1
AIEEE 2003
+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
$$2$$
2
AIEEE 2002
+4
-1
The maximum distance from origin of a point on the curve
$$x = a\sin t - b\sin \left( {{{at} \over b}} \right)$$
$$y = a\cos t - b\cos \left( {{{at} \over b}} \right),$$ both $$a,b > 0$$ is
A
$$a-b$$
B
$$a+b$$
C
$$\sqrt {{a^2} + {b^2}}$$
D
$$\sqrt {{a^2} - {b^2}}$$
3
AIEEE 2002
+4
-1
If $$2a+3b+6c=0,$$ $$\left( {a,b,c \in R} \right)$$ then the quadratic equation $$a{x^2} + bx + c = 0$$ has
A
at least one root in $$\left[ {0,1} \right]$$
B
at least one root in $$\left[ {2,3} \right]$$
C
at least one root in $$\left[ {4,5} \right]$$
D
none of these
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