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

A(– 2, 3, 4), B(1, 1, 2) and C(4, –1, 0) are three points. Find the Cartesian equations of the line AB and show that points A, B, C are collinear.

Show that the lines given by `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1) and (x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/(4)` intersect. Also, find the coordinates of their point of intersection.

A line passes through (3, –1, 2) and is perpendicular to lines `bar"r" = (hat"i" + hat"j" - hat"k") + lambda(2hat"i" - 2hat"j" + hat"k") and bar"r" = (2hat"i" + hat"j" - 3hat"k") + mu(hat"i" - 2hat"j" + 2hat"k")`. Find its equation.

Show that the line `(x - 2)/(1) = (y - 4)/(2) = (z + 4)/(-2)` passes through the origin.

Find the principal solution of the following equation: 

cosθ = `(1)/(2)`

Find the principal solution of the following equation: 

Sec θ = `(2)/sqrt(3)`

Find the principal solution of the following equation :

cot θ = `sqrt(3)`

Find the principal solution of the following equation:

cot θ = 0

Find the principal solution of the following equation:

sin θ = `-1/2`

Find the principal solution of the following equation: 

tan θ = – 1

Find the principal solution of the following equation:

`sqrt(3)` cosecθ + 2 = 0 

Find the general solution of the following equation:

sinθ = `1/2`.

Find the general solution of the following equation :

cosθ = `sqrt(3)/(2)`

Find the general solution of the following equation:

tan θ = `(1)/(sqrt(3))`

Find the general solution of the following equation:

cot θ = 0.

Find the general solution of the following equation:

sec θ = `sqrt(2)`.

Find the general solution of the following equation:

cosec θ = - √2.

Find the general solution of the following equation:

tan θ = - 1

Find the general solution of the following equation:

sin 2θ = `1/2`

Find the general solution of the following equation:

tan `(2θ)/(3) = sqrt3`