + x₂ ≤ 5.

The feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4x + 3y occurs at the point.

`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.

If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.

Which of the following is the principal value branch of `"cos"^-1 "x"`

If A `= [(0,2),(2,0)],` then A² is ____________.

It is given that at x = 1, the function x⁴ - 62x² + ax + 9 attains its maximum value on the interval [0, 2]. Find the value of a.