1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $$5$$ phone calls during $$10$$ minute time intervals. The probability that there is at the most one phone call during a $$10$$-minute time period is :
A
$${6 \over {{5^e}}}$$
B
$${5 \over 6}$$
C
$${6 \over 55}$$
D
$${6 \over {{e^5}}}$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k$$ and $$a\widehat i - 3\widehat j + \widehat k$$ respectively are the vertices of a right angled triangle with $$C = {\pi \over 2}$$ are :
A
$$2$$ and $$1$$
B
$$-2$$ and $$-1$$
C
$$-2$$ and $$1$$
D
$$2$$ and $$-1$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The two lines $$x=ay+b, z=cy+d;$$ and $$x=a'y+b' ,$$ $$z=c'y+d'$$ are perpendicular to each other if :
A
$$aa'+cc'=-1$$
B
$$aa'+cc'=1$$
C
$${a \over {a'}} + {c \over {c'}} = - 1$$
D
$${a \over {a'}} + {c \over {c'}} = 1$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :
A
$${{\left( {1 - \sqrt 7 } \right)} \over 4}$$
B
$${{\left( {4 - \sqrt 7 } \right)} \over 3}$$
C
$$ - {{\left( {4 + \sqrt 7 } \right)} \over 3}$$
D
$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$
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