HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Solve the following equations by the reduction method.

2x + y = 5, 3x + 5y = – 3

Solve the following equations by the reduction method.

x + 3y = 2, 3x + 5y = 4

Solve the following equations by the reduction method.

3x – y = 1, 4x + y = 6

Solve the following equations by the reduction method.

5x + 2y = 4, 7x + 3y = 5

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

`(sqrt(2), pi/4)`

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)`

Solve the following equations by inversion method:

x + y = 4, 2x - y = 5

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.

Solve the following equation by the method of inversion:

2x - y = - 2, 3x + 4y = 3

Solve the following equations by the method of inversion:

x + y+ z = 1, 2x + 3y + 2z = 2,
ax + ay + 2az = 4, a ≠ 0.

Solve the following equation by the method of inversion:

5x − y + 4z = 5, 2x + 3y + 5z = 2 and 5x − 2y + 6z = −1

Solve the following equations by the method of inversion:

x + y + z = - 1, y + z = 2, x + y - z = 3

Express the following equations in matrix form and solve them by the method of reduction:

x − y + z = 1, 2x − y = 1, 3x + 3y − 4z = 2

Express the following equations in matrix form and solve them by the method of reduction:

`x + y = 1, y + z = 5/3, z + x 4/33`.