HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t

State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.

State whether the following statement is True or False.

If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`

Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx

Evaluate `int (5"x" + 1)^(4/9)` dx

Evaluate `int 1/((2"x" + 3))` dx

Evaluate `int "x - 1"/sqrt("x + 4")` dx

Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).

Evaluate: ∫ |x| dx if x < 0

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

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

Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx

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

Evaluate: `int "x" * "e"^"2x"` dx

Evaluate: `int log ("x"^2 + "x")` dx

Evaluate: `int "e"^sqrt"x"` dx

Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx

Evaluate: `int sqrt(x^2 - 8x + 7)` dx

Choose the correct alternative:

There are ______ types of regression equations

The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years of service and their monthly incomes.

1. Find the regression equation of income on years of service.
2. What initial start would you recommend for a person applying for the job after having served in a similar capacity in another company for 13 years?