IIT-JEE 2006 | 3D Geometry Question 43 | Mathematics

1

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

A

(i)-(A); (ii)-(D); (iii)-(C)

B

(i)-(B); (ii)-(D); (iii)-(C)

C

(i)-(B); (ii)-(A); (iii)-(C)

D

(i)-(A); (ii)-(D); (iii)-(B)

2

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:

A

0

B

1

C

$\sqrt{2}$

D

$2 \sqrt{2}$

3

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

A

$$3$$

B

$$1$$

C

$${1 \over 3}$$

D

$$9$$

4

IIT-JEE 2005 Mains

MCQ (Single Correct Answer)

+3

-1

Find the equation of the plane containing the line $$2 x-y+z-3=0,3 x+y+z=5$$ and at a distance of $$\frac{1}{\sqrt{6}}$$ from the point $$(2,1,-1)$$.

A

$$62x+19y+29z-105=0$$

B

$$62x+29y+z-105=0$$

C

$$29x+62y+19z-105=0$$

D

$$62x+29y+19z-105=0$$

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