HSC Science (Electronics) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

If the slope of one of the lines given by ax² + 2hxy + by² = 0 is four times the other, show that 16h² = 25ab.

If one of the lines given by ax² + 2hxy + by² = 0 bisects an angle between the coordinate axes, then show that (a + b)² = 4h².

If p ∧ q is false and p ∨ q is true, then ______ is not true.

Show that the following equation represents a pair of line. Find the acute angle between them:

9x² - 6xy + y² + 18x - 6y + 8 = 0

If the lines represented by ax² + 2hxy + by² = 0 make angles of equal measure with the coordinate axes, then show that a ± b. 

OR

Show that, one of the lines represented by ax² + 2hxy + by² = 0 will make an angle of the same measure with the X-axis as the other makes with the Y-axis, if a = ± b.

Construct the truth table of the following:

p → (q → p)

Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]

Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q

Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]

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

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)`

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))`.