1

IIT-JEE 2002

Subjective
A straight line $$L$$ with negative slope passes through the point $$(8, 2)$$ and cuts the positive coordinate axes at points $$P$$ and $$Q$$. Find the absolute minimum value of $$OP + OQ,$$ as $$L$$ varies, where $$O$$ is the origin.

Answer

18
2

IIT-JEE 2002

Subjective
A straight line $$L$$ through the origin meets the lines $$x + y = 1$$ and $$x + y = 3$$ at $$P $$ and $$Q$$ respectively. Through $$P$$ and $$Q$$ two straight lines $${L_1}$$ and $${L_2}$$ are drawn, parallel to $$2x - y = 5$$ and $$3x + y = 5$$ respectively. Lines $${L_1}$$ and $${L_2}$$ intersect at $$R$$. Show that the locus of $$R$$, as $$L$$ varies is a straight line.

Answer

Solve it.
3

IIT-JEE 2001

Subjective
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that

the equation $$\left| {\matrix{ {ax - by - c} & {bx + ay} & {cx + a} \cr {bx + ay} & { - ax + by - c} & {cy + b} \cr {cx + a} & {cy + b} & { - ax - by + c} \cr } } \right| = 0$$


represents a straight line.

Answer

Solve it.
4

IIT-JEE 2000

Subjective
Let $$ABC$$ and $$PQR$$ be any two triangles in the same plane. Assume that the prependiculars from the points $$A, B, C$$ to the sides $$QR, RP, PQ$$ respectively are concurrent. Using vector methods or otherwise, prove that the prependiculars from $$P, Q, R $$ to $$BC,$$ $$CA$$, $$AB$$ respectively are also concurrent.

Answer

Solve it.

Joint Entrance Examination

JEE Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12