Jee Advanced
3d Geometry
IIT-JEE 2006
MCQ+3 / -02006
Match the following:
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
.tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}
.tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top}
.tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top}
| (i) | \(\sum\limits_{i = 1}^\infty {{{\tan }^{ - 1}}\left( {{1 \over {2{i^2}}}} \right) = t}\) then \(\tan t=\) | (A) | 0 |
|---|---|---|---|
| (ii) | Sides \(a,b,c\) of a triangle ABC are in AP and \(\cos {\theta _1} = {a \over {b + c}},\cos {\theta _2} = {b \over {a + c}},\cos {\theta _3} = {c \over {a + b}}\), then \({\tan ^2}\left( {{{{\theta _1}} \over 2}} \right) + {\tan ^2}\left( {{{{\theta _3}} \over 2}} \right) =\) | (B) | 1 |
| (iii) | A line is perpendicular to \(x + 2y + 2z = 0\) and passes through (0, 1, 0). The perpendicular distance of this line from the origin is | (C) | \({{\sqrt 5 } \over 3}\) |
| (D) | 2/3 |