1
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
A curve $$y=f(x)$$ passes through $$(1,1)$$ and at $$P(x,y),$$ tangent cuts the $$x$$-axis and $$y$$-axis at $$A$$ and $$B$$ respectively such that $$BP:AP=3:1,$$ then
A
equation of curve is $$xy'-3y=0$$
B
normal at $$(1,1)$$ is $$x+3y=4$$
C
curve passes through $$(2, 1/8)$$
D
equation of curve is $$xy'+3y=0$$
2
IIT-JEE 2006
MCQ (Single Correct Answer)
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

If $$P\left( {{u_i}} \right) \propto i,\,$$ where $$i=1,2,3,.......,n,$$ then $$\mathop {\lim }\limits_{n \to \infty } P\left( w \right) = $$

A
$$1$$
B
$$2/3$$
C
$$3/4$$
D
$$1/4$$
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

Let $$P\left( {{u_i}} \right) = {1 \over n},$$ if $$n$$ is even and $$E$$ denotes the event of choosing even numbered urn, then the value of $$P\left( {w/E} \right)$$ is

A
$${{n + 2} \over {2n + 1}}$$
B
$${{n + 2} \over {2\left( {n + 1} \right)}}$$
C
$${n \over {n + 1}}$$
D
$${1 \over {n + 1}}$$
4
IIT-JEE 2006
MCQ (Single Correct Answer)
+5
-1.25
There are $$n$$ urns, each of these contain $$n+1$$ balls. The ith urn contains $$i$$ white balls and $$(n+1-i)$$ red balls. Let $${u_i}$$ be the event of selecting ith urn, $$i=1,2,3........,n$$ and $$w$$ the event of getting a white ball.

If $$P\left( {{u_i}} \right) = c,$$ (a constant) then $$P\left( {{u_n}/w} \right) = $$

A
$${2 \over {n + 1}}$$
B
$${1 \over {n + 1}}$$
C
$${n \over {n + 1}}$$
D
$${1 \over 2}$$
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