1
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
$${1 \over {n + 1}}$$
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 $$P\left( {{u_i}} \right) = c,$$ (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
$${1 \over 2}$$
3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
Let $$\overrightarrow a = \widehat i + 2\widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i + \widehat j - \widehat k.$$ A vector in the plane of $$\overrightarrow a $$ and $$\overrightarrow b $$ whose projection on $$\overrightarrow c $$ is $${1 \over {\sqrt 3 }},$$ is
A
$$4\widehat i - \widehat j + 4\widehat k$$
B
$$3\widehat i + \widehat j - 3\widehat k$$
C
$$2\widehat i + \widehat j - 2\widehat k$$
D
$$4\widehat i + \widehat j - 4\widehat k$$
4
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0.75
Let $$\theta \in \left( {0,{\pi \over 4}} \right)$$ and $${t_1} = {\left( {\tan \theta } \right)^{\tan \theta }},\,\,\,\,{t_2} = \,\,{\left( {\tan \theta } \right)^{\cot \theta }}$$, $${t_3}\, = \,\,{\left( {\cot \theta } \right)^{\tan \theta }}$$ and $${t_4}\, = \,\,{\left( {\cot \theta } \right)^{\cot \theta }},$$then
A
$${t_1} > {t_2} > {t_3} > {t_4}$$
B
$${t_4} > {t_3} > {t_1} > {t_2}$$
C
$${t_3} > {t_1} > {t_2} > {t_4}$$
D
$${t_2} > {t_3} > {t_1} > {t_4}$$
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