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

Find the values of x such that f(x) = 2x³ – 15x² + 36x + 1 is increasing function

Find the values of x such that f(x) = 2x³ – 15x² – 144x – 7 is decreasing function

Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing

By completing the following activity, find the values of x such that f(x) = 2x³ – 15x² – 84x – 7 is decreasing function.

Solution: f(x) = 2x³ – 15x² – 84x – 7

∴ f'(x) = `square`

∴ f'(x) = 6`(square) (square)`

Since f(x) is decreasing function.

∴ f'(x) < 0

Case 1: `(square)` > 0 and (x + 2) < 0

∴ x ∈ `square`

Case 2: `(square)` < 0 and (x + 2) > 0

∴ x ∈ `square`

∴ f(x) is decreasing function if and only if x ∈ `square`

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

`int (7x + 9)^13  "d"x` ______ + c

To find the value of `int ((1 + logx))/x` dx the proper substitution is ______

State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`

State whether the following statement is True or False:

`int3^(2x + 3)  "d"x = (3^(2x + 3))/2 + "c"`

State whether the following statement is True or False:

`int"e"^(4x - 7)  "d"x = ("e"^(4x - 7))/(-7) + "c"`

State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`

Evaluate `int(3x^2 - 5)^2  "d"x`

Evaluate  `int"e"^x (1/x - 1/x^2)  "d"x`

`int x^3"e"^(x^2) "d"x`

`int (1 + x)/(x + "e"^(-x))  "d"x`

The order and degree of `((dy)/(dx))^3 - (d^3y)/(dx^3) + ye^x` = 0 are ______.

Choose the correct alternative:

The order and degree of `(1 + (("d"y)/("d"x))^3)^(2/3) = 8 ("d"^3y)/("d"x^3)` are respectively

Order of highest derivative occurring in the differential equation is called the ______ of the differential equation

Order and degree of differential equation are always ______ integers

The power of highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any is called ______ of the differential equation