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

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

Evaluate: `int_0^oo xe^-x.dx`

Evaluate: `int_0^π sin^3x (1 + 2cosx)(1 + cosx)^2.dx`

Verify which of the following is p.d.f. of r.v. X:

 f(x) = sin x, for 0 ≤ x ≤ `π/2`

Evaluate the following:

`int_0^a (1)/(x + sqrt(a^2 - x^2)).dx`

Choose the correct option from the given alternatives : 

`int_0^(pi/2) (sin^2x*dx)/(1 + cosx)^2` = ______.

Verify which of the following is p.d.f. of r.v. X:

f(x) = x, for 0 ≤ x ≤ 1 and 2 - x for 1 < x < 2

Verify which of the following is p.d.f. of r.v. X:

 f(x) = 2, for 0 ≤ x ≤ 1.

It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by

f (x) = `x^2/ 3` , for –1 < x < 2 and = 0 otherwise