HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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`

Solve the following differential equation:

x dx + 2y dx = 0, when x = 2, y = 1

Solve the following differential equation:

`x^2 dy/dx = x^2 + xy + y^2`

Solve the following differential equation:

(9x + 5y) dy + (15x + 11y)dx = 0

Solve the following differential equation:

(x² + 3xy + y2)dx - x² dy = 0

Evaluate: `int_0^(pi/2) x sin x.dx`

Solve the following differential equation:

(x² – y²)dx + 2xy dy = 0