Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

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.

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.

Assertion (A): The acute angle between the line `barr = hati + hatj + 2hatk  + λ(hati - hatj)` and the x-axis is `π/4`

Reason(R): The acute angle 𝜃 between the lines `barr = x_1hati + y_1hatj + z_1hatk  + λ(a_1hati + b_1hatj + c_1hatk)` and  `barr = x_2hati + y_2hatj + z_2hatk  + μ(a_2hati + b_2hatj + c_2hatk)` is given by cosθ = `(|a_1a_2 + b_1b_2 + c_1c_2|)/sqrt(a_1^2 + b_1^2 + c_1^2 sqrt(a_2^2 + b_2^2 + c_2^2)`

Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)

If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to ______.

Find the general solution of the differential equation:

(xy – x²) dy = y² dx

The angle between the lines 2x = 3y = – z and 6x = – y = – 4z is ______.