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

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which profit is increasing.

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.

Find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as E_c = (0.0003) I² + (0.075) I ; When I = 1000.

Fill in the blank:

A road of 108 m length is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are _______.

Fill in the blank:

The integrating factor of the differential equation `dy/dx – y = x` is __________

Verify y = log x + c is a solution of the differential equation

`x(d^2y)/dx^2 + dy/dx = 0`

Solve the differential equation:

`dy/dx = 1 +x+ y + xy`

Solve `dy/dx = (x+y+1)/(x+y-1)  when  x = 2/3 and y = 1/3`

Solve

y dx – x dy = −log x dx

Solve

`y log  y dy/dx + x  – log y = 0`

Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx

Evaluate:

`int (2x + 1)/(x(x - 1)(x - 4)) dx`.

Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx

Evaluate:

`int x/((x - 1)^2(x + 2)) dx`

The resale value of a machine decreases over a 10 year period at a rate that depends on the age of the machine. When the machine is x years old, the rate at which its value is changing is ₹ 2200 (x − 10) per year. Express the value of the machine as a function of its age and initial value. If the machine was originally worth ₹1,20,000, how much will it be worth when it is 10 years old?

Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx

Evaluate: `int 1/("x"("x"^5 + 1))` dx

Evaluate: `int 1/("x"("x"^"n" + 1))` dx

Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx