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

Integrate the following w.r.t. x: `(1 + log x)^2/x`

Integrate the following w.r.t.x : cot^–1 (1 – x + x²)

Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`

Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`

Integrate the following w.r.t.x : `log (1 + cosx) - xtan(x/2)`

Integrate the following w.r.t.x : log (log x)+(log x)^–2 

Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`

Integrate the following w.r.t.x : log (x² + 1)

Integrate the following w.r.t.x : e^2x sin x cos x

Integrate the following w.r.t.x : sec⁴x cosec²x

Solve the following differential equation:

`"x" sin ("y"/"x") "dy" = ["y" sin ("y"/"x") - "x"] "dx"`

Solve the following differential equation:

`(1 + 2"e"^("x"/"y")) + 2"e"^("x"/"y")(1 - "x"/"y") "dy"/"dx" = 0`

Solve the following differential equation:

y² dx + (xy + x²)dy = 0

Solve the following differential equation:

`"dy"/"dx" + ("x" - "2y")/("2x" - "y") = 0`

Solve the following differential equation:

`x * dy/dx - y + x * sin(y/x) = 0`

Evaluate: `int_0^(π/4) cot^2x.dx`

Solve the following differential equation:

`(1 + "e"^("x"/"y"))"dx" + "e"^("x"/"y")(1 - "x"/"y")"dy" = 0`

Solve the following differential equation:

`"y"^2 - "x"^2 "dy"/"dx" = "xy""dy"/"dx"`

Solve the following differential equation:

`"xy" "dy"/"dx" = "x"^2 + "2y"^2, "y"(1) = 0`

Evaluate: `int_0^1 (x^2 - 2)/(x^2 + 1).dx`