1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
In a triangle $$ABC$$, medians $$AD$$ and $$BE$$ are drawn. If $$AD=4$$,
$$\angle DAB = {\pi \over 6}$$ and $$\angle ABE = {\pi \over 3}$$, then the area of the $$\angle \Delta ABC$$ is :
A
$${{64} \over 3}$$
B
$${8 \over 3}$$
C
$${{16} \over 3}$$
D
$${{32} \over {3\sqrt 3 }}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If in a $$\Delta ABC$$ $$a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2},$$ then the sides $$a, b$$ and $$c$$ :
A
satisfy $$a+b=c$$
B
are in A.P
C
are in G.P
D
are in H.P
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The trigonometric equation $${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$ has a solution for :
A
$$\left| a \right| \ge {1 \over {\sqrt 2 }}$$
B
$${1 \over 2} < \left| a \right| < {1 \over {\sqrt 2 }}$$
C
all real values of $$a$$
D
$$\left| a \right| \le {1 \over {\sqrt 2 }}$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If the function $$f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,$$ where $$a>0,$$ attains its maximum and minimum at $$p$$ and $$q$$ respectively such that $${p^2} = q$$ , then $$a$$ equals
A
$${1 \over 2}$$
B
$$3$$
C
$$1$$
D
$$2$$
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