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

Find the value of x, such that f(x) is decreasing function.

f(x) = 2x³ – 15x² – 84x – 7 

Find the value of x such that f(x) is decreasing function.

f(x) = x⁴ − 2x³ + 1

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the values of x for which Revenue is increasing.

Choose the correct alternative.

The function f(x) = x³ - 3x² + 3x - 100, x ∈ R is

State whether the following statement is True or False:

The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.

Choose the correct alternative.

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

Choose the correct alternative.

The order and degree of `[ 1+ (dy/dx)^3]^(2/3) = 8 (d^3y)/dx^3` are respectively.

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

Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.

Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx

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

Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx

Evaluate `int (3"x"^2 - 5)^2` dx

Evaluate `int 1/("x" ("x" - 1))` dx

If f'(x) = x² + 5 and f(0) = −1, then find the value of f(x).

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

If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).

Evaluate the following.

`int "x" sqrt(1 + "x"^2)` dx

Evaluate the following.

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

Evaluate the following.

`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx