1
IIT-JEE 2004
Subjective
+4
-0
If $$a,\,b,c$$ are positive real numbers. Then prove that $$${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left( {c + 1} \right)^7} > {7^7}\,{a^4}{b^4}{c^4}$$$
2
IIT-JEE 2004
Subjective
+2
-0
Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.
3
IIT-JEE 2004
Subjective
+4
-0
Find the equation of circle touching the line 2x + 3y + 1 = 0 at (1, -1) and cutting orthogonally the circle having line segment joining (0, 3) and (- 2, -1) as diameter.
4
IIT-JEE 2004
Subjective
+4
-0
Tangent is drawn to parabola $${y^2} - 2y - 4x + 5 = 0$$ at a point $$P$$ which cuts the directrix at the point $$Q$$. $$A$$ point $$R$$ is such that it divides $$QP$$ externally in the ratio $$1/2:1$$. Find the locus of point $$R$$
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