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

For the following assignment problem minimize total man hours:

Subtract the `square` element of each `square` from every element of that `square`

Subtract the smallest element in each column from `square` of that column.

The lines covering all zeros is `square` to the order of matrix `square`

The assignment is made as follows:

Optimum solution is shown as follows:

A → `square, square` → III, C → `square, square` → IV

Minimum hours required is `square` hours

Use quantifiers to convert the following open sentence defined on N, into a true statement.

3x - 4 < 9

`int 1/sqrt(x^2 - 9) dx` = ______.

The slope of a tangent to the curve y = 3x² – x + 1 at (1, 3) is ______.

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.

Solve the following differential equations:

x²ydx – (x³ – y³)dy = 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` = ______.

Shraddho wants to invest at most ₹ 25,000/- in saving certificates and fixed deposits. She wants to invest at least ₹ 10,000/- in saving certificate and at least ₹ 15,000/- in fixed deposits. The rate of interest on saving certificate is 5% and that on fixed deposits is 7% per annum. Formulate the above problem as LPP to determine maximum income yearly.

`int 1/(4x^2 - 1) 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`