HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

Find the cartesian equations of the line passing through A(–1, 2, 1) and having direction ratios 2, 3, 1.

Find the Cartesian equations of the line passing through A(2, 2, 1) and B(1, 3, 0).

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