Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

A feasible solution to a linear programming problem

The corner points of the bounded feasible region of a LPP are A(0,50), B(20, 40), C(50, 100) and D(0, 200) and the objective function is Z = x + 2y. Then the maximum value is ____________.

The feasible region (shaded) for a L.P.P is shown in the figure. The maximum Z = 5x + 7y is ____________.

The maximum value of Z = 3x + 4y subjected to contraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is ____________.

If A is a square matrix such that A² = A, then (I + A)² - 3A is ____________.

If a matrix A is both symmetric and skew symmetric then matrix A is ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.).

Based on the information given above, answer the following questions:

• The equations in terms x and y are ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.).

Based on the information given above, answer the following questions:

• Which of the following matrix equations represent the information given above?

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• The number of children who were given some money by Seema, is ____________.

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• How much amount is given to each child by Seema?

On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were 8 children less, everyone would have got Rs.10 more. However, if there were 16 children more, everyone would have got Rs. 10 less. Let the number of children be x and the amount distributed by Seema for one child be y(in Rs.)

Based on the information given above, answer the following questions:

• How much amount Seema spends in distributing the money to all the students of the Orphanage?

If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.

A function is said to be continuous for x ∈ R, if ____________.

Find all the points of local maxima and local minima of the function f(x) = (x - 1)³ (x + 1)²

Find the local minimum value of the function f(x) `= "sin"^4" x + cos"^4 "x", 0 < "x" < pi/2`

Find the points of local maxima and local minima respectively for the function f(x) = sin 2x - x, where `-pi/2 le "x" le pi/2`

If y `= "ax - b"/(("x" - 1)("x" - 4))` has a turning point P(2, -1), then find the value of a and b respectively.

Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

If y = x³ + x² + x + 1, then y ____________.

Find both the maximum and minimum values respectively of 3x⁴ - 8x³ + 12x² - 48x + 1 on the interval [1, 4].