Consider the lines,
$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$
$${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$
The shortest distance between $${L_1}$$ and $${L_2}$$ is :
Consider three points $$P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )$$ and $$R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))$$ where $$0 < \alpha ,\beta ,\theta < {\pi \over 4}$$. Then :
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent is :
Consider the lines given by:
$${L_1}:x + 3y - 5 = 0$$
$${L_2}:3x - ky - 1 = 0$$
$${L_3}:5x + 2y - 12 = 0$$
Match the Statement/Expressions in Column I with the Statements/Expressions in Column II.
| Column I | Column II | ||
|---|---|---|---|
| (A) | L$$_1$$, L$$_2$$, L$$_3$$ are concurrent, if | (P) | $$K = - 9$$ |
| (B) | One of L$$_1$$, L$$_2$$, L$$_3$$ is parallel to atleast one of the other two, if | (Q) | $$K = - {6 \over 5}$$ |
| (C) | L$$_1$$, L$$_2$$, L$$_3$$ form a triangle, if | (R) | $$K = {5 \over 6}$$ |
| (D) | L$$_1$$, L$$_2$$, L$$_3$$ do not form a triangle, if | (S) | $$K = 5$$ |