HSC Commerce (Marathi Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

`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:

Find`dy/dx if, y = x^(e^x)`

Find `dy/dx  "if",y=x^(e^x) `

FInd `dy/dx` if,`x=e^(3t), y=e^sqrtt`

Find `dy/dx  "if",  y = x^(e^x)`

Find `dy/dx` if, y = `x^(e^x)`

Solve the following

`int_0^1 e^(x^2) x^3 dx`

Find `dy/dx` if, y = `x^(e^x)`

Find `dy/dx if, y =  x^(e^x)`

Three new machines M1, M2, M3 are to be installed in a machine shop. There are four vacant places A, B, C, D. Due to limited space, machine M2 can not be placed at B. The cost matrix (in hundred rupees) is as follows:

Determine the optimum assignment schedule and find the minimum cost.

Determine the minimum value of the function.

f(x) = 2x³ – 21x² + 36x – 20

Find `dy / dx` if, `y = x^(e^x)`