1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
The eccentricity of an ellipse, with its centre at the origin, is $${1 \over 2}$$. If one of the directrices is $$x=4$$, then the equation of the ellipse is :
A
$$4{x^2} + 3{y^2} = 1$$
B
$$3{x^2} + 4{y^2} = 12$$
C
$$4{x^2} + 3{y^2} = 12$$
D
$$3{x^2} + 4{y^2} = 1$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is
A
$${{1 + x} \over x}$$
B
$${1 \over x}$$
C
$${{1 - x} \over x}$$
D
$${x \over {1 + x}}$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $${60^ \circ }$$ and when he retires $$40$$ meters away from the tree the angle of elevation becomes $${30^ \circ }$$. The breadth of the river is :
A
$$60\,\,m$$
B
$$30\,\,m$$
C
$$40\,\,m$$
D
$$20\,\,m$$
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The sides of a triangle are $$\sin \alpha ,\,\cos \alpha $$ and $$\sqrt {1 + \sin \alpha \cos \alpha } $$ for some $$0 < \alpha < {\pi \over 2}$$. Then the greatest angle of the triangle is :
A
$${150^ \circ }$$
B
$${90^ \circ }$$
C
$${120^ \circ }$$
D
$${60^ \circ }$$
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