1
IIT-JEE 2005
Subjective
+2
-0
Find the equation of the plane containing the line $$2x-y+z-3=0,3x+y+z=5$$ and at a distance of $${1 \over {\sqrt 6 }}$$ from the point $$(2, 1, -1).$$
2
IIT-JEE 2004
Subjective
+2
-0
A parallelopiped $$'S'$$ has base points $$A, B, C$$ and $$D$$ and upper face points $$A',$$ $$B',$$ $$C'$$ and $$D'.$$ This parallelopiped is compressed by upper face $$A'B'C'D'$$ to form a new parallelopiped $$'T'$$ having upper face points $$A'',B'',C''$$ and $$D''.$$ Volume of parallelopiped $$T$$ is $$90$$ percent of the volume of parallelopiped $$S.$$ Prove that the locus of $$'A''',$$ is a plane.
3
IIT-JEE 2004
Subjective
+4
-0
$${P_1}$$ and $${P_2}$$ are planes passing through origin. $${L_1}$$ and $${L_2}$$ are two line on $${P_1}$$ and $${P_2}$$ respectively such that their intersection is origin. Show that there exists points $$A, B, C,$$ whose permutation $$A',B',C'$$ can be chosen such that (i) $$A$$ is on $${L_1},$$ $$B$$ on $${P_1}$$ but not on $${L_1}$$ and $$C$$ not on $${P_1}$$ (ii) $$A'$$ is on $${L_2},$$ $$B'$$ on $${P_2}$$ but not on $${L_2}$$ and $$C'$$ not on $${P_2}$$
4
IIT-JEE 2004
Subjective
+2
-0
Find the equation of plane passing through $$(1, 1, 1)$$ & parallel to the lines $${L_1},{L_2}$$ having direction ratios $$(1,0,-1),(1,-1,0).$$ Find the volume of tetrahedron formed by origin and the points where these planes intersect the coordinate axes.
JEE Advanced Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12