HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

State whether the following is True or False:

The derivative of `log_ax`, where a is constant is `1/(x.loga)`.

State whether the following is True or False:

If y = log x, then `"dy"/"dx" = 1/"x"`

State whether the following is True or False:

If y = e², then `"dy"/"dx" = 2"e"`

The derivative of a^x is a^x log a.

Solve the following:

If y = [log(log(logx))]², find `"dy"/"dx"`

Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`

Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`

Differentiate log (1 + x²) with respect to a^x.

Determine the maximum and minimum value of the following function.

f(x) = 2x³ – 21x² + 36x – 20

Determine the maximum and minimum value of the following function.

f(x) = x log x

Determine the maximum and minimum value of the following function.

f(x) = `x^2 + 16/x`

Divide the number 20 into two parts such that their product is maximum.

A metal wire of  36 cm length is bent to form a rectangle. Find its dimensions when its area is maximum.

The total cost of producing x units is ₹ (x² + 60x + 50) and the price is ₹ (180 − x) per unit. For what units is the profit maximum?

If f(x) = x.log.x then its maximum value is ______.

State whether the following statement is True or False:

An absolute maximum must occur at a critical point or at an end point.

If x + y = 3 show that the maximum value of x²y is 4.

Examine the function for maxima and minima f(x) = x³ - 9x² + 24x

The differential equation by eliminating arbitrary constants from bx + ay = ab is __________.

Solve the differential equation:

Find the differential equation of family of curves y = e^x (ax + bx²), where A and B are arbitrary constants.