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

Evaluate the following.

`int (x^3)/(sqrt(1 + x^4))dx`

Solve the following

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

Evaluate the following.

`intx^3  e^(x^2) dx`

Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.

Complete the following activity:

`int_0^2 dx/(4 + x - x^2) `

= `int_0^2 dx/(-x^2 + square + square)`

= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`

= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`

= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`

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

Evaluate the following:

`intx^3e^(x^2)dx` 

Evaluate the following.

`intx^3/sqrt(1+x^4)dx`

Evaluate the following.

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

Evaluate the following.

`intx^3/sqrt(1+x^4)  dx`

Evaluate the following.

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

Evaluate `int (1 + x + x^2/(2!))dx`

Choose the correct pair:

If f'(x) = 4x³ - 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x)

If f′(x) = 4x³ − 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Evaluate the following. 

`int x sqrt(1 + x^2)  dx`  

Evaluate the following.

`int x^3 e^(x^2) dx` 

Evaluate the following.

`intx^3/sqrt(1+x^4)`dx

Evaluate the following.

`intx^2e^(4x)dx`