HSC Commerce (Marathi Medium) 12th Standard Board Exam [इयत्ता १२ वी] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

y² = (x + c)³ is the general solution of the differential equation ______.

Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."

Solve the following LP.P.

Maximize z = 13x + 9y,

Subject to 3x + 2y ≤ 12,

x + y ≥ 4,

x ≥ 0,

y ≥ 0.

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

Evaluated the following

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

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

Evaluate the following.

`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`

if `f(x) = 4x^3 - 3x^2 + 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 1/(x^2+4x-5)  dx`

Evaluate the following

`int1/(x^2 +4x-5)dx`

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

Evaluate.

`int(5"x"^2 - 6"x" + 3)/(2"x" - 3)  "dx"`

Evaluate the following.

`int 1/(x^2 + 4x - 5)  dx`

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

Evaluate the following.

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

Evaluate `int1/(x(x - 1))dx`

Solve the following Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)dx`

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

Evaluate the following.

`int 1/(x^2 + 4x - 5)dx`