1
IIT-JEE 2004
Subjective
+4
-0
A curve $$'C''$$ passes through $$(2,0)$$ and the slope at $$(x,y|)$$ as $$\,{{{{\left( {x + 1} \right)}^2} + \left( {y - 3} \right)} \over {x + 3}}$$. Find the equation of the curve. Find the area bounded by curve and $$x$$-axis in fourth quadrant.
2
IIT-JEE 2004
Subjective
+2
-0
$$A$$ and $$B$$ are two independent events. $$C$$ is even in which exactly one of $$A$$ or $$B$$ occurs. Prove that $$P\left( C \right) \ge P\left( {A \cup B} \right)P\left( {\overline A \cap \overline B } \right)$$
3
IIT-JEE 2004
Subjective
+4
-0
A box contains $$12$$ red and $$6$$ white balls. Balls are drawn from the box one at a time without replacement. If in $$6$$ draws there are at least $$4$$ white balls, find the probability that exactly one white is drawn in the next two draws. (binomial coefficients can be left as such)
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.
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