HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

The area of the region bounded by the curve y = x², x = 0, x = 3, and the X-axis is ______.

State whether the following statement is true or false.

If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2e^x – 5| + c, where c is the constant of integration, then A = 5.

`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`

Find the area between the two curves (parabolas)

y² = 7x and x² = 7y.

Divide 20 into two ports, so that their product is maximum.

State whether the following statement is true or false:

To convert a maximization-type assignment problem into a minimization problem, the smallest element in the matrix is deducted from all elements of the matrix.

Calculate the cost of living index number for the following data by aggregative expenditure method:

For an annuity due, C = ₹ 2000, rate = 16% p.a. compounded quarterly for 1 year

∴ Rate of interest per quarter = `square/4` = 4

⇒ r = 4%

⇒ i = `square/100 = 4/100` = 0.04

n = Number of quarters

= 4 × 1

= `square`

⇒ P' = `(C(1 + i))/i [1 - (1 + i)^-n]`

⇒ P' = `(square(1 + square))/0.04 [1 - (square + 0.04)^-square]`

= `(2000(square))/square [1 - (square)^-4]`

= 50,000`(square)`[1 – 0.8548]

= ₹ 7,550.40

A function f(x) is maximum at x = a when f'(a) > 0.

Area of the region bounded by y= x⁴, x = 1, x = 5 and the X-axis is ______.

`int 1/sqrt(x^2 - a^2)dx` = ______.

Obtain the differential equation by eliminating arbitrary constants from the following equation:

y = Ae^3x + Be^–3x

Solve: `int sqrt(4x^2 + 5)dx`

A marketing manager has list of salesmen and territories. Considering the travelling cost of the salesmen and the nature of territory, the marketing manager estimates the total of cost per month (in thousand rupees) for each salesman in each territory. Suppose these amounts are as follows:

Find the assignment of salesman to territories that will result in minimum cost.

Evaluate :

`int(4x - 6)/(x^2 - 3x + 5)^(3/2)  dx`

`int(1-x)^-2 dx` = ______

`int1/sqrt(x^2 - a^2) dx` = ______

`intsqrt(1+x)  dx` = ______

Solution of the equation `xdy/dx=y log y` is ______

Evaluate the following.

`int x^3 e^(x^2) dx`