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

Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)

Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T

Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F

Determine the truth values of p and q in the following case:

(p ∧ q) is F and (p ∧ q) → q is T

Solve the following equations by inversion method.

x + 2y = 2, 2x + 3y = 3

Solve the following equations by inversion method.

2x + 6y = 8, x + 3y = 5

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.