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

Find the Cartesian coordinates of the point whose polar coordinates are :

`(4,  pi/2)`

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(3/4, (3pi)/4)`

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(1/2, (7pi)/3)`

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(sqrt(2), sqrt(2))`

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(0, 1/2)`

Find the polar coordinates of the point whose Cartesian coordinates are `(1, - sqrt(3))`.

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(3/2, (3√3)/2)`.

In ΔABC, if cot A, cot B, cot C are in A.P. then show that a², b², c² are also in A.P.

Integrate the following w.r.t. x : x³ + x2 – x + 1

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

Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`

Integrate the following w.r.t. x:

`2x^3 - 5x + 3/x + 4/x^5`

Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`

Evaluate the following integrals:

tan²x dx

Evaluate the following integrals : `int (sin2x)/(cosx)dx`

Evaluate the following integrals : `int sin x/cos^2x dx`

Evaluate the following integrals:

`int (cos2x)/sin^2x dx` 

Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`

Evaluate the following integrals : `int sinx/(1 + sinx)dx`

Evaluate the following integrals : `int tanx/(sec x + tan x)dx`