1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :
A
$$5$$
B
$$13$$
C
$$-2$$
D
$$7$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one failure is greater than or equal to $${{31} \over 32},$$ then $$p$$ lies in the interval :
A
$$\left( {{3 \over 4},{{11} \over {12}}} \right]$$
B
$$\left[ {0,{1 \over 2}} \right]$$
C
$$\left( {{11 \over 12},1} \right]$$
D
$$\left( {{1 \over 2},{{3} \over {4}}} \right]$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is :
A
$$P\left( {{C \over D}} \right)$$$$ \ge P\left( C \right)$$
B
$$P\left( {{C \over D}} \right)$$$$ < P\left( C \right)$$
C
$$P\left( {{C \over D}} \right)$$$$ = {{P\left( D \right)} \over {P\left( C \right)}}$$
D
$$P\left( {{C \over D}} \right)$$$$ = P\left( C \right)$$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If the angle between the line $$x = {{y - 1} \over 2} = {{z - 3} \over \lambda }$$ and the plane

$$x+2y+3z=4$$ is $${\cos ^{ - 1}}\left( {\sqrt {{5 \over {14}}} } \right),$$ then $$\lambda $$ equals :
A
$${3 \over 2}$$
B
$${2 \over 5}$$
C
$${5 \over 3}$$
D
$${2 \over 3}$$
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