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

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].

The function f(x) = x⁵ - 5x⁴ + 5x³ - 1 has ____________.

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.

The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is ____________.

Find the area of the largest isosceles triangle having a perimeter of 18 meters.

The coordinates of the point on the parabola y² = 8x which is at minimum distance from the circle x² + (y + 6)² = 1 are ____________.

The distance of that point on y = x⁴ + 3x² + 2x which is nearest to the line y = 2x - 1 is ____________.

The function `"f"("x") = "x" + 4/"x"` has ____________.

The combined resistance R of two resistors R₁ and R₂ (R₁, R₂ > 0) is given by `1/"R" = 1/"R"_1 + 1/"R"_2`. If R₁ + R₂ = C (a constant), then maximum resistance R is obtained if ____________.