1
AIEEE 2008
+4
-1
Suppose the cubic $${x^3} - px + q$$ has three distinct real roots
where $$p>0$$ and $$q>0$$. Then which one of the following holds?
A
The cubic has minima at $$\sqrt {{p \over 3}}$$ and maxima at $$-\sqrt {{p \over 3}}$$
B
The cubic has minima at $$-\sqrt {{p \over 3}}$$ and maxima at $$\sqrt {{p \over 3}}$$
C
The cubic has minima at both $$\sqrt {{p \over 3}}$$ and $$-\sqrt {{p \over 3}}$$
D
The cubic has maxima at both $$\sqrt {{p \over 3}}$$ and $$-\sqrt {{p \over 3}}$$
2
AIEEE 2007
+4
-1
The function $$f\left( x \right) = {\tan ^{ - 1}}\left( {\sin x + \cos x} \right)$$ is an incresing function in
A
$$\left( {0,{\pi \over 2}} \right)$$
B
$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
C
$$\left( { {\pi \over 4},{\pi \over 2}} \right)$$
D
$$\left( { - {\pi \over 2},{\pi \over 4}} \right)$$
3
AIEEE 2007
+4
-1
A value of $$c$$ for which conclusion of Mean Value Theorem holds for the function $$f\left( x \right) = {\log _e}x$$ on the interval $$\left[ {1,3} \right]$$ is
A
$${\log _3}e$$
B
$${\log _e}3$$
C
$$2\,\,{\log _3}e$$
D
$${1 \over 2}{\log _3}e$$
4
AIEEE 2007
+4
-1
If $$p$$ and $$q$$ are positive real numbers such that $${p^2} + {q^2} = 1$$, then the maximum value of $$(p+q)$$ is
A
$${1 \over 2}$$
B
$${1 \over {\sqrt 2 }}$$
C
$${\sqrt 2 }$$
D
$$2$$
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