HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Important Questions

Select the correct option from the given alternatives:

If cos pθ = cos qθ, p ≠ q, then ______.

`cos[tan^-1  1/3 + tan^-1  1/2]` = ______

Find the principal solutions of the following equation:

sin 2θ = `-1/2`

If | x | < 1, then prove that

`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`

In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______.

If polar co-ordinates of a point are `(3/4, (3pi)/4)`, then its Cartesian co-ordinate are ______

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

Find the principal solutions of cosec x = 2

In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B

In ∆ABC, prove that `(cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2`

In ∆ABC, if `(2cos "A")/"a" + (cos "B")/"b" + (2cos"C")/"c" = "a"/"bc" + "b"/"ca"`, then show that the triangle is a right angled

In ∆ABC, prove that `sin  ((A - B)/2) = ((a - b)/c) cos  C/2` 

In ΔABC, prove that `("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")` = 0

In ΔABC, prove that `("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C"` = 0

Find the principal solutions of cot θ = 0

Find the cartesian co-ordinates of the point whose polar co-ordinates are `(1/2, π/3)`.

If 2 tan^–1(cos x) = tan^–1(2 cosec x). then find the value of x.

Find the general solution of sin θ + sin 3θ + sin 5θ = 0

If a line drawn from the point A( 1, 2, 1) is perpendicular to the line joining P(1, 4, 6) and Q(5, 4, 4) then find the co-ordinates of the foot of the perpendicular.

The Cartesian equations of line are 3x -1 = 6y + 2 = 1 - z. Find the vector equation of line.