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

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`

Find the general solution of the following equation:

cot 4θ = – 1