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

Examine the function for maxima and minima f(x) = x³ - 9x² + 24x

The differential equation by eliminating arbitrary constants from bx + ay = ab is __________.

Solve the differential equation:

Find the differential equation of family of curves y = e^x (ax + bx²), where A and B are arbitrary constants.

Evaluate the following.

∫ x log x dx

Evaluate the following.

`int x^2 e^4x`dx

Evaluate the following.

`int "x"^2 *"e"^"3x"`dx

Evaluate the following.

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

Evaluate the following.

`int e^x (1/x - 1/x^2)`dx

Evaluate the following.

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

Evaluate the following.

`int "e"^"x" "x - 1"/("x + 1")^3` dx

Evaluate the following.

`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx

Evaluate the following.

`int [1/(log "x") - 1/(log "x")^2]` dx

Evaluate the following.

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

`int ("x" + 1/"x")^3 "dx"` = ______

Choose the correct alternative from the following.

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

Choose the correct alternative from the following.

`int (1 - "x")^(-2) "dx"` = 

Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 

Evaluate: Find the primitive of `1/(1 + "e"^"x")`

Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx

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