1
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Consider the planes $$3 x-6 y-2 z=15$$ and $$2 x+y-2 z=5$$.
STATEMENT - 1 : The parametric equations of the line of intersection of the given planes are $$x=3+14 t, y=1+2 t, z=15 t$$
STATEMENT - 2 : The vectors $$14 \hat{i}+2 \hat{j}+15 \hat{k}$$ is parallel to the line of intersection of the given planes.
2
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0
Match the following:
| (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 |
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1
A plane passes through $(1,-2,1)$ and is perpendicular to two planes $2 x-2 y+z=0$ and $x-y+2 z=4$. The distance of the plane from the point $(1,2,2)$ is:
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+4
-1
A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If the centroid $$D$$ $$(x, y, z)$$ of triangle $$ABC$$ satisfies the relation $${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = k,$$ then the value $$k$$ is
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